· 2020. 9. 10. · nd 3 1 Raja Sir Income Tax Inspector 14 Years’ teaching experience •CAT...

SSC CDS

BANKrAILWAY

ª Concepts with Visual Understanding

ª Core Physics (Detailed Theory)

Physics

ª Practical Applications of Physics

ª Previous year Questions from

1999 to till date

C L A S S E S

Chapter - 05

(Gravitation)

1

Raja Sir Income Tax Inspector

14 Years’ teaching experience

•CAT •GMAT •UPSC •SSC •BANK

GRAVITATION Famous Scientists

Galileo

Studied that all bodies fall towards earth with constant acceleration

Tycho-Brahe

Studied planets with naked eye.

Theories

Geocentric

Earth at center By Ptolemy

Heliocentric

Sun at center By Copernicus

Newton

Universal law of gravitation (1665)

1st Law

Every planet revolves around the sun in an

elliptical orbit. 1st Law is based on Inverse

Square Law. Closest point –Perihelion Farthest point - Epihelion

2nd Law

2nd Law (Law of Areas) Based on Law of conservation

of Angular Momentum.

3rd Law

3rd Law (Law of Periods) (Time period) T2 R3(Semi major axis)

Kepler Laws

Some Concepts

Newton's Law of Gravitation

The force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the

square of distance between them.

F ∝ 1 22

m m

r⇒ F = 1 2

2

Gm m

r

where,

G = universal gravitational constant = 6.67 × 10-11 N-m2/kg2.

Acceleration Due to Gravity

The force of attraction exerted by the earth on a body is called gravitational pull or gravity. When this force acts on a body, it

products acceleration to the body.

The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity. It is denoted by g

(9.8 m/s2). Its SI unit is m/s2. Then,

Where, Me = mass of the earth Re = radius of the earth

2

Manisha Bansal Ma'am (Director & Author)


•CAT •GMAT •GRE •SSC •BANK

3




Gravitational Field

The space surrounding the material body in which its gravitational force of attraction can be experienced is called gravitational

field. The intensity of gravitational field at a point is equal to the force acting on the unit mass at that point and it is given by 2

GM.

r

Gravitational Potential

Gravitational potential at a point in gravitational field is equal to the work done in carrying a unit mass from infinity to that point.

Gravitational potential due to mass m at a distance r is V = –GM

r

Gravitational Potential Energy

Gravitational potential energy of a body at a point is equal to work done in assembling the system of masses from the infinity to its

present configuration. Gravitational potential energy of mass m at a distance r is U = - eGM m

r

Potential energy of a particle of mass m on the earth's surface is U = - e

e

GM m

R

Satellite

A satellite is a body which is revolving continuously in an orbit around a comparatively much larger body.

Natural

The satellite are made by nature

Earth: moon is a natural satellite

Jupiter: Has 16 natural satellites

Saturn: 18 natural satellites (moons)

Artificial

These are man-made

• 1st artificial satellite was launched by RUSSIANS'

(Sputnik I on 4 oct, 1957)

• India: 1st Artificial satellite, Aryabhatta in 1975

• Some other satellites launched by India

• Bhasker, Rohini, Apple, IA, IB, Insat, IRS.

4




Types of Satellite

Geo Stationary Satellite/

Geosynchronous Satellite

• It appears stationary to an observer on earth. • It rotates with same angular speed as that of earth. • Sospeed of satellite Relative to Earth = 0 • Its period of revolution is24 hours. • It should be at a height nearly 36000 km above the equator of earth. • Its orbital speed is nearly 3.1 km/s • These are used for short range warning

Polar Satellite

• These are those satellites which revolve in polar orbits around earth. • The altitude of polar satellites is about 500 to 800 km from the surface of the earth. • The time period of revolution of polar satellites is about 100 minutes. • A polar satellite crosses any location on earth many times a day. • Every location on earth lies within the observation of polar satellite twice each day. • These are used for long term forecasting.

Meteorology:It is a branch of atmospheric sciences which involves atmospheric physics and atmospheric chemistry with a major

focus on weather forecasting.

ISRO

This is the Umbrella organisation for the satellite programming in India. Its main launch centre is at Sriharikota (SHAR).

It is a space Agency of Government of India.

In 1984 Rakesh Sharma become the first Indian to go into space

IRS: Indian remote sensing satellite launched by Indian space Agency – ISRO (Indian Space Research Organisation)

INSAT: Indian National Satellite System.

It is a series of multipurpose Geo stationary satellites.

Satellite launched by it are used for

Broadcasting

Telecommunication

Meteorology

Search and Rescue operation

5




Centres of ISRO

Satish Dhawan Space Centre Sriharikota, Andhra Pradesh (SDSC - SHAR)

• Rocket Launching Centre

Vikram Sarabhai Space Centre (VSSC) ThiruVananthapuram, Kerala • Major Space Research Centre

Antrix Corporation It is a commercial arm of ISRO.

Some key terms

Orbital Speed

It is the minimum speed required to put the satellite into a given orbit around

earth.

Orbital Speed of a satellite

(i) It is independent of the mass of satellite

(ii) It decreases with an increase in the radius of orbit or increase in the height

of satellite.

(iii) It depends upon the mass and radius of the earth/planet around which the

revolution of satellite is taking place.

Direction of orbital speed of satellite at an instant is along the tangent to the

orbital path of satellite at the instant.

Binding Energy

The energy required to remove the satellite from its orbit around the earth to infinity is called Binding energy of the satellite.

Binding energy is equal to negative value of total mechanical energy of a satellite in its orbit.

Escape Velocity/ Speed

Escape speed on earth (or any other planet) is defined as the minimum speed with which a body has to be projected vertically

upwards from the surface of earth (or any other planet) so that it just crosses the gravitational field of earth (or of that planet) and

never returns on its own.

Time Period

It is the time taken by satellite to complete one revolution around the earth and is denoted by T.

Terms Related to Satellite

Orbital Speed0

When a satellite is orbiting

very close to the surface of

earth.

0 = 7.92 km s–1

Binding Energy

BE = - Total Mechanical

Energy of Satellite

Escape Velocity/ Speed

For earth = 11.2 km/sec

For moon = 2.3 km/sec

For sun = 618 km/sec

Time Period

For Earth,T = 84.6

minutes

Variation in value of g

⦁ The value of g is minimum at equator and maximum at poles (it happens due to shape of the earth).

Variation of g

Variation with height

As height increases,

gravity decreases

At h = radius of earth

h = 6400 km, G' = g/4

Depth

As depth inside earth , g

At centre of earth, g = 0

g = max at surface of earth

Shape of Earth

Value of g is max. at poles

and min at equator

Speed of Rotation of

Earth

As rotational of earth

increases, g at all places

except at poles.

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Gravity becomes one

fourth Equator

Poles g increase

As we move from equator to

poles, value of g increases

g' = g – R2 cos2

( = angular speed of

rotation of earth

= 90° at poles 0 at

equator)

( means INCREASE, means DECREASE)

⦁ The observed value of g at the latitude λ is gA = g - Re2 cos2λ

At equator,

g λ = g - Re 2 (∵λ = 0, cos 0 = 1)

At pole, gλ = g (∵λ = 900, cos 90= 0)

⦁ The value of g at height h above earth's surface decreases as

g' = 2

e

e

g 2hg 1

Rh1

R

⦁ The value of g at depth h below earth's surface decreases as

g' = g e

2h1

R

⦁ The value of g varies due to non-spherity of the earth.

⦁ The value of g varies due to non-uniformity of the earth (density of the earth).

⦁ If the earth stops rotation about its own axis, then at the equator the value of g increases by 2R and consequently the weight of

body lying there increases by m2R.

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Mass

Quantity of matter contained in the body.

Inertial Mass

• Inertial mass of a body is related to its inertia in linear

motion as defined by Newton's second law of motion.

mi = F/a

• The magnitude of external force required to produce

unit acceleration in the body.

• Inertial mass of a body is the measure of the ability of

the body to oppose the production of acceleration in its

motion along a straight line by an external force.

• Gravity has no effect on inertial mass of a body.

Gravitational Mass

• Gravitational mass of a body is related to gravitational

pull on the body, and is defined by Newton's law of

gravitation.

• The inertia of the body has no effect on the gravitational

mass of the body.

• Gravitational mass of a body is affected by the presence

of other bodies near it whereas the inertial mass of a body

remains unaffected by the presence of other bodies near

it.

Weight = mass × gravity

Properties of inertial mass

1. Inertial mass of a body is proportional to the quantity of matter contained in the body.

2. Inertial mass of a body does not depend upon the temperature of the body.

3. Inertial mass of a body is not affected by the presence or absence of other bodies near it.

4. Inertial mass can be added by simple laws of algebra, irrespective of the materials of the bodies.

5. Inertial mass of a body increase with the speed of the body. When a body moves with a velocity , its inertial mass m is given by

m = 0

2 2

m

1 / c

Where m0 is the rest mass of the body, c is the velocity of light in vacuum. The mass m is effected only when the velocity of the body

is comparable with the velocity of light.(Here ,Einstein Theory of relativity comes into existence)

Weightlessness

It is a situation in which the observed weight of the body becomes zero.

The object is in weightless , when it is in free fall.

Problems of weightlessness

1. If an astronaut is walking in a space craft, he may be pushed away from the floor and may crash against the ceiling of the space

craft.

2. The space-flight for a long time, adversely affects the human organism.

3. The experiment of simple pendulum cannot be performed in the weightlessness state because

T = 2 L / g

So, T= as g = 0

Free Fall: When we do not apply any force on the ground and body is allowed to fall freely under the effect of gravity. In this case,

observed weight will be zero.

8




Case of Satellite

When a satellite is orbiting around the earth, then satellite and every object inside the satellite has an acceleration equal to the

acceleration due to gravity , directed towards the centre of the earth. It means every object inside the satellite is in a state of free

fall.

Weight of Body at moon.

At moon, g' = g/6

So, weight w' = w/6

i.e., weight on moon becomes one-sixth of your weight on earth.

9




Practice Questions 1. The earliest model for planetary motion was

(a) geocentric model (b) heliocentric model

(c) geostationary (d) None of these

2. According to geocentric model of planetary motions,

(a) stars revolved around the earth

(b) planets revolved around the earth

(c) sun revolved around the earth

(d) All of the above

3. A model in which the sun was the centre around which

the planets revolved is

(a) heliocentric model (b) geocentric model

(c) geostationary model (d) None of these

4. All planets move is elliptical orbits with the sun situated

at one of the foci of the ellipse. The point at which the

planet is closest to the sun is

(a) perihelion (b) aphelion

(c) helion (d) none of t these

5. For planets moving around the sun in elliptical orbit, the

point at which the planet is farthest to the sun is

(a) aphelion (b) perihelion

(c) helion (d) None of these

6. The velocity of the planet when it is closest to sun is

(a) maximum (b) minimum

(c) can have an value (d) None of these

7. The law of areas can e understood as a consequence of

(a) conservation of angular momentum

(b) conservation of energy

(c) conservation of linear momentum

(d) Both (a) and (b)

8. Law of areas is valid only when gravitational force is

(a) conservative force (b) central force

(c) attractive force (d) weak force

9. The law of areas can be interpreted as

(a) A

t

= constant (b)

A L

t m

(c) 1

2

Ar P

t

(d)

2dA L

dt m

10. The force of attraction due to a hollow spherical shell of

mass M, radius R and uniform density, on a point mass m

situated inside it is

(a) 2

GmM

r (b)

2

Gm M

R (c) Zero (d) Data insufficient

11. Earth is flattened at the poles and bulges at the equator.

This is due to the fact that

(a) The earth revolves around the sun in an elliptical

other

(b) the angular velocity of spinning about its axis is more

at the equator.

(c) The centrifugal force is more at the equator that at

poles.

(d) None of these

12. If the gravitational potential energy at infinity is

assumed to be zero, the potential energy at distance (Re

+ h) from the centre of the earth is

(a) PE =

e

e

GmM

R h (b) PE =

e

e

GmM

R h

(c) PE = mgh (d) PE= 2

e

e

GmM

R h

13. Which of the following statements is correct about

satellites?

(a) A satellite cannot move in a stable orbit in a plane

passing through the earth's centre.

(b) Geostationary satellites are launched in the

equatorial plane.

(c) We can use just one geostationary satellite for global

communication around the globe.

(d) The speed of satellite increases with an increase in

the radius of its orbit.

14. Which one of the following statements is correct?

(a) The energy required to rocket an orbiting satellite

out of earth's gravitational influence is more than the

energy required to project a stationary object at the

same height (as the satellite) out of earth's influence

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(b) If the zero of potential energy is at infinity, the total

energy of an orbiting satellite is negative of potential

energy.

(c) The first artificial satellite sputnik I was launched in

the year 2001.

(d) The time period of rotation of the SYNCOMS

(Synchronous communications satellite) is 24 hours.

15. The scheme of the motions put forward put forward by

Ptolemy in order to describe the observed motion of the

planets is that.

I. the planets are moving in circles with the centre of the

circles themselves moving in larger circles.

II. the planets are moving in circles with the centre of

circles themselves remaining stationary.

III. The planets are moving in an elliptical orbit with the

centre of the ellipse moving in a circle.

Choose the correct option.

(a) Only I (b) Only II

(c) Only III (d) None of these

16. Which of the following statements is/are true for a

'geocentric model'?

I. All celestial objects, stars, the sun and the planets, all

revolved around the earth.

II. The only motion that was thought to be possible for

celestial objects was motion in a circle.

III. The star, the earth and the planets, all revolved

around the sun



(c) Only III (d) I and II

17. With reference to the 'heliocentric model' of planetary

motion, which of the given statements is/are correct.?

I. The planets revolved around the sun as its centre

II. The planets revolved around the earth and earth

revolved around the sun as its centre.

III. The sun revolved around the earth as its centre.

IV. The planets revolved around the sun in elliptical orbit



(c) Only III (d) Only IV

18. Which of the given statements is true for the centripetal

force required by the satellite to remain in orbit?

I. The centripetal force is directed towards the centre of

the earth.

11




II. The centripetal force is provided by the gravitational

force.

III. The magnitude of the gravitational force acting on the

satellite is

2

egravitational

e

GmMF

R h

Where Me is the mass of the earth

and it is same as centripetal force.



(c) I and II (d) I, II and III

19. The orbit of a geostationary satellite is circular, the time

period of satellite depends on

I. mass of the satellite

II. mass of the satellite.

III. radius of the orbit.

IV. height of the satellite from the earth.

Which of the following option is correct.?

(a) Only I (b) I and II

(c) I, II and III (d) II, III and IV

20. Which of the given statements is correct about the polar

satellites?

I. A strip on earth's surface is visible from satellite in one

cycle.

II. The whole earth can be viewed strip during the entire

day from the polar satellite.

III. These satellites can view polar and equatorial regions

at close distances with good resolution

Choose the correct

(a) Only I (b) I and II

(c) II and III (d) I, II and III

Matching Type

21. A satellite of mass m revolving with a velocity v around

the earth. With reference to the above situation, match

the items in Column I with terms in Column II and

choose the options from the codes given below.

Column I Column II

A. Kinetic energy of the satellite 1. 21

2mv

B. Potential energy of the satellite 2. 21

2mv

C. Total energy of the satellite 3. –mv2

( ) ( )3 31 2 2 1

( ) ( )3 32 1 1 2

C CA B A B

a b

c d

22. Both the earth the moon are subject of the gravitational

force of the sun. As observed from the sun, the orbit of

the moon.

(a) will be elliptical

(b) will not be strictly elliptical because the total

gravitational force on it is not central.

(c) is not elliptical but will necessarily be a closed curve

(d) deviates considerably from being elliptical due to

influence of planets other than the earth.

23. In our solar system, the inter-planetary region has

chunks of matter (much smaller in size compared to

planets) called asteroids. They.

(a) will not move around the sun, since they have very

small masses compared to the sun

(b) will move irregular way because of their small

masses and will drift away into outer space.

(c) will move around the sun in closed orbits but not

obey Kepler's laws

(d) will move in orbits like planets and obey Kepler's

laws

24. Which of the following are true?

(a) A polar satellite goes around the earth's pole in

north-south direction

(b) A geostationary satellite goes around the earthin

east-west direction.

(c) A geostationary satellite goes around the earth in east

–west direction.

(d) A polar satellite goes around the earth in east-west

direction.

25. Match the items in Column I with terms in Column II and

choose the correct options from the codes given below.

Column I Column II

A. Direction of motion of

polar satellite

1. 36000 km

B. Direction of motion of

geostationary satellite

2. West-East

C. Height above the

surface of the earth for

polar satellite

3. 512 km

D. Height above the

surface of the earth for

geostationary satellite

4. North-South

12




A B C D A B C D

(a) 2 4 1 3 (b) 4 2 1 3

(c) 4 2 31 (d) 2 4 3 1

26. Gas escapes from the surface of a planet because it

acquires an escape velocity. The escape velocity will

depend on which of the following factors:

(a) Mass of the planet

(b) Mass of the particle escaping

(c) Temperature of the planet

(d) Radius of the planet

27. Which of the following options are correct?

(a) Acceleration due to gravity decreases with altitude

(b) Acceleration due to gravity increases with increasing

depth (assume the earth of be a sphere of the uniform

density)

(c) Acceleration due to gravity increases with latitude

(d) Acceleration due to gravity is independent of the

mass of the object

ANSWER KEY

1 A 2 D 3 A 4 A 5 A

6 A 7 A 8 B 9 A 10 C

11 C 12 B 13 B 14 D 15 A

16 D 17 A 18 D 19 D 20 D

21 B 22 B 23 D 24 A,C 25 C

26 AD 27 ACD

SOLUTION

1. (a) The earliest mode for planetary motion was geocentric

model.

2. (d) In geocentric model of planetary motions, stars, plants

and sum all revolved around the earth.

3. (a) Heliocentric model for motion of planets was more

elegant model in which the sun was the centre around

which the planets revolved.

4. (a) The figure shown is an ellipse which is traced out by a

planet around the sun. The closed point is P called

Perihelion and the farthest point is A which is called

Aphelion.

5. (a) The farthest point is A which is called Aphelion.

6. (a) From conservation of angular momentum,

Velocity planet (v) ∝

1

tanDis ce of the planet from sun r

So, rp is minimum for perihelion (P).

⇒ vp is maximum.

7. (a) The law of areas is derived using the idea of conservation

of angular momentum for central forces like

gravitational force.

The area swept out by the planet of mass in time interval

‘Δt’ is given as, ΔA =1

2(r × Δv)/Δt

or 1

2

A

t

(r × P)/m = L/2m = constant (law of areas)

As for a central fore which is directed along r, L is a

constant.

8. (b) The law of areas can be understood as a consequence of

conservation of angular momentum which is valid for

any central force. (Refer also to solution 7)

9. (a) The law of areas states that the line joining any planet to

the sum sweeps equal areas ‘ΔA’ in equal intervals of

time ‘Δt’. So, magnitude of areal velocity = A

t

is a

constant.

10. (c) Net resultant force at point P is

13




|Fp(net)| = Zero.

11. (c) Higher centrifugal force causes bulging of earth at

equator.

12. (b) Gravitational Potential Energy (GPE) = eGmM

r

where, r = distance from centre of the earth

∵ r = Re + h GPE =

e

e

GmM

R h

13. (b) Orbital speed of satellite, v0 = eGM

r

So, orbit speed of satellite decrease with the increase in

the radius of its orbit.

We need more than one satellite for global

communication.

For stable orbit plane of orbit of satellite must pass

through the centre of earth. Only (b) is a correct

statement.

14. (d) The energy required to rocket an orbiting satellite out of

earth’s gravitational influence is less than the energy

required to project a stationary object at the same height

(as the satellite) out of earth’s influence.

Hence, option (a) is an incorrect statement.

If zero of potential energy is at infinity, the total energy

of an orbiting satellite is negative of its kinetic energy.

Hence, option (b) is an incorrect statement.

The first artificial satellite was launched by Soviet

scientists in the year 1957.

Hence, option (c) is an incorrect statement.

The time period of the SYNCOMS is 24 hours.

Hence, option (d) is a correct statement.

15. (a) The pattern of motion of the planets was put forward by

Ptolemy. According to his scheme of motion, the planets

are moving in circles with the centre of the circle

themselves moving in larger circles.

16. (d) In a ‘geocentric model’ all celestial object, stars, the sun

and the planets, all revolved around the earth. The only

possible motion for celestial objects was motion in a

circle.

17. (a) With reference to the ‘heliocentric model’ of planetary

motions, the planets revolved around the sun as its

centre.

18. (d) The centripetal force required for the satellite to remain

in circular orbit is provided by the gravitational force

which is directed towards the centre of the earth.

F(centripetal) = F(gravitational) =

2

e

e

GmM

R h

19. (d) Time-period of satellite =

3/22 e

e

R h

GM

… (i)

From the above equation, it is evident that the time-

period of a satellite depends on mass of the Earth (Me),

radius of the orbit (r = Re + h) and height of the satellite

from the surface of the Earth (h).

14




20. (d) Since, for polar satellite height h above the earth is about

500-800 km, a camera fixed on it can view only small

strips of the Earth in one orbit. Adjacent strips are

viewed in the next orbit so that in effect the whole earth

can be viewed strip by strip during the entire day. These

satellite can view polar and equatorial regions at close

distance with good resolution.

21. (b)

22. (b) As observed from the sun, two types of forces are acting

on the moon one is due to gravitational attraction

between the sun and the moon and the other is due to

gravitational attraction between the earth and the moon.

Hence, total force on the moon is not central.

23. (d) Asteroids are also being acted upon by central

gravitational forces, hence they are moving in circular

orbits like planets and obey Kepler’s laws.

24. (a, c) A geostationary satellite is having same sense of rotation

as that of earth i.e., west-east direction. A polar satellite

goes around the earth’s pole in north-south direction.

25. (c) A. Direction of motion of polar satellite is north-south.

B. Geostationary satellite goes around earth in the same

direction as the earth’s rotation about its own axis.

C. Polar satellite are approximately (h = 500 – 800 km)

above the earth’s surface.

D. For geostationary satellite the height above the earth’s

surface is around 36000 km.

26. (a, d) ve =2GM

R

27. (a, c, d)

Acceleration due to gravity at altitude h,

gh =

2

g 2hg 1

R1 h /R

At depth d, gd = d

g 1R

In both cases with increase in h and d, g decreases.

At latitude , g = g – 2 R cos2

As increases g increases. Also, we can conclude from

the formulae, that it is independent of mass.

SSC CDS

BANKrAILWAY



Physics



1999 to till date

C L A S S E S

Chapter - 06

(Electrodynamics)

1




ELECTRODYNAMICS Matter: It is defined as anything that has mass and takes up space (i.e. has volume)

Matter

Solid Liquid Gas

Conductor

(Conducts electricity to

great extent)

Semi Conductor

(conducts electricity but to

small extend)

Insulator (Does not conduct

electricity)

SOLID LIQUID GAS

Charged

particles(carriers):

Free electrons

Fixed shape

Fixed volume

Positive ions negative ions

Shape of container

Free surface

Fixed Volume

Ions, free electrons

Shape of container

Volume of container

Concept of charge: - As we know, every material is made up of atom.

Concept of Atom

Wall Any matter(non-living)

break

Bricks finally made

break up of

Stones

Crush it Atoms

Powder [electrons, protons, neutrons]

–ve +ve Zero

Molecules

Atoms

Atom: The smallest individual unit of a material/matter

Structure of Atom: Many scientists such as Thomson, Rutherford, etc. proposed structure of atom but the present structure was

proposed by Neil Bohr.

According to Neil Bohr,

2




3




Atom is made up of 3 main particles

(e) electrons ,e [negatively charged]

(p) protons, p [positively charged]

(n) neutrons, n [neutral means no charge]

Atom is made of

Nucleus

(Center heavy part)

(Contains)

Protons Neutrons

[+vely charged

& heavy]

[Zero charge

Neutral & heavy]

Extra Nuclear Part

(Shells)

Electrons

[–vely charged &

light weight]

np

e

e

e

e

e

e e

e

e

In an atom, in neutral State(i.e when it is not charged)

No. of electrons = no. of protons

i.e. Total negative charge = Total positive Charge

So, Atom is electrically neutral in general.

But Due to friction or any other mechanical effect, sometimes

Atom Looses an Electron

Ne< np

Net positive charge appears

Material is positively charged

Atom gains an Electron

Ne> np

Net negative charge appears

Material is negatively charged

It's structure can be expressed as.

P

n

e

e

e

e e

e

e

e

e

e

Shells (energy levels)

Nucleus (+vely charged

due to protons) Lower Energy

Level

Higher energy level

4




At centre, lies the nucleus which is

Positively charged due to protons

Heavy due to heavy mass of n & p when mp = mn.

Electrons are very light in weight and they revolve around the nucleus in fixed orbits/energy shells.

Note: Electrons revolve in fixed energy levels hence they do not loose energy while revolving.

If they jump from one energy level to another energy level only then they show change in energy.

P

n

e–

e

Transfer of electrons from one energy level to other.

Whenever e– gains energy, it jumps from lower energy level to higher energy level.

Electron in higher energy level is called excited electron and it is always unstable at excited state.

Every electron tends to be in stable state so it looses its energy and jumps/falls back to lower energy level.

p1 n

e

e–

e–

e

Lower energy level

energy is released out in form of heat,

light, EM radiation

The energy lost or released out can be in the form of light, heat or other E-M radiation depending on the material and wavelength of

energy released.

So, depending on the no. of electrons, a body acquires +ve or –ve charge.

When these charges are at Rest, study is static electricity

When these charges are in motion, study is current electricity

Electricity

It is a physical phenomenon associated with the presence ormotion of a charged particle, It can broadly be divided

into 2 types

Electrostatics/Static Electricity/Frictional Electricity

• Charges are at Rest

• Only Electric field is observed

Current Electricity

• Charge are in motion

• Electric field as well as magnetic field is observed

5




• No motion of electrons/ charge participle so, No current

so NO electro-magnetism

Ex:

1. Plastic comb when rubbed gets electrified and

used to attract light weight plastic

2. Glass rod when rubbed will attract bits of paper.

• current exists

• Electro magnetism is observed.

Ex:

1. AC circuits used at home, electronic industry

2. DC batteries

Key terms and their Units

ChargeQ C – Columb

CurrentI A–Ampere

VoltageV V – Volt

Magnetic Flux wb - weber

Magnetic Flux Intensity H Tesla

ResistanceR ohm

Resistivity ohm m (ohm metre)

Conductivity mho or siemens

Impedence Z Ohm ()

Susceptance Y Mho

Capacitance C Farad

Inductance L Henry

Inductive Reactance XL Ohm

Capacitive Reactance XC Ohm

Frequency hertz

6




ELECTROSTATICS [ELECTRIC FIELD] Charge or Electric Charge: It is the physical property of matter that causes it to experience a force when placed in an external

electromagnetic field.

Electric Charge is of 2 types

Positive Charge (+) Negative Charge (–)

It is a scalar quantity.

Charge on electron or proton is e where 1 e = 1.6 × 10-19 coulomb (C).

Properties of Electric Charge

⦁ Two like charges repel each other, while two unlike charges attract each other.

⦁ Electrification by friction can be explained on the basis of transfer of electron (i.e. negative charged particles of an

atom) from one object to other, when these are rubbed to each other. Charges are always distributed on the surface of

the conductor.

⦁ Charge is invariant.

⦁ A charged body attracts lighter neutral body.

⦁ During any process, the net electric charge of an isolated system remains constant.

⦁ Charge is conserved i.e., it can neither be created nor be destroyed.

Charge is Quantised: It states that charge on anybody will always be an integer multiple of 1 unit of charge

i.e. charge Q = ne. ;

n = no. of electrons e = charge on 1 electron

Ex: If an atom gains 10 electrons from outside, charge = –ve = 10 × 1.6 × 10–19 C

Charge on electron is considered negative

Charge on proton is considered positive

Like charges and Unlike charges

Repel

Attract

Like charges repel each other Unlike charges attract each other

Density and charge Density Mass

DensityVolume

Linear Charge Density Surface Charge Density Volume Charge Density

(lembda) = Charge

Length (Sigma) =

Charge

Area (rho) =

Charge

Volume

As Area ,

Sharp point has high charge (Area is very small) ( high)

1. Long chains are provided at the bottom of trucks carryinginflammable materials

It is to avoid the risk of high flames as when a vehicle moves at high speed, it gets charged due to friction with air. This charge may

produce spark and cause huge fire.

So, this charge is transferred to earth via long iron chairs.

7




8




2. Walls and roofs of Building housing heavy machines (electrical) are made up of metal

Process involved is Electromagnetic shielding.

As when high voltage machines are operated, they produce heavy electric field and in turn may produce charges.

it is the property of a metal shield that all the excess charge moves to its outer surface.

So, Excess charge is moved to outer surface from where it is transferred to Earth [Earthing].

Quantization of Electric Charge

The quantization of electric charge is the property by virtue of which, the charge on a body is integral multiple of a basic unit of

charge of an electron/proton, represented by e.

q = ne

e = 1.6 × 10–19 coulomb

Additivity of Charge

Additivity of charge is a property by virtue of which total charge of system is obtained simply by adding algebraically all the

charges present anywhere on the system.

q = q1 + q2 + q3 + …… + qn.

power signs have to be used while adding the charges in a system. For example, if a system contains charge + q, – 2 q, + 3 q and + 3

q and + 5 q, then the total charge of the system is = + q – 2 q + 3q + 5 q = + 7 q

Conservation of Charge

Conservation of charge is the property by virtue of which total charge of an isolated system always remains constant or conserved.

(Isolated system is the system in which there is no effect of external environment on the internal properties of the system)

Superposition Principle

According to superposition principle, total force on any charge due to a number of other charges at rest is the vector sum of all the

forces on that charge due to other charges, taken one at a time. The forces due to individual charges are unaffected by the presence

or absence of other charges.

0 01 02 03 0nF F F F F

Current: Movement of charge or charge carriers is known as current.

Explanation:

From where does these free electrons and fixed ions occur in wire.

Whenever any wire is made from a material, it is obviously struck by a hammer or some other mechanism so, in short as per

law of conservation of energy say external energy gets transferred to it. Hence electrons inside it ,gets energy to escape from

atom and move independently in matter.

These escaped electrons are free electrons when electrons had moved out of atom, it gets the charge, the left atom (nucleus+

shells) is called fixed +veions(positive ion).

(Fixed because it is too heavy to move)

e e e e e

e e

e

e e e e

Note: As normal room temperature is at 25°C, we have Heat energy = mct. This energy causes electrons to move but

9




Despite of movement of electron we don't get current in wire unless it is attached to a battery/power source.

Electrons move due to thermal energy but as there is no power source so, there is no fixed direction for e– to move and they

move in a random direction.

e– e – e–

e e e

So, whenthere is movement of electron but inrandom direction, we don't get current.

Direction of Current: Electrons flow from negative(–ve) to positive(+ve)direction

But By convention, we consider flow of electric current from positive (+ve)to negative(–ve)

So,

Current: It is movement of charge carries in a particular direction.

Current Conduction in Metal Wires.

e– e e–

e e e

e e e e

e e

+ e–

electrons

enter

electrons leave

When a battery source is connected to a wire, it creates a force on electrons due to which electrons move in fixed direction and this

movement of electrons produces a current.

Or Current is a term to represent movement of charge carriers.

Symbol unit

Current

Charge

Resistance

Conductance

I

Q

R

G

Ampere (A)

Columb (C)

Ohm ()

Siemens or mho (Ʊ)

Formula for Current

As current = flow of charge carriers

= movement of charge carriers

= change in position of charge carries with time

Current = Charge

time

I = Q

t or 1 Ampere =

1 Coloumb

1 Sec

or Q = IT

10




11




Types of Electric Current

According to its magnitude and direction, electric current is of two types as given below

1. Direct Current (DC)

An electric current whose magnitude and direction do not change with time, is called direct current.

`

e.g. a cell, battery or DC dynamo are the sources of direct current.

2. Alternating Current (AC)

An electric current, whose magnitude changes continuously and direction changes periodically is called alternating

current, e.g. AC dynamo is the source of AC.

Alternating current

Current Density

Current Density (J) at a point in a conductor is defined as the amount of current flowing per unit area of the conductor around that

point provided the area is held in a direction normal to the current.

I be the current

Cross-sectional area A

J = q / t

A A

I

I = JA cos = J. A

Current Density being the dot product of two vectors is a scalar quantity.

Mobility

Mobility of charge carrier (), responsible for current is defined as the magnitude of drift velocity of charge per unit electric field

applied, i.e.

= ddrift velocity

electric field E

where Drift Velocity(vd) is the velocity acquired by the electrons present inside a wire when it is placed inside external electric

field(E).

Average Relaxation

Average Relaxation time = mean free path of electron/drift speed of electron.

12




Drift Velocity

Drift velocity is defined as the average velocity with which the free electrons get drifted towards the positive end of the conductor

under the influence of an external electric field applied.

The drift velocity of electrons is of the order of 10–4ms–1. It is denoted by Vd.

Resistance

e e

e

e e

+ –

It is an obstruction/hindrance in the path of charge carries resulting in the loss of energy.

Higher is the resistance of material , Lower is its conductance.

Here, when e– moves due to external applied electric field , the internal fixed positive ions also attracts the electrons as

+ve ions attracts –ve electrons,

Like charges repel each other and unlike charges attract each other.

So, an electron gets attracted and looses some energy so ions hinders electronsfrom its path. This property of hindering the flow of

electrons from its original path is called Resistance. Later on it again regains its path and moves.

Formula for Resistance (R)

R = l length of wire

A

Area of wire

resistivity

= RA

l

if we put A = l, l = 1

= R or R =

So,

= Resistivity =Resistance of unit area and unit length.

R =

It is a property of material ,The material with higher, possess higher R and less conductance i.e. it is a Bad conductor of electricity

and vice versa.

Dependence of R on l and A.

1. R l(Length of conductor) (Directly Proportional)

e

A B

e e e–

e

A B

Here e– has to travel smaller distance to

reach from A to B

So, faces less hindrance

Here e– has to travel more distance to

reach from B to A

So, faces more hindrance

13




Hence R = less HenceR = high

2. R 1

A (Cross sectional area of conductor)(Inversely Proportional)

e– A

e– A e–

e–has more space to cross so, faces less

hindrance

i.e. R = less

e– has to cross narrow space so faces

more hindrance,

i.e. R = high

Materials used for making Resistance

Manganin

Eurika

Constantan

Variation of Electrical Resistivity of a conductor with Temperature.

• Resistivity of a conductor increases with increase in Temperature.

e

e e

e e

These fixed ions vibrates with greater velocity producing more hindrance in the path of moving electrons, there by increasing

resistance.

Temperature effect on Resistance

Conductor

Temperature , R

(fixed ion vibration )

Semi-Conductor

Temperature , R

(Because more charge carriers are present)

14




Electrical Conductivity ()

Electric conductivity () of a conductor is defined as the reciprocal of its resistivity. It is represented by ,

i.e. = 1/

Electrical conductivity depends on the following factors:

(i) Nature of material of conductor: As number density of electrons is different and n (number density of electrons in a

conductor), so conductivity of different material is different.

(ii) Temperature of the conductor: When temperature of the conductor increase then the value of relaxation time decreases.

As , so, conductivity of a conductor decreases.

Relaxation time is the time interval between two successive collisions of electrons in a conductor, when current flows.

Super Conductivity

As the temperature decrease, the resistance of the material also decreases, but when the temperature reaches a certain critical

value (called critical temperature or transition temperature), the resistance of the material completely disappears i.e., it becomes

zero.

So, Superconductivity is the property by virtue of which a metal alloy or oxide etc. shows zero resistance at a very low temperature.

Application of super conductors

1. Super conductor are used for making very strong electromagnets.

2. Super conductivity plays an important role in material science research and high energy particle physics.

3. Super conductivity is used to produce very high speed computers.

4. Super conductors are used for the transmission of electric power.

Facts:

• Scientist who named 2 kinds of charges: Benjamin Franklin

• Scientist who showed 2 kinds of charges: Due Fay

• Value of 1 unit of charge: 1.6 × 10–19 C

• Charge on an electron: 1 unit = 1.6 × 10–19 C

Ohm's Law

It states that the ,Current flowing through a conductor is directly proportional to the potential difference (V) applied across the

conductor, provided physical conditions such as temperature, mechanical strain are kept constant

(Dependent)

(independent) V

I

15




Conductor can be categorized as

Ohmic

Conductors which obey

Ohm's Law

Graph is a Straight line

Ex: conductors(metals)

Non-Ohmic

Conductors which do not obey Ohm's Law.

Graph is not a straight line

Ex: Diode, Transistor ,Mosfet

V

I

V

I

Electrostatic Shielding

Electrostatic shielding/screening is the phenomenon of protecting a certain region of space from external electric field.

Human body is a good conductor of electricity, i.e., charge can flow easily through the human body.

If human body is wet, it Resistance decreases considerably leading to higher possibility of electric discharge through human body

and humans may get shock due to electric current, Electric current flows through human body only when it allows current to pass

through it to the ground(earth), thereby completing the circuit.

The NIOSH states "Under dry conditions, the resistance offered by the human body may be as high as 100,000 ohms. Wet or

broken skin may drop the body's resistance to 1,000 ohms," adding that "high-voltage electrical energy quickly breaks

down human skin, reducing the human body's resistance to 500 ohms"

NIOSH stands for National Institute for Occupational Safety and Health

Electrical Capacity

Electrical capacity of a conductor is numerically equal to the charge required to raise its potential by unity. Capacitance is a positive

quantity only.

The unit of capacitance is farad.

1 farad (F) =

1 coulomb C

1 volt V, i.e.,

16




A conductor is said to have a capacity of one farad, when a charge of one coulomb raises its potential by one volt.

Electrostatics of Conductors

Important results regarding electrostatics of conductors:

1. In electrostatic equilibrium, electric field is zero everywhere inside the conductor.

2. Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.

3. Net charge in the interior of a conductor is zero.

According to Gauss's theorem; 0

qE.ds

Inside a conductor, E 0 q 0 i.e. net charge inside a conductor is zero.

4. Electrostatic potential is constant throughout the volume of the conductor and has the same value as on its surface.

5. Electric field at the surface of a charged conductor is 0

E n

, where is surface charge density and n is a unit vector normal to

the surface in the outward direction.

Capacity of Earth

We can calculate electrical capacity of earth, taking it to be a conducting sphere of radius,

r = 6400 km = 6.4 × 106 m

As C = 4 0r C = 9

1

9 10 (6.4 × 106) = 0.711 × 10–3 farad = 0.711 × 10–3 × 106 F = 711 F

Thus the capacity of earth is only 711 F, which is the biggest sphere we come across,

Farad is too big a unit of capacitance.

Capacitor

A capacitor is an arrangement for storing large amounts of electric charge and hence electric energy in a

small space. It consists of 2 conducting plates filled by a dielectric or mica or airinside, To charge a

capacitor, We connect a battery. So positive and Negative charge appears on both plates of the capacitor,

Dielectric is used to increase the charge storing capacity of a capacitor. Capacitors can be categorized on

the basis of its shape and the material filled between the plates.

Capacitors or condensers are used in many electrical appliances, like electric fans, electric motors, in

oscillator circuits, in radio tuning, in ignition system of engines in vehicles, in filter circuits etc. In the

microelectronic age we live, microscopic capacitors form the memory banks of computers.

What is a defibrillator? Explain Briefly.

A defibrillator is a device used to save the life of a person suffering a heart stroke.

Due to rapid, uncoordinated twitching of the heart muscles, the heart undergoes ventricular fibrillation. To save the person's life,

regular beating of the heart is to be restored by delivering a jolt to the heart usingdefibrillator.

Suppose, a 70 F capacitor of a defibrillator is charged to a potential of 5000 V. The energy stored

= 1

2CV2 =

1

2(70 × 10–6)(5000)2 J = 875J.

Typically, about 200 J of energy is allowed to pass through person's body in a pulse lasting 2 milli second. Therefore, power

delivered to the body= 3

200

2 10 = 105 W = 100 kW, which is much larger than the power delivered by the battery.

Thus energy stored in the capacitor discharged at a much higher provides the much needed jolt to save the person's life.

17




Action of Sharp Points

When a spherical conductor of radius r carries a charge q, the surface density of charge() is given by

= 2

charge q

area 4 r

For a pointed end, r is very small, therefore is very large. Electric field intensity E = /0 becomes large. As a result, air around

the sharp end becomes ionized and a bluish glow, called corona is seen. Though air does not transfer electric charges easily, ionized

air is a good conductor and hence the charges leak from the surface into the surrounding air.

Why are lighting storms so dangerous?

During lightning storm, electric field developed is on the verge of causing electrical breakdown in the surrounding air. therefore,

lightning storms are dangerous for the following reasons:

(i) If lightning strikes us or something we are touching, it produces a fatal charge flow in our body.

(ii) If lightning strikes any object near us, a portion of charge flow may jump to us through the air.

(iii) If lightning strikes the ground near us, part of charge flow along the ground can be diverted through our body.

(iv) Sometimes, negatively charged base of an overhead cloud results in the movement of some of conduction electrons in our

body into the ground, leaving us highly positively charged. This would produce what is called an upward streamer, which

is dangerous because resulting ionization of molecules in air sets free, tremendous number electrons from those

molecules.

Band Theory

It describes materials on the basis of presence or absence ofelectrons in valence band and conduction band.

Electrons conduct Electricity only when they are in conduction Band

Insulators Semi-Conductor Conductors

Due to large band gap between valence

and conduction band, electrons are not

available in conduction band so Poor

conductors of electricity.

Due to large band gap, electrons do not

reach Conduction Band. Hence insulators

do not conduct electricity.

A small band gap is present between

conduction band and valence band.

The energy to cover this gap can be

easily provided so it serves as good

conductors in Electronics Industry.

Due to small gap between VB & CB,

semiconductor conducts electricity to

a lesser extend then conductors

There is no gap between valence band and

conduction band so entire electrons of

valence band lies in conduction band as

well So it serves as Good conductors of

electricity

Due to overlapping of VB, CB, e– are

present in CB so as external electric field

is applied, current appears.

C.B means Conduction band, V.B means valence band

18




Examples of

Insulator

• Wood

• Rubber

• Glass

• Plastic

• Mica

• War

• Ebonite

• Paper

Semi-Conductors

• Si (Silicon) Ge (Germanium)

• Some doped elements of group 13, 14, 15 of periodic table.

Group 13 Group 14 Group 15

(Boron)

(Aluminum)

(Gallium)

(Indium)

(Thallium)

B

Al

Ga

In

Th

C(Carbon)

Si(silicon)

Ge(Germanium)

Sn (Tin)

Pb (Lead)

N

P

Ar

Sb

Bi

Nitrogen

Phosphorous

Arsenic

Antimony

Bismuth

Conductors

• Silver

• Human Body

• Earth

• Copper, Iron, Aluminium

• Coal

• Mercury (Hg)

•Salt, solutions, Acids,

Alkali's

Open Circuit: When no load is connected across batteryClosed Circuit: When current flows through load.

Circuit is Incomplete So, No current flows As the circuit is complete so current flows

Series: Current remains same Parallel: Voltage is same

voltage divides as per Resistance current divides as per resistance

19




20




Total voltage = V1 + V2Total Current = I1 + I2

Electric Field: It is an imaginary space around the charge, where its presence can be experienced.

Experienced means if you bring another charged participle, it shows some response. (Attraction or repulsion)

To study electric field and its direction, we draw electric field lines. (Imaginary lines)

When we add or remove an electron from an atom, we get charge on it. As the electrons in the outer orbit are loosely bound so by

providing small amount of energy to the atom, we can create charge on it.

If an atom losses an electron it acquires positive charge as number of electrons are less than the number of protons present in the

nucleus so overall effect of positive charge increases

On the other hand , if we add an electron to the atom, the number of electrons in the outer shell increases than the number of

protons in the nucleus so overall negative charge appears on the atom.

For positive charge

+

Electric field lines are radially outwards

For negative Charge

21




Electric field lines are radially inwards.

For positive and Negative Kept Together

Electric field lines move from positive to negative charge forming continous curves

+

-

For 2 Like Charges

neutral point

EF = 0

We obtain a neutral point here, a place where electric field is zero.

same pattern is obtained for two negative charges kept together but the direction of Electric field is radially inwards.

Properties of electric field lines.

• Continuous lines

• Do not form closed loops

• Never intersect [as else at that point, we get two directions]

• Tangent on electric field gives direction of electrons field intensity.

22




• Always normal (perpendicular) to the surface of conductor.

• Magnitude of field is represented by Density of field lines.

Dense field lines Highly Distributed Field lines

Electric field Intensity: Electric field intensity (E) at any point is defined as the electrostatic force acting per unit positive charge

(q0) at that point.

or Number of field lines crossing normally per unit area at that point.

or E = 0

F Electrostatic force

q unit ve charge

Unit = E = Newton

Columb = NC–1

Electric Potential: It is the work done in bringing a unit test charge q0 from infinity to that point.

V= 0 0

Work done W

Charge q q

unit = Joule

Columb

Electric Power: Power =2work I Rt

time t = I2R.

As V = 1R,I = V

R, R =

V

I P = VI

23




So, P = I2R =

2 2V VR

R R

1 Watt = 1 ampere volt

P = I2R = 2 V

II

= VI. 1 Kilowatt = 103 W

So, P = I2R = VI =

2V

R 1 Megawatt = 106 W

1 horse power (hp) = 746 Walt

Q. A bulb of 484 is producing light when connected to 220 V supply. What is electric power of bulb.

P =

22 220V 220 220

R 484 484

= 100 Watt

Electrical Energy: It is the total electric work done or energy supplied by source of emf in maintaining the current in electric

circuit for given time.

Energy = E = VIt = electric power × time

SI unit: Joule,1 joule = 1 volt ×1 ampere ×1second

Commercial unit of electricity = 1 KWh = Board of Trade Unit (BOT)

1 KWh = 1000 watt × 1 hour

So, 1 KWh is the total electric energy consumed when an electrical appliance of power 1 KW works for one hour.

1 KWh = 3.6 × 106 Joule

No. of units of electricity consumed = No. of KWh = Watt hour

1000

Ex: A bulb of 100 W is operating for 6 hours a day. Find units of energy consumed in 7 days.

Energy consumed = Power × time

= 100 × (6 × 7) = 4200 Wh

Units = 1 KWh = 4200

1000 kWh = 4.2 kWh

Dipole: An electric dipole consists of an equal and opposite point charges, separated by a small distance.

+q

Very small

Distance –q

Ideal Dipole Charge is very high

Distance is very small.

Dipole moment ,p = (either charge)q× (distance between charges )

Dipole moment(p): It tells the strength of Dipole

It is a vector quantity

NOTE: Direction of electric field positive to negative

Direction of electric Dipole moment Negative to positive

24




Electron Proton

charge = 1.6 × 10–19 C charge = 1.6 × 10–19 C

mass = 9.1 × 10–31 kg mass = 1.6 × 10–27 kg

Current Direction

Current + to –

E.F. + to –

Dipole moment – to +

Current(I) – Scalar quantity

Current Density(J) – Vector quantity

Columb's Law: ItStates that two Stationary point charges attract or repel with a force,

q1

distance between

them q2

Stationary

point charges

r

F = 1 2

20

q q1

4 r

Where F q1 q2 (directly proportional to magnitude of charges)

25




F 2

1

r (Inversely proportional to square of distance between them)

Where 0 = Electrical permittivity = 8.85 × 10–12 units

Unit of E0,

As F =1 2

20

q q1

4 r

0 =

1 22

q q1

F 4 r=

2

C . C

N. m

0 =C2/N – m2and 0

1

4 = constant = 9 × 109 Nm2/c2

Heating effect of current or Joule's Heating Effect or Joule's Law of Heating

Whenever electric current is passed through a conductor, it becomes hot after some time so, we mostly keep

FAN to cool it or a coolant to eject out heat.

Heat Produced = H = I2Rt joule = 2

4.2

I RtCalorie

I = Current R = Resistance T = Time

Heat = work = Energy

Cause of heat: Collisions of electrons with fixed ions/atoms of conductor.

Here, Converted

toElectrical Energy Heat Energy

Kirchhoff's Law

• Kirchhoff's Current Law (KCL)/ Junction Law

It states that, the net current on a junction in an electrical circuit will be zero, i.e. net incoming current to the junction

is equal to net outgoing current to the junction.

i.e. the net current at the junction O is given by

i1 - i2 + i3 - i4 + i5 - i6 = 0

⇒ i1 + i3 + i5 = i2 + i4 + i6

26




Incoming current = Outgoing current

It is based on the law of conservation of charge.

• Kirchhoff's Voltage Law (KVL)

In any closed circuit, the algebraic sum of the products of the current and resistance of each part of the circuit is equal

to the total emf in the circuit.

ΣiR = ΣE

i.e. sum of voltage drops of all the resistors is equal to the source voltage in magnitude. It is based on law of

conservation of energy

Equipotential surface: A surface at every point of which, electric potential is same

V = 0

W

q

VB VA

Here VA = VB

So, WAB = 0

So,work done in moving a charge on equipotential surface = Zero.

Dielectrics: These are insulating materials which transmit electric effects without actually conducting electricity.

Polar Non-Polar

Cl

H

Has net permanent Dipole moment

H H

No net dipole moment

Center of positive charge do not coincide with centre of

negative charge

Centre of +ve = Centre of –ve (coincide)

EMF: Electro motive force(E)

It is the maximum potential difference between 2 electrodes of a cell when cell is in open circuit.

Terminal Potential difference(V): It is difference of potentials between two terminals of a cell when it is in closed circuit,

EMF > P.D.

EMF = Potential Difference + Voltage due to Initial Resistance

E = V+ Ir

where I= Current flowing through the circuit when cell is in use

r= internal resistance of battery

27




MAGNETS AND MAGNETIC FIELD Magnet

It is any piece which attracts small pieces of iron. It shows the process of

• Attraction (for dissimilar poles)

• Repulsion (for similar poles)

Any magnet always has 2 poles. N S

North Pole (N) and South Pole (S)

Magnetic field lines: These are the imaginary lines drawn to study the magnetic field.

N S

These travel

• N to S = Outside the magnet

• S to N = Inside the magnet.

Magnetic field: It is an imaginary space where its

presence can be experienced.

Unit of magnetic field

Gauss – Cgs unit

Tesla (T) = SI unit

1 T = 104Guass.

Note: Magnetic field is a vector quantity.

Direction of magnetic field: By right hand thumb rule or Maxwell's screw rule.

According to Right Hand thumb rule, if we imagine, linear wire to be held in grip of right hand, where

ThumbPoints directions of current

Fingers Points direction of M. field

i.e. if current up M.F. anticlock wise direction

if current down M.F. Clockwise direction

Earth's magnetic field at its surface = 3.5 × 10–5T (Approx)

28




Types of Magnet

Permanent Magnets

Bar Magnet

Horse Shoe

Circular Magnet

Temporary Magnets

Solenoid

Toroid

Magnets

Natural

• These are found in nature

• Irregular in Shape

Artificial

• These are man made

• Posses Definite shape

Gauss Theorem

In Electrostatics

Electric flux through a closed

surface

E

o

qE.ds

In Magnetism

It tells that the net magnetic flux

(B) through any closed surface is

zero.

B B.ds O

Where, flux = number of field lines passing through a particular area.

29




Types of Magnetic Materials

Diamagnetic Substance

The diamagnetic substances are

those in which the individual

atoms/molecules/ions do not

possess any net magnetic moment on their own.

When such substances are placed in

an external magnetising field, they

get feebly magnetised in a

direction opposite to the

magnetising field.

Ex:- Antimony, Bismuth, Copper, Lead, Gold, Silver, Diamond, Zinc, Quartz; Water, Alcohol, Mercury;

Air, Hydrogen, Nitrogen and all inert gases like Helium, Neon,

Argon, etc.

Paramagnetic Substances

Paramagnetic substances are those

in which each individual

atom/molecule/ion has some net

non zero magnetic field of its own.

When such substances are placed in

an external magnetised field, they

get feebly magnetised in the

direction of the magnetising field.

Ferromagnetic Substance

Ferromagnetic substances are

those in which each individual atom/molecule/ion has a non

zero magnetic moment, as in a paramagnetic substance.

When such substances are placed in an external magnetising field,

they get strongly magnetised in the direction of the field.

Soft

When external magnetic field is

removed, magnetization disappears

in some of the materials like soft iron.

These materials are Soft Ferromagnets.

Hard

The magnetization persists even

after removal of external magnetic

field. Such materials are Hard

Ferromagnets.

Curie Temperature

When a magnet is heated, it loses its magnetization. The temperature at which ferromagnetic substance becomes paramagnetic is

called curie Temperature.

Curie Temperature

HeatingFerromagnetic Paramagnetic

Hysteresis Curve

It tells us the behavior of the natural when it is magnetized and demagnetized i.e. it is taken through the cycle of magnetization

Hysteresis curve for

• narrow and large

• Less Hysteresis Loss

• Good for making Transformer cores, electromagnetic.

• Wide and short

• More Hysteresis loss

• Good for making permanent magnets.

30




Geomagnetism: The branch of Physics which deals with the study of magnetism of earth is called terrestrial magnetism or

geomagnetism.

The strength of this field at the surface of earth is approximately 0.1 gauss or 10–5 tesla. The field is not confined only to earth's

surface, it extends upto a height nearly 5 times the radius of earth ( 5 × 6400 km = 32000 km).

Magnetic elements of earth

These are the quantities which describe completely in magnitude as well as direction, the magnetic field of earth at that place.

Following are three magnetic elements of earth:

1. Magnetic declination (),

2. Magnetic inclination or Magnetic dip (),

3. Horizontal component (H) of earth's magnetic field.

Tangent Galvanometer: It is an instrument which is used for detection and measurement of low electric currents. It is based on

tangent law in magnetism.

Bohr Magneton(μB): Bohr magneton is the minimum magnetic dipole moment associated with an atom due to orbital motion of an

electron in the first stationary orbit of the atom.

Magnetic field strength: Magnetic field strength or magnetic field induction or flux density of magnetic field being equal to

the force experienced by a unit positive charge moving with unit velocity in a direction perpendicular to the magnetic field.

Magnetic Permeability (): It is the ability of a material to permit the passage of magnetic lines of force through it.

Relative magnetic permeability of a material: It is defined as the ratio of magnetic permeability of the material () and magnetic

permeability of free space (0)

31




MAGNETISM FROM ELECTRICITY Every current carrying conductor produces a magnetic field around it. It is due to spin of electrons.

Note:

Static charge (at rest)Produces only electric field

Moving charge Produces Electric field & Magnetic field

Force on a charged particle in EOF and MOF:

Whenever a charged particle is kept in uniform E.F. or M.F. or both,it experiences a force and shows Trajectory

In uniform electric field In uniform magnetic field + electric field Magnetic field only

• follows a parabolic path

• used in CRT (Cathode Ray

Tubes) of Televisions.

• follows helical path

Circular + linear

• follows a circular path

Lorentz force

It is the force experienced by a charged particle when it moves in a space having both electric and

Magnetic fields.

Lorentz Force = Force due to electric field + force due to magnetic field

F = qE + qv × B

The force exerted on a charged particle q moving with velocity v through an electric field E and

magnetic field B.

Induction: Charges of opposite nature are induced on the opposite body without actual

contact

32




neutral ball

After Some Time

induction

1. BiotSavart Law/Laplace Law

It tells us the value of magnetic field or magnetic induction at any point due to small current element.

Wire carrying current

Magnetic field at this point due to current in the wire

(A point)

2. Ampere CircuitalLaw

It is an alternative form ofBiot Savart Law in Magnetostatics

It tells the value of magnetic field due to symmetrical current elements (like a wire, cylinder)

3. Gauss's Law for Magnetism

According to Gauss's law for magnetism, the net magnetic flux (B) through any closed surface is always zero.

B = S

B. ds = 0

4. Gauss's law in electrostatics

The surface integral of electrostatic field E produced by any source over any closed surface S enclosing a volume V in vacuum i.e.,

total electric flux over the closed surface S in vacuum, is 1/0 times the total charge (Q) contained inside S, i.e.,

E = 0S

qE. ds

33




ELECTRICITY FROM MAGNETISM Whenever there is a change in Magnetic flux (field/area) around a conductor, an emf is induced in the conductor. This induction of

electrical energy from magnetic energy is called Electro Magnetic Induction [EMI]

If the conductor is in the form of closed circuit, current flows through it and it is known as induced current

NOTE: Current always flows in closed circuit only, never in open circuit.

Magnetic flux[]: It is the total number of magnetic field lines of force crossing a surface normally.

Where = B . A = BA cos

i.e. Dot produce of magnetic field and area vector

unit of magnetic flux Weber = SI unit

1 Weber = 1 Tesla × 1m2

C.g.s. unit Maxwell (Mx)

Where, 1 weber = 108maxwell

Faraday's Laws of Electro Magnetic Induction

• E.M.F. is induced only when there is a change in magnetic flux. The induced emf lasts as long as change continuous.

The magnitude of emf induced is directly proportional to the rate of change of magnetic flux linked with the circuit.

induced emf e =d

dt

= rate of change of Magnetic flux.

This –ve sign is due to lenz's Law.

Lenz's Law: It states that the direction of induced current is such that it always opposes the change in magnetic flux, responsible

for its production.

Explanation: -

If North pole is coming towards it, coil tends to oppose it.So, make North pole on this side of coil.

If North pole is going away from the coil, it tries to oppose the motion by creating South pole on its side

If South pole is coming towards it, coil tends to oppose it. So, make South pole on this side of coil.

If South pole is going away from the coil, it tries to oppose the motion by creating North pole on its side

By convention

34




Law of Energy Conservation in EMI and LenzLaw

Mechanical energy used in moving a magnet Converted

to electrical energy of coil

If there is no movement, no work is done so no conversion of energy hence induced EMF = 0 (Zero)

Fleming's Right Hand Rule:

It gives us the direction of induced emf/ current in a conductor moving in a magnetic field.

First finger Magnetic field (North to South)

Thumb Motion of Conductor

Middle finger induced current

This concept is used in Generator [Mechanical Energy Electrical Energy]

Fleming Left Hand Rule:

When a current carrying conductor is placed in external magnetic field, it experiences a force.

First finger direction of magnetic field

Central finger direction of electric current (current in conductor)

Thumb Direction of force experienced by conductor

This is used in Motor [Electrical EnergyMechanical Energy]

INDUCTION

Self Induction

When the induced emf is in the same device or coil. It

Mutual Induction

Emf is induced in the second coil due to change in emf

35




works as an inductor.

(current)in the first coil

Meissner Effect

The Meissner effect states that at or below the transition temperature, there is no magnetic field or magnetic flux density inside

the super-conductor when the specimen is placed inside a uniform magnetic field.

Eddy Currents or Foucault Currents

Eddy currents are the currents induced in the bulk pieces of conductors when the amount of magnetic flux linked with the

conductor changes.

Their flow patterns resemble swirling eddies in water. That is why they are called eddy currents. These were discovered by

Foucault in the year 1895 and hence they are called Foucault currents.

Application of Eddy Currents

(a) Electro-magnetic damping: To avoid the delay in reading galvanometer deflection , the coil is wound over a non magnetic

metallic frame. As the coil is deflected, eddy currents set up in the metallic frame oppose its motion. Therefore, the coil attains its

equilibrium position almost instantly. Thus, the motion of coil is damped. This is called electromagnetic damping.

(b) Induction Furnace: It is used to produce high temperatures which are utilized in preparing alloys by melting the constituent

metals. A high frequency alternating current is passed through a coil which surrounds the constituent metals. The large eddy

currents generated in the metals produce high temperatures sufficient to melt the metals.

(c) Magnetic Brakes: In some electrically powered trains, strong electromagnets are situated in the train, just above the rails.

When electromagnets are activated, the eddy currents induced in the rails oppose the motion of the train. As there are no

mechanical linkages, therefore, the braking action is smooth.

(d) Electric Power Meters: In the power meter of your house, you must have observed a rotating shiny disc. This is a metal disc

which rotates due to eddy currents developed in the disc, by magnetic fields produced by alternating currents.

(e) Induction Motor: An induction motor or a.c. motor is yet another important application of eddy currents. A rotating magnetic

field produces strong eddy currents in a rotor, which starts rotating in the direction of the rotating magnetic field.

(f) In speedometers of automobiles and energy meters.

(g) Eddy currents are also used in dia-thermy, i.e., in deep heat treatment of human body.

Some of the undesirable effect of eddy currents are:

(i) They oppose the relative motion.

(ii) They involve loss of energy in the form of heat.

(iii) The excessive heating may break the insulation in the appliances and reduce their life.

To minimize the eddy currents, the metal core to be used in an appliance like dynamo, transformer, choke, coil, motor etc. is

taken in the form of thin sheets. Each sheet is electrically insulted from the other by insulating varnish like lacquer. Such a core is

called a laminated core.

Maximum Power Transfer Theorem

36




It states that the power output across a certain load due to a cell or battery is maximum if the load resistance is equal to the

effective internal resistance of cell or battery.

If Load resistance = Internal Resistance of Cell/Battery

Output power will be maximum.

37




FORMULA'S 1. E.F. due to charge

E = 2

0

q

4 r

2. Force between charges/columb's Law,

F = 1 2

2

0

q q

4 r

3. Potential due to charge (V)

V = 0

q

4 r

4. Potential energy between 2 charges (PE)

PE = 1 2

0

q q

4 r

5. F = qE, E =

V

l

6. Capacitor

Q = CV, C = Q

V = 1 Farad =

1Columb

1Volt , V =

0

Q

4 r

To increase 1V, how much Q is required 1 Farad

7. Gauss's Law for Magnetism

B = S

B. ds = 0

Gauss's law in electrostatics

E = 0S

qE. ds

Heat Produced = H = I2Rt joule = 2

4.2

I RtCalorie

10. Current I = Charge (Q)/ Time (t)

11. Voltage V= Current(I) × Resistance(R)

12. Current density J

J = q / t

A A

I

I = JA cos = J. A

I be the current

Cross-sectional area A

13. Power P = I2R = VI =

2V

R

14. Dipole moment,p = (either charge)q× (distance between charges)

15. Lorentz Force = Force due to electric field + force due to magnetic field

F = qE + qv × B

38




Practice Questions 1. White taking of synthetic clothes, seeing a spark or

hearing a crackle, are due to

(a) motion of ions through air

(b) production of shock waves due to motion of electrons

(c) electric discharge

(d) cannot be explained

2. In general, metallic ropes are suspended from the

carriers to the ground which take inflammable material.

The reason is

(a) their speed is controlled

(b) to keep the gravity of the carrier nearer to the earth

(c) to keep the body of the carrier in contact with the

earth

(d) nothing should be placed under the carrier

3. If a plastic rod rubbed with fur is made to touch two

small pith balls suspended nearby, then which figure

shows their final configuration?

(a)

(b)

(c)

(d)

4. For the figure shown, the instrument

Ball (metal knob)

Rubber

Metal rod

Glass bottleGold leaves

(a) is used to measure quantity of a fluid

(b) is used to measure wind velocity is called wind meter

(c) is used to measure viscosity of a fluid

(d) is used to detect presence of charge on a body, is

called electroscope

5. When a body is connected to earth, electrons from the

earth flow into the body. The means the body is ………

(a) unchanged (b) charged positively

(c) charged negatively (d) as insulator

6. One metallic sphere A is given positive charge whereas

another identical metallic sphere B of exactly same mass

as of A is given equal amount of negative charge. Then

(a) mass of A and mass of B still remain equal

(b) mass of A increases

(c) mass of B decreases

(d) mass of B increases

7. Electric wiring in our houses has

(a) only one wire : live

(b) two wires : neutral, earth

(c) three wires, live, neutral, earth

(d) no wire

8. If two bodies are rubbed and one of them acquires q1

charge and another acquires q2 charge, then ratio q1 : q2

is

(a) 1 : 2 (b) 2 : 1

(c) – 1 : 1 (d) 1 : 4

9. Two bodies are rubbed and one of them is negatively

charged. For this body, if mi = initial mass, mf = mass

after charging, then

(a) mi = mf (b) mi< mf

(c) mi> mf (d) mi + mf= 2mf

10. In charging by induction,

(a) body to be charged must be an insulator

(b) body to be charged must be a semiconductor

39




(c) body to be charged must be a conductor

(d) any type of body can be charged by induction

11. A body A is being charged by another charged body B by

induction process. Then, charge acquired by A depends

on

(a) nature of material of A

(b) distance between A and B

(c) nature of medium separating A and B


12. Additive nature of charge means

(a) total charge on a system remains constant

(b) total charge on an isolated system is always zero

(c) charge are of two types positive and negative

(d) it tells about the scalar nature of charge

13. Conservation of charge follows from law of conservation

of mass. Above statement is

(a) correct

(b) incorrect

(c) nothing can be said

(d) mass and charge are two different physical quantities

following conservation law

14. Charge of a body is always an integral multiple of

(a) charge present in its one atom

(b) charge present in one mole of material of body

(c) charge present on an electron

(d) charge of its one nucleus

15. When a glass road is rubbed with a silk cloth, charge

appears on both. This observation is consistent with law

of conservation of charge was

(a) charge on both causes attraction

(b) charge on both causes repulsion

(c) charges appearing on both bodies are equal and

opposite

(d) charge on first body is more than that of second body

16. Magnitude of force between two point charges q1 and q2

which are separated by a distance r is given by

(a) F = 1 2|q q |k

r (b) F = 1 2

2

|q q |rk

r

(c) F = k

2

1 2|q q

r

(d) F = 1 22

|q .q |k

r

17. Suppose charge on a metallic sphere is q. If the sphere is

put in contact with an identical uncharged sphere, the

charge will spread over the two spheres. By symmetry

charge on each sphere will be …………

When distance between two charged spheres is varied so

that it becomes half the initial distance, force between

them will become ……….

(a) 2

q, half (b)

2

q, four times

(c) 2q, half (d) 2q, double

18. Force between two charges q1 and q2 separated by a

distance r is proportional to q1q2/r2. Proportionality

constant is

(a) 0

4

(b) 4πε0

(c) 0

1

4 (d) 1

19. Force between two charges varies with distance between

them as

(a)

F

r

(b)

F

r

(c)

F

r

(d)

40




F

r

20. Two electrically charged particles, having charges of

different magnitudes, when placed at a distance d from

each other, experience a force of attraction F.

These two particles are put in contact and again placed

at the same distance from each other.

What is the nature of new force between them?

(a) Attractive

(b) Repulsive

(c) Attractive or repulsive depending upon magnitude of

charges present on them

(d) Cannot predicted

21. A field line is a space curve, means

(a) field lines are hypothetical curves

(b) field lines are two dimensional curves

(c) field lines are three-dimensional curves

(d) field lines are straight lines

22. Two field lines can never cross each other because

(a) field lines are closed curves

(b) field lines repels each other

(c) field lines crowded only near the charge

(d) field has a unique direction at each point

23. In the diagram shown below.

(a) field strength at P is less t4han field strength at Q

(b) field strength at P and Q are equal

(c) field is more strong at P and less strong at Q

(d) cannot be tell from the figure

24. An area vector is a vector of magnitude equal to the area

and it is directed

(a) parallel to area

(b) at an angle of 450 with the plane of area

(c) at an angle of 900 with the area

(d) at an angle of 450 with the normal to the area

25. Electric flux through an element area ΔS when area is

placed in region of uniform field E is

(a) E × ΔS (b) E . ΔS

(c) ΔS × E (d) E(ΔS) . sin θ

26. If the centre of mass of positive charge does not coincide

with that of the molecule, then

(a) molecule is called polar and it have an intrinsic dipole

moment

(b) molecule is called polar but it does not have any

dipole moment

(c) molecule is called non-polar and it has a dipole

moment of its own

(d) molecule is called non-polar and it has a zero dipole

moment

27. Match the first part of a sentence given in Column I with

its second part in Column II, so that sentence is complete

meaningful and electrostatic ally true.

Column I Column II

41




A. Like charges 1. of two types

B. Unlike charges 2. Repel each other

C. Charge can be 3. Attract each other

D. Charges are 4. Neutralised, if they are equal

and opposite

A B C D

(a) 1 2 3 4

(b) 2 1 3 4

(c) 4 1 3 2

(d) 2 3 4 1

28. Match the field lines given in Column I with the charge

configuration due to which field lines exist in Column II.

A B C D A B C D

(a) 1 2 3 4 (b) 3 2 1 4

(c) 3 4 1 2 (d) 3 4 2 1

29. Which of these are properties of charge?

(a) Charges are additive in nature

(b) Charges are conservation in nature

(c) Charges are quantized in nature


30. Work done by an external force in bringing a unit

positive charge from infinity to a point is

(a) equal to the electrostatic potential (V) at that point

(b) equal to the negative of work done by electrostatic

forces

(c) Both (a) and (b)

(d) Neither (a) nor (b)

31. For a uniform electric field E, along the X-axis, the

equipotential surfaces

(a) Planes perpendicular to the X-axis

(b) Planes parallel to the YZ-plane



32. Work done in moving a test charge over an equipotential

surface?

(a) No (b) Yes

(c) Constant (d) Zero

33. Work done in moving a charge from one point to other inside

a uniformly charged conducting sphere is

(a) always zero (b) non-zero

(c) may be zero (d) None of these

34. What happens when a conductor is placed in an external

electric field?

(a) The free charge carriers move and charge

distribution in the conductor adjusts itself in such a way

that the electric field due to induced charge opposes the

external field within the conductor

(b) In the static situation, the two fields cancel each other and

the electrostatic field in the conductor is zero



35. Which of the following is/are the example of non-polar

molecules?

(a) Oxygen (b) Hydrogen

(c) Nitrogen (d) All (a), (b) and (c)

36. The examples of polar molecules are

(a) HCl (b) H2O

(c) NH3 (d) All (a), (b) and (c)

37. The extent of polarization depends on

(a) the dipole potential energy in the external field

tending to align the dipoles with the field

(b) thermal energy tending to disrupt the alignment

(c) both (a) and (b)


38. The symbols of a capacitor with fixed capacitance and

with variable capacitance is

(a)

,

(b)

,

42




(c)

,

(d)

,

39. The maximum electric field that a dielectric medium of a

capacitor can withstand without break down (of its

insulating property) is called its

(a) polarisation (b) capacitance

(c) dielectric strength (d) None of these

40. Van de Graaff generator is used to

(a) store electrical energy

(b) build up high voltages of million volts

(c) decelerate charged particle like electrons

(d) Both (a) and (b) are correct

41. Which of the following statement(s) is/are true about

the principle of Van de Graff generator?

(a) The action of sharp points

(b) The charge given to a hollow conductor is transferred

to outer surface and is distributed uniformly over it

(c) It is used for accelerating uncharged particle

(d) Both (a) and (b) are true

42. Match the following columns.

Column I Column II

A. 1 keV 1. 1.6 × 10-7 J

B. 1 MeV 2. 1.6 × 10-10 J

C. 1 GeV 3. 1.6 × 10-16 J

D. 1 TeV 4. 1.6 × 10-13 J

A B C D A B C D

(a) 4 2 3 1 (b) 3 4 2 1

(c) 2 3 4 1 (d) 1 4 3 2

43. Equipotential surfaces

(a) are closer in regions of large electric fields compared

to regions of lower electric fields

(b) will be more crowded near sharp edges of a

conductor

(c) will be more crowded near regions of large charge

densities

(d) will always be equally spaced

44. In which material, electric currents develop when an

electric field is applied?

(a) Conductor (b) Wooden piece

(c) Non-conductor (d) Insulator

45. In which conductors, positive and negative charges both

can move?

(a) Non-electrolytic solution

(b) Electrolytic solution



46. If we consider a mechanism where, the ends of the

cylinder are supplied with fresh charges to make up for

any charges neutralized by electrons moving inside the

conductor, in that case

(a) there will be a steady electric field in the body of the

conductor

(b) there will be in a continuous current rather than a

current for a short period of time


(d) neither (a) nor (b)

47. When current flows through copper wire, current

density J, electric field E and motion of electrons have

directions such that

(a) J and E are in opposite directions

(b) motion of electrons and E are in opposite directions

(c) J and motion of electrons are in same direction

(d) J, E and motion of electrons are in same direction

43




48. A steady current flows in a metallic conductor of non-

uniform cross-section. The quantity/quantities constant

along the length of conductor is/are

(a) current, electric field and drift speed

(b) only drift speed

(c) current and drift speed

(d) only current

49. The V – i graph for a good conductor makes angle 400

with V – axis. Here, V denotes voltage and i denotes

current. The resistance of the conductor will be

(a) sin 400 (b) cos 400

(c) tan 400 (d) cot 400

50. If charges moved without collisions through the

conductor, their kinetic energy would also change so that

the total energy is

(a) changed (b) unchanged

(c) doubled (d) halved

51. The current i and voltage V graph for a given metallic

wire at two different temperatures T1 and T2 are shown

in the figure. It is concluded that

(a) T1> T2 (b) T1< T2

(c) T1 = T2 (d) T1 = 2T2

52. Five resistors are connected as shown in figure. Find the

equivalent resistance between the points B and C.

(a) 70

19Ω (b)

19

70Ω

(c) 16

5Ω (d)

15

8Ω

53. An electric bulb is marked 100 W, 230 V. If the supply

voltage drops to 115 V, what is the heat and light energy

produced by the bulb in 20 min?

(a) 20000 J (b) 25000 J

(c) 30000 J (d) 35000 J

54. To draw maximum current from a combination of cells,

how should be cells be grouped?

(a) Parallel

(b) Series

(c) Mixed grouping

(d) Depends upon the relative values of internal and

external

55. The algebraic sum of changes in potential around any

closed loop involving resistor and cells in the loop is

(a) more than zero (b) less than zero

(c) zero (d) constant

56. The current remains same in

(a) series (b) parallel

(c) both (d) none of the above

57. The Wheatstone bridge and its balance condition

provide a practical method for determination of an

(a) known resistance

(b) unknown resistance


(d) None of the above

58. Which of the following draws no current from the

voltage source being measured?

(a) Meter bridge (b) Wheatstone bridge

(c) Potentiometer (d) None of these

59. In a potentiometer, the null point is received at 7th wire.

If now we have to change the null point at the 9th wire,

what should we do?

(a) Attach resistance in series with battery

(b) Increase resistance in main circuit

(c) Decrease resistance in main circuit

(d) Decrease applied emf

60. Potentiometer measures the potential difference more

accurately than a voltmeter because

(a) it has a wire of high resistance

(b) it has a wire of low resistance

(c) it does not draw current from external circuit

(d) it draws a heavy current from external circuit

44




II Statement Based Questions Type I

Directions (Q. Nos. 61-63) In the following questions, a

statement I is followed by a corresponding statement II.

Of the following statements, choose the correct one.

(a) Both Statement I and Statement II are correct and

Statement II is the correct explanation of Statement I.

(b) Both Statement I and Statement II are correct but

Statement II is not the correct explanation of Statement I.

(c) Statement I is correct but Statement II is incorrect.

(d) Statement I is incorrect but Statement II is correct.

61. Statement I In electrostatics all charges whether free or

bound, are considered to be at rest.

Statement II The charges in motion constitute an

electric current.

62. Statement I Conductivity arises from mobile charge

carriers.

Statement II In metals, these mobile charge carriers are

electrons with fixed positive ions in background; these

can be both positive and negative ions in an electrolyte.

63. Statement I For insulators and semiconductors, number

of electrons increases with increasing temperature.

Statement II This increase of number of electrons more

effective than any decrease in τ, so that for such

materials decreases with temperature.

64. Ohm’ law is not true

(a) for metallic conductors at low temperature

(b) for metallic conductors at high temperature

(c) for electrolytes when current passes through them

(d) for diode when current flow

65. Temperature dependence of resistivity (T) of

semiconductor insulators and metals is significantly

based on the following factors.

(a) Number of charge carries can change with

temperature T.

(b) Time interval between two successive collision which

depends on T.

(c) Length of material can be a function of T.

(d) Mass of carries is a function of T.

66. The resistance of a conductor increases with

(a) increase in length

(b) increase in temperature

(c) decrease in cross-sectional area


67. Which of the following characteristics of electrons

determines the current in a conductors?

(a) Drift velocity alone

(b) Thermal velocity alone

(c) Both drift velocity and thermal velocity

45




(d) Neither drift nor thermal velocity

68. If a proton is projected in a direction perpendicular to a

uniform magnetic field with velocity v and an electron is

projected along the lines of force, what will happen to

proton and electron?

(a) The electron will travel along a circle with constant

speed and the proton will move along a straight line

(b) Proton will move in a circle with constant speed and

there will be no effect on the motion of electron

(c) There will not be any effect on the motion of electron

and proton

(d) The electron and proton both will follow the path of a

parabola

69. Magnetic field produced by a wire carrying current

(a) is parallel along the axis of wire

(b) is perpendicular to the plane of the wire

(c) forms circular loops along the axis of wire and

coplanar to the wire

(d) direction of field is not constant

70. An electron is travelling horizontally towards East. A

magnetic field in vertically downward direction exerts a

force on the electron along

(a) East (b) West

(c) North (d) South

71. When a charged particle moves in the region of magnetic

field, then

(a) magnitude of its velocity keeps on changing

(b) velocity of particle remains constant

(c) direction of momentum keeps on changing

(d) kinetic energy of particle keep on changing

72. Which one is a correct figure to represent path of a

moving charge in magnetic field?

73. A cyclotron is used to accelerate charged particles or

ions to high energies. It uses

(a) only electric field

(b) only magnetic field

(c) Both electric and magnetic fields


74. A current loop in a magnetic field

(a) experience a torque whether the field is uniform or

non-uniform in all orientations

(b) can be in equilibrium in one orientations

(c) can be equilibrium in two orientations, both the

equilibrium states are unstable

(d) can be in equilibrium in two orientations, both the

while the other is unstable

75. A loop of flexible wire of irregular shape carrying current

is placed in an external field. Then

(a) it rotates in a direction perpendicular to its axis

(b) it rotates along an axis perpendicular to its plane

(c) it does not show any change

(d) it assumes a circular shape

76. A moving coil galvanometer is an instrument which

(a) is used to measure EMF

(b) is used to measure potential difference

(c) is used to measure resistance

(d) is a deflection instrument which gives a deflection

when a current flows through its coil

77. To make the field radial in a moving coil galvanometer

(a) number of turns of coil is kept small

(b) magnet is take in the form of horse-shoe

(c) poles are of very strong magnets

(d) poles are cylindrically cut

78. The deflections in a moving coil galvanometer is

(a) directly proportional to torsional constant of spring

(b) directly proportional to the number of turns in the

coil

(c) inversely proportional to the area of the coil

(d) inversely proportional to the current in the coil

79. What is the shape of magnet used in moving coil

galvanometer to make the magnetic field radial

(a) concave (b) horse-shoe magnet

(c) convex (d) None of these

80. In ballistic galvanometer, the frame on which the coil is

wound is non-metallic to

(a) avoid the production of induced emf

(b) avoid the production of eddy current

(c) increase the production of eddy current

(d) increase the production of induced emf

81. For the given ammeter circuit,

46




(a) IgS = IG (b) (I - Ig)S = IgG

(c) IgG = (I + Ig)S (d) g

I G

I S

82. To convert a galvanometer into an ammeter,

(a) a low resistance is connected in series with the coil of

galvanometer

(b) a low resistance is connected in parallel with the coil

of galvanometer

(c) a high resistance is connected in series with

galvanometer coil

(d) a high resistance is connected in parallel with the

galvanometer coil

83. To convert a galvanometer into a voltmeter,

(a) a low resistance in parallel is used

(b) a low resistance in series is used

(c) a high resistance in series is used

(d) a high resistance in parallel is used

84. A charged particle with some initial velocity is projected

in a region where non-zero electric and/or magnetic

fields are present. In Column I, information about the

existence of electric and/or magnetic field and direction

of initial velocity of charged particle are given, while in

Column II the probable path of the charged particle is

mentioned. Match the entries of Column I with the

entries of Column II.

Column I Column II

A. E = 0, B ≠ 0, and initial

velocity is at any angle

with B

1. Straight line

B. E ≠ 0, B = 0, and initial

velocity is at any angle

with E

2. Parabola

C. E ≠ 0, B ≠ 0, E||B and

initial velocity is to

both

3. Circular

D. E ≠ 0, B ≠ 0, E

perpendicular to B and v

perpendicular to both E

and B

4. Helical path with non-

uniform pitch

A B C D

(a) 1, 3 1, 2 4 1

(b) 1, 2 3, 4 4 1, 3

(c) 2 3 1 4

(d) 4 1 2 3

47




85. The tip of a suspended magnet which points to the

geographic North is called

(a) South-pole (b) North-pole

(c) East-pole (d) West-pole

86. The pattern of iron fillings suggests that the

(a) magnet has only one pole

(b) magnet has two poles

(c) magnet is a magnetic dipole

(d) Both (b) and (c)

87. The pattern of iron filling permit us

(a) to plot the North-South poles

(b) to plot the geographic North-South poles

(c) to plot the magnetic field lines

(d) to plot the electric dipole

88. Magnetic field lines show the direction (at every point)

along which a small magnetized needle aligns. Do the

magnetic field lines also represent the lines of force on a

moving charge at every point?

(a) No

(b) Yes

(c) Neither (a) nor (b)

(d) Given information is not sufficient

89. Gauss’s law for magnetism is

(a) the net magnetic flux through any closed surface is B.

ΔS

(b) the net magnetic flux through any closed surface is E.

ΔS

(c) the net magnetic flux through any closed surface is 0

(d) Both (a) and (c)

90. Many of the diagrams given in figure, show magnetic

field lines (thick lines in the figure). Point out which one

is/are correct?

(a) Both (i) and (iv) (b) Both (ii) and (iv)

(c) Both (iii) and (iv) (d) Only (iii)

91. The pole near the geographic North-pole of the earth is called

the ………… magnetic pole and the pole near the geographic

South-pole is called the ………

(a) South-North (b) South-East

(c) North-East (d) North-South

92. The vertical plane containing the longitude circle and the

axis of rotation of the earth is called the

(a) geographic meridian

(b) magnetic meridian

(c) magnetic declination

(d) magnetic inclination

93. One can define ………. of a place as the vertical plane

which passes through the imaginary line joining the

magnetic North and the South-poles.

(a) geographic meridian

(b) magnetic meridian


(d) magnetic inclination

94. Dip is the angle that the total ………. of the of earth makes

with the surface of the earth.

(a) magnetic field BE

(b) magnetic inclination


(d) magnetic meridian

95. The angle of dip at a certain place where the horizontal

and vertical components of the earth’s magnetic field are

equal is

(a) 300 (b) 900

(c) 600 (d) 450

96. Which of the following substances have tendency to

move from stronger to the weaker part of the external

magnetic field?

(a) Paramagnetic (b) Diamagnetic

(c) Ferromagnetic (d) All of these

97. Diamagnetic substances are the ones in which resultant

magnetic moment in an atom is

(a) zero (b) half

(c) one-fourth (d) three-fourth

98. The most exotic diamagnetic materials are

(a) conductors (b) superconductors

(c) semiconductors (d) poor conductors

99. If superconductors are cooled to very low temperature,

then the exhibit perfect

(a) conductivity (b) diamagnetism

48




(c) Both (a) and (b) (d) Neither (a) nor (b)

100. The phenomenon of perfect diamagnetism in super-

conductors is called the

(a) Tidal effect (b) Meissnereffect

(c) Humuseffect (d) None of these

101. Which of the following are used for running magnetically

levitated superfast trains?

(a) Diamagnets

(b) Paramagnets

(c) Ferromagnets

(d) Superconducting magnets

102. Which of the following possesses a permanent magnetic

dipole moment of their own?

(a) Diamagnetic (b) Paramagnetic

(c) Copper (d) Lead

103. When the external field is removed in ferromagnetic

materials the magnetization persists, such materials are

called

(a) soft ferromagnetic materials

(b) hard ferromagnetic materials

(c) Neither (a) nor (b)


104. In which type of material the magnetic susceptibility

does not depend of temperature?

(a) Diamagnetic (b) Paramagnetic

(c) Ferromagnetic (d) Ferrite

105. Above Curie temperature

(a) a ferromagnetic substance becomes paramagnetic

(b) a paramagnetic substance becomes diamagnetic

(c) a diamagnetic substance becomes paramagnetic

(d) a paramagnetic substance becomes ferromagnetic

106. The correct measure of magnetic hardness of material is

(a) remanent magnetism

(b) hysteresis loss

(c) coercivity

(d) Curie temperature

107. Liquid oxygen remains suspended between two poles of

magnet because is

(a) diamagnetic (b) paramagnetic

(c) ferromagnetic (d) anti-ferromagnetic

108. If a diamagnetic substance is brought near the North or

the South-pole of a bar magnet, then it is

(a) attracted by the both poles

(b) repelled by both the poles

(c) repelled by the North-pole and attracted by the

south-pole

(d) attracted by the North-pole and repelled by the

South-pole

(e) None of the above

109. At Curie point, a ferromagnetic material becomes

(a) non-magnetic (b) diamagnetic

(c) paramagnetic (d) strongly ferromagnetic

110. The substance which at room temperature retain their

ferromagnetic property for a long period of time are

called

(a) permanent magnets

(b) electromagnets

(c) ferromagnets

(d) paramagnets

111. It is possible to make magnets out of

(a) iron and its alloys

(b) aluminium and its alloys

(c) copper and its alloys


112. For making permanent magnet which material is better

than soft iron?

(a) Steel (b) Chromium

(c) Copper (d) Nickel

113. Core of electromagnetic are made of ferromagnetic

materials which have

(a) high permeability (b) low retentivity

(c) Both (a) and (b) (e) None of these

114. In which application the material goes through an AC

cycle of magnetization for a long period?

(a) Transformer cores

(b) Telephone diaphragms

(c) Generator


115. The hysteresis cycle for the material of permanent

magnet is

(a) short and wide (b) tall and narrow

(c) tall and wide (d) short and narrow

116. Electromagnets are made of soft iron because soft iron

has

(a) low susceptibility and low retentively

(b) low susceptibility and high retentively

49




(c) high permeability and low retentively

(d) high permeability and high coercively

117. Hysteresis loops for two magnetic materials A and B are

as given below:

These materials are used to make magnets for electric

generators, transformer core and electromagnet core.

Then, it is proper to use

(a) A for electric generators and transformers

(b) A for electromagnets and B for electric generation

(c) A for transformers and B for electric generators

(d) B for electromagnets and transformers

118. Assertion The pole of magnet cannot be separated by

breaking into two pieces.

Reason The magnetic moment will be reduced to half

when a magnet is broken into two equal pieces.

(a) Both Assertion and Reason are correct and Reason is

the correct explanation of Assertion.

(b) Both Assertion and Reason are correct but Reason is

not the correct explanation of Assertion.

(c) Assertion is correct but Reason is incorrect.

(d) Assertion is incorrect but Reason is Correct.

119. Which of the following charactering are correct

associated with a ferromagnetic material?

(a) It is strongly attracted by a magnetic

(b) It tends to move from a region of strong magnetic

field to a region of weak magnetic field

(c) It origin is the spin of electron

(d) Above the Curie temperature, it exhibits

paramagnetic properties.

120. The experiments of Michael Faraday in England and

Joseph Henry in USA conducted around 1830,

demonstrated concussively that changing magnetic

fields, induced the electric currents in

(a) open coils (b) closed coils

(c) generator (d) dynamo

121. The phenomenon in which electric current is generated

by varying magnetic fields its appropriately called

(a) electromagnetic wave

(b) electromagnetic flux

(c) electromagnetic induction

(d) displacement of insulator

122. The pioneering experiments of Faraday and Henry have

led directly to the development of modern day’s

(a) generator (b) transformer

(c) dynamo (d) Both (a) and (b)

123. Which of the following phenomena is utilized in the

functioning of mouth piece of a telephone

(a) Thermoelectric effect

(b) Photoelectric effect

(c) Change of resistance with pressure

(d) Electromagnetic induction

124. Which scientist demonstrated that electric currents were

induced in closed coils when subjected to changing

magnetic fields?

(a) Faraday (b) Maxwell

50




(c) Hertz (d) Marconi

125. Moving magnet produces

(a) electric current in closed coil

(b) static magnetic field

(c) static electric field

(d) displacement of insulator

126. The discovery and understanding of electromagnetic

induction are based on a long series of experiments

carried out by

(a) Faraday (b) Henry

(c) Maxwell (d) Both (a) and (b)

127. When the north pole of a bar magnet is pushed towards

the coil along axis of coil, the pointer in the galvanometer

deflects, this is indicating the

(a) absence of current in the coil

(b) presence of current in the coil

(c) induction in the coil


128. In which direction will the galvanometer deflection be,

when the magnet is pulled away from the coil?

(Given deflection was towards a when magnet was

pushed towards coil)

(a) towards a

(b) no deflection

(c) towards b

(d) Indicator oscillates between a and b

129. Current in the coil is larger

(a) when the magnet is pushed towards the coil faster

(b) when the magnet is pulled away the coil faster



130. What will happen with the galvanometer when the

tapping key K is pressed?

(a) A momentary deflection

(b) A long time deflection

(c) No deflection

(d) None of these

131. An …………. is induced in a coil when magnetic flux

through the coil changes with time.

(a) electric current (b) emf

(c) Both (a) and (b) (d) Neither (a) and (b)

132. The time rate of change of magnetic flux through a circuit

induces ……….. in circuit.

(a) electric current (b) change in mass

(c) change of size (d) emf

133. The magnitude of the induced emf in a circuit is equal to

the time rate of change of magnetic flux through the

circuit, is statement of

(a) Fleming’s right hand rule

(b) Fleming’s left hand rule

(c) Newton’s third law

(d) Faraday’s law of electromagnetic induction

134. Wire loop is rotated in a magnetic field.

The frequency of change of direction of the induced emf

is

(a) once per revolution

(b) twice per revolution

(c) four times per revolution

(d) six times per revolution

135. Which of the following is the fundamental significance of

the Faraday’s discovery?

(a) A changing magnetic field can exert a force on the

stationary charge

(b) A changing magnetic field can exert a force on the

neutral particle

(c) A constant magnetic field can exert a force on the

stationary charge

51




(d) A constant magnetic field can exert a force on the

neutral particle

136. The polarity of induced emf is such that it tends to

produce a current which opposes the change in magnetic

flux that produced it, is statement of

(a) Faraday’s

(b) Lenz’s law

(c) Fleming’s right hand rule

(d) Fleming’s left hand rule

137. What will happen, if an open circuit is used in place of

the closed loop (in figure below CD is open circuit)?

(a) emf is induced across the open ends with C positive

(b) emf is not induced across the open ends of the circuit

(c) emf is induced across ends with C negative

(d) emf is induced with both C, D positive and mid-point

negative

138. Suppose that the induced current was in the direction

opposite to the one depicted in the given figure. In this

case, the ……….. pole due to the induced current will face

the approaching ………. pole of the magnet.

(a) North, North (b) South, South

(c) North, South (d) South, North

139. In the given situation, the bar magnet experience a ………

force due to the ……… in coil.

(a) an attractive, air

(b) an attractive, induced current

(c) repulsive, induced current

(d) attractive, vacuum

140. A closed loop moves normal to the constant electric field

between the plates of a large capacitor. Is the current

induced in the loop when it is wholly inside the region

between the capacitor plates?

(a) Yes (b) No

52




(c) May be possible (d) May not be possible

141. The north pole of a magnet is falling on a metallic ring as

shown in the figure. The direction of induced current, if

looked from upsite in the ring will be

(a) clockwise or anti-clockwise depending on metal of

the ring

(b) no induced current

(c) anti-clockwise

(d) clockwise

142. According to Lenz’s law of electromagnetic induction,

(a) the induced emf is not in the direction opposing the

change in magnetic flux

(b) the relative motion between the coil and magnet

produces change in magnetic flux

(c) only the magnet should be moved towards coil

(d) only the coil should be moved towards magnet

143. There is a uniform magnetic field directed perpendicular

and into the plane of the paper. An irregular shaped

conducting loop is slowly changing into a circular loop in

the plane of the paper. Then

(a) current is induced in the loop in the anti-clockwise

direction

(b) current is induced in the loop in the clockwise

direction

(c) AC is induced in the loop

(d) no current is induced in the loop

144. Eddy currents are generated in

(a) insulator (b) conductor


145. If the geometry of the coil does not vary with time, then

(a) Bd

dt

dI

dt

(b) dB∝dI


146. Two coils are placed close to each other. The mutual

inductance of the pair of coils depends upon

(a) the rates at which currents are changing in the two

coils

(b) relative position and orientation of the two coils

(c) the materials of the wires of the coils

(d) the currents in the two coils

147. Which of the following plays the role of inertia for

current following in coil?

(a) Resistance of coil (b) Self-inductance

(c) Both (a) and (b) (d) emf applied to coil

148. The self-induced emf a always opposes

(a) any change of current in the coil

(b) decrease of current in coil

(c) increase of current in coil


149. Which method is used to induce an emf or current in a

loop in AC generator?

(a) A change in the loop’s orientation

(b) A change in its effective area



150. The instantaneous value of the emf is …………

(given, = NBA)

(a) 0 sin t (b) sin t

(c) sin t (d) sin t

151. The maximum value of emf is, when θ is equal to (given,

=sin t)

(a) 900 (b) 2700

(c) 1800 (d) Both (a) and (b)

152. The change of flux is greatest at θ is equal to (given, B =

NBA cos t)

(a) 900, 2700 (b) 900, 450

(c) 600, 90 (d) 1800, 900

153. Consider coil and magnet.

Current is induced in coil when

I. coil and magnet both are at rest.

II. coil is at rest and magnet moves along x.

III. magnet is at rest and coil moves along x.

53




IV. Both coil and magnet move along y with same speed.

Correct statement are

(a) I and IV (b) I and II

(c) III and IV (d) II and III

154. Which of the following statements are false?

(refer figure below)

I. AC generator consists of a coil mounted on a rotor

shaft.

II. The axis of rotation of the coil is perpendicular to the

direction of the magnetic field.

III. The coil (called armature) is mechanically rotated in

the uniform magnetic field by come external means.

IV. The rotation of coil cuases the magnetic flux through

coil to change, so an emf is induced in the coil.

(a) I, II and III (b) I, II and IV

(c) II, III and IV (d) None of these

155. The man components of AC generator are

(a) armature (b) slip rings

(c) brushes (d) commutator

ANSWER KEY 1 c 2 c 3 b 4 d 5 b 6 d 7 c 8 c 9 b 10 c 11 d 12 d 13 d 14 c 15 c 16 d 17 b 18 c 19 c 20 b 21 c 22 d 23 c 24 c 25 b 26 a 27 d 28 d 29 a,b,c 30 a 31 c 32 d 33 a 34 c 35 d 36 d 37 c 38 a 39 c 40 b 41 d 42 b 43 a,b,c 44 a 45 b 46 c 47 a 48 d 49 d 50 b 51 a 52 a 53 c 54 d 55 c 56 a 57 b 58 c 59 b 60 c 61 c 62 a 63 b 64 a,d 65 a

b 66 a,b,c 67 a 68 b 69 d 70 d 71 c 72 d 73 c 74 d 75 d 76 d 77 d 78 b 79 a 80 b 81 b 82 b 83 c 84 a 85 b

86 d 87 c 88 a 89 c 90 d 91 d 92 a 93 b 94 a 95 d 96 b 97 a 98 b 99 c 100 b 101 d 102 b 103 b 104 a 105 a 106 c 107 b 108 b 109 c 110 a 111 a 112 a 113 c 114 d 115 c 116 c 117 d 118 b 119 a,c,d 120 b 121 c 122 d 123 d 124 a 125 a 126 d 127 d 128 c 129 c 130 a 131 c 132 d 133 d 134 b 135 a 136 b 137 a 138 d 139 c 140 b 141 c 142 b 143 a 144 b 145 c 146 b 147 b 148 d 149 c 150 a 151 d 152 a 153 d 154 d 155 a

b c

54




SOLUTION 1. (c) The reason for these experience is a discharge of electric

charges which were accumulated due to rubbing of

insulating surfaces.

2. (c) During its motion, body of carrier is charged due to

rubbing with dry air dust. If spark occurs near container,

then inflammable material may catch fire. So, metallic

ropes are suspended to that excess charge flows away

from carrier, to ground (for earthing).

3. (b) Each pith ball acquires same charge due to the

conduction (transfer) from plastic rod. So, they repel

each other.

4. (d)

5. (b)

6. (d) When a body is negatively charged, more electrons are

given to it, so its mass increases.

7. (c) Electric wiring of our house has three wire- live, neutral,

earth.

8. (c) Due to friction, if one body loses few electrons, other

gains them and so charges appearing on both are equal

and opposite.

9. (b) A negatively charged body acquires some electrons, so

its mass is more than its neutral mass.

10. (c) Induction requires shifting of free charge carrier which

are present only in conductors.

11. (d) When body is being charged body B by induction

process. Then charge acquired by A depends on

Nature of Material A

Distance between A and B

Nature of medium separating A and B.

Because q = I

t , I =

VR P

R A

12. (d) If a system contains two point charges q1 and q2 and total

charge of the system is obtained simply by adding

algebraically, i.e., charge add up like real numbers or

they are scalars like mass of the body.

13. (d) Charge and mass are two different physical quantities

and they following their own different law as

conservation of mass and conservation of charge.

14. (c) Charge of a body is always on integral multiple of charge

present on an electron.

q = ne here n = no. of electron, e = charge of electron.

15. (c) Initially, both the glass rod and silk cloth are electricity

neutral. Net charge is zero. Finally, the positive charge on

glass road is exactly equal to the negative charge on the

silk cloth. So, net charge is again zero.

16. (d)

17. (b) Charges on both spheres will be equal, each q/2. When

distance is made half of original, force becomes four

times of original because force varies inversely with

square of distance.

18. (c) F ∝ 1 22

q q

r

F = 1 22

Kq q

r here k =

0

1

4 E

19. (c) According to Coulomb's law, force between two point

charges, i.e. F ∝ 2

1

r.Therefore, the graph between F and r

will be as shown in Fig. (c).

20. (b) Force of attraction is caused by dissimilar charges. So

initially.

r

+q1 +q2

They are then touched

+q1 +q2

Net value of charge qnet = | q1 – q2 |

When separated, they share same type of charge.

21. (c) Field lines exist in 3-D space, we draw field lines on

paper but actual they are in space.

Field lines are in space around line joining q1 and q2.

22. (d) Two field lines can never cross each other because field

has a unique direction at each point.

23. (c) Areas of P-Q are equal but more lines pass through area

at P, So, field is stronger at P as compared to Q.

24. (c) S n S where, S is magnitude of the area element

and n is a unit vector in the direction outward 90° at

that point..

25. (b) d = E. S here, E = electric field S = area.

26. (a) If the centre of mass of the positive charge does not

coincide with that of the negative charge, the molecule

55




has intrinsic (or permanent) dipole moment. Such

molecules are called polar molecules.

27. (d)

28. (d)

29. (a, b, c)

Charges are additive, conservative and quantized in

nature.

30. (a) Considering potential to be zero at infinity. Work done

by an external force in bringing a unit positive charge

from infinity to a point without acceleration

= - Work done by electrostatic forces

= Electrostatic potential (V) at that point

31. (c) For a uniform electric field E say, along the X-axis, the

equipotential surfaces are places normal to the X-axis,

i.e., planes parallel to the YZ-plane.

32. (d) Potential difference between any two points on an

equipotential surface is zero, i.e., ΔV = 0

33. (a) Since, E = 0 inside the conductor and has no tangential

component on the surface, no work is done in moving a

small test charge within the conductor and on its surface.

34. (c) The free charge carriers move and charge distribution in

the conductor adjusts itself in such a way that the

electric field due to induced charges opposes the

external field within the conductor. This happens until in

the static situation, the two fields cancel each other and

the net electrostatic field in the conductor is zero.

35. (d) Oxygen and hydrogen and nitrogen are the examples of

non-polar molecules.

36. (d) HCl and H2O and NH3 are the examples of polar

molecules.

37. (c) The extent of polarization depends on the relative

strength of mutually opposite factors : the dipole

potential energy in the external field tending to align the

dipoles with the field and thermal energy tending to

disrupt the alignment. There may be, in addition, the

'induced dipole moment' effect as for non-polar

molecules, but generally the alignment effect is more

important for polar molecules.

38. (a) The symbol of a capacitor with fixed capacitance and

with variable capacitance is -||- and -||-. For fixed

capacitance, the capacitance value (c) remains same but

for variable capacitance C can be changed as per out

requirement within the given range.

39. (c) The maximum electric field that a dielectric medium can

withstand without break down (of its insulating

property) is called its dielectric strength; for air it is

about 3 × 106 Vm-1. For a separation between conductors

of the order of 1 cm or so, this field corresponds to a

potential difference of 3 × 104 V between the conductors.

Thus, for a capacitor to store a large amount of charge

without leaking, its capacitance should be high enough

so that the potential difference and hence the electric

field do not exceed the break down limits. Put differently,

there is a limit to the amount of charge can be stored on

a given capacitor without significant leaking.

40. (b) Van de Graaff generator is a machine that can build up

high voltage of the order of a few million volts. The

resulting large electric fields are used to accelerate

charged particle, (electron, proton ions) to high energies

needed for experiments to probe the small scale

structure of matter.

41. (d)

42. (b) 1 keV = 103 eV = 1.6 × 10-16 J, 1 MeV = 106 eV

= 1.6 × 10-13 J, 1 GeV = 109 eV = 1.6 × 10-10J

and 1 TeV = 1012 eV = 1.6 × 10-7 J

43. (a,b,c) The electric field intensity E is inversely proportional to

the separation between equipotential surfaces. So,

equipotential surfaces are closer in regions of large

electric fields.

Since, the electric field intensity is large near sharp edges

of charged conductor and near regions of large charge

densities.

Therefore, equipotential surfaces are closer at such

places.

44. (a) In some materials like wooden piece and other

insulators the electrons are bound, i.e., they will not

56




accelerate even, if an electric field is applied. In other

materials, notably metals, some of the electrons are

practically free to move within the bulk material. These

materials, generally called conductors, develop electric

currents in them when an electric field is applied.

45. (b) In electrolyte charge carriers are + ve and –ve ions.

46. (c) In that case, there will be a steady electric field in the

body of the conductor. This will result in a continuous

current rather than a current for a short period of time.

Mechanism, which maintain a steady electric field are

cells or batteries.

47. (a) Current density is the amount of charge per unit time

that flows through a unit area of a chosen cross section.

It's direction being that of the motion of the charges at

this point.

J (current density) = I

A

Direction of electric field is always opposite of the charge

flow.

So, J and E are in same direction and they are opposite to

direction of electron-s.

48. (d) When a steady current flows in a metallic conductor of

non-uniform cross section, the current flowing through

the conductor is constant. Current density, electric field

and drift speed are inversely proportional to the area of

cross section. They are not constant.

49. (d)

According to Ohm’s law, we get

Current I =V

R. So, slope AB

i.e., tan 400 =I

V⇒

0

1

tan 40

V

I ⇒ cot 400 =

V

I

. .,V

slope of AB i e RI

50. (b) If the charges in the conductor move without collision.

Their kinetic energy would also change. But total energy

will not change because of law of conservation of energy.

51. (a) Slope2> Slope1

2 1

1 1

R R

R1> R2

T1> T2

52. (a) Resistance in the branch ADC,

R1 = 3Ω+ 7Ω = 10Ω

Since, arms ADC (10Ω) and AC (10Ω) are in parallel their

equivalent resistance, R2 =10 10

10 10

Ω = 5Ω

Since, R2 is in series 9Ω in arm AB, equivalent resistance,

R3 =5Ω +9Ω = 14Ω.

As R3 is in parallel with 5Ω in arm BC, equivalent

resistance between B and C,

i.e., RBC =14 5 70

14 5 19

Ω

53. (c) R =2V

R=

2230

100= 529Ω

When the voltage drops to 115 V, heat and light energy

produced by the bulb in 20 min is given by

W =

22 115

529

Vt

R × 20 × 60 = 30000 J

54. (d) To get maximum current from a combination of cell. Cell

be grouped so that we can get maximum current and

minimum resistance. if we grouped them in series then

resistance will be high if we grouped them in parallel

then current will not be maximum.

55. (c) In accordance with Kirchoff's second law (Kirchoff's

voltage law), the algebraic sum of all the potential

difference in a closed electric circuit or closed loop that

contains one or more calls and resistance is always equal

to zero.

56. (a)

57. (b) With the help of wheat stone bridge we can determine

the unknown resistance.

58. (c) the potentiometer has the advantage that it draws no

current from the voltage source being measured. As such

is unaffected by the internal resistance of the source.

59. (b) The working of potentiometer is based on the fact that

the fall of potential across any portion of the wire is

directly proportional to the length of that portion

provided the wire is of uniform area of cross-section and

a constant current is flowing through it.

To shift the balance point on higher length, the potential

gradient of the wire to be decreased. The same can be

obtained by decreasing the current of the main circuit,

which is possible by increasing the resistance in series of

potentiometer wire.

57




58




60. (c) When we measure the emf of a cell by the potentiometer

then no current flows in the circuit in zero-deflection

condition i.e., cell is in open circuit. Thus, in this

condition the actual value of emf of a cell is found. In this

way, potentiometer is equivalent to an ideal voltmeter of

infinite resistance.

61. (c) In electrostatics all charges whether free or bound, are

considered to be at rest. Net charges in motion constitute

an electric current.

62. (a) As we have seen, conductivity arises from mobile charge

carriers. In metals, these mobile charge carriers are

electrons, with fixed positive ions in background, they

are negative ions and positive charged ions, in an

electrolyte.

63. (b) Resistivity of a material is given by = 2

1 m

ne

thus depends inversely both on the number n of free

electrons per unit volume and on the average time

between collisions. For insulators and semiconductors, n

increases with temperature. This increase more than

compensates any decrease in , so that for such

materials, decreases with temperature.

64. (a, d) (a) Low temperature resistance is negligible.

(d) Because for diode V – I curve is not linear.

V

I

65.(a, b) The resistivity of a metallic conductor is given by

e = 2

m

ne

Where , n is number of charge per unit volume which can

change with temperature T and is time interval

between two successive collision which decreases with

the increase of temperature.

66. (a, b, c)

Resistance, R =l

A

i.e., R ∝∝ T

i.e., R ∝ l

R ∝l

A

67. (a) The relationship between current and drift speed is

given by I = ne Avd

Here, I is the current and vd is the drift velocity.

So, I ∝ vd

68. (b) For proton, v B and for electron v || B. So, force on

proton = q (v × B) = Bqv whereas, force on electron = 0.

69. (d) The Oersterd found that the alignment of the magnetic

needle is tangential to an imaginary circle which has the

straight current-carrying wire, as its centre has its plane

perpendicular to the wire as shown in figure.

70. (d)

If an electron is travelling horizontally towards East and

magnetic field in vertically downward, then according to

left hand rule. So, force on electron is towards North.

71. (c) When a charged particle moves in the region of magnetic

field, then force is perpendicular to the velocity and it

produces a change of direction.

72. (d) When a particle moves perpendicular to the magnetic

field. It has a tendency to perform circular motion in a

plane perpendicular to the magnetic field. When this is

coupled with the velocity parallel to the field, then

resulting trajectory will be a helix along the magnetic

field line as shown in figure.

73. (c) The cyclotron is a machine to accelerate charged

particles or ions to high energies. The cyclotron used

both electric and magnetic fields in combination to

increase the energy of charged particles.

59




74. (d) For parallel M is stable and for anti-parallel is unstable.

75. (d) Each segment experience a force, so it tends to assume a

circular shape.

76. (d) A moving coil galvanometer is a sensitive instrument

which is used to measure a deflection when a current

flows through its coil.

77. (d) Uniform field is made radial by cutting pose pieces

radial.

78. (b) The deflection in a moving coil galvanometer.

= NAB

k. I or ∝ N, where N is number of turns in a coil,

B is magnetic field, A is area of cross-section.

79. (a)

80. (b) Because due to eddy current, losses are accused.

81. (b) According to ammeter circuit, we get

(I - Ig)S = IgG

where, G is resistance of galvanometer.

82. (b) To convert a galvanometer into ammeter, a low

resistance is connected in parallel with the coil of

galvanometer.

83. (c) To convert a galvanometer into voltmeter, a high

resistance in series is to be connected with

galvanometer.

84. (a) A. Since, E = 0 and B ≠ 0 so path will be straight line. If

velocity is parallel to B, or path will be circular if v B,

or path will be helical (with uniform pitch) if v is at same

other angle to B.

Hence, A → 1, 3

B. Since, E ≠ 0 and B = 0. So, path will be straight line

parallel to E or parabola otherwise.

Hence, B → 1, 2

C. E ≠ 0, B ≠ 0, E || B

Helical path with non-uniform pitch.

Hence, C → 4

D. Straight line path if v × B = E

Hence, D → 1

85. (b) The tip of a bar magnet which points to the geographic

North is called North-pole.

86. (d) The pattern of iron fillings suggests that the magnet has

two poles similar to the positive and negative charge of

an electric dipole.

87. (c) The pattern of iron filling permits us to plot the magnetic

field lines.

88. (a) No, the magnetic force is always normal to B (remember

magnetic force = qv × B). It is misleading to call magnetic

field lines as lines of force.

60




89. (c) Gauss’s law for magnetism is the net magnetic flux

through any closed surface is zero.

90. (d)

(a) Wrong Magnetic field lines can never emanate from a

point, as shown in figure over any closed surface, the net

flux of B must always be zero, i.e., pictorially as many

field lines should seem to enter the surface, as the

number of lines leaving it. The field lines shown, in fact,

represent electric field of a long positively charged wire.

The correct magnetic field lines are circling the straight

conductor.

(b)Wrong Magnetic field time as (like electric field lines)

can never cross each other, because otherwise the

direction of field at the point of intersection is

ambiguous. There is further error in the figure

magnetostatic field lines can never from closed loops

around empty space.

A closed loop of static magnetic field line must enclose a

region across which a current is passing. By contrast,

electrostatic field lines can never form closed loops,

neither in empty space nor when the loop encloses

chargers.

(c)Right Magnetic lines are completely confined within a

toroid. Nothing wrong here in field lines forming closed

loops, since each loop encloses a region across which a

current passes. Note, for clarity of figure only a few field

lines within the toroid have been shown. Actually, the

entire region enclosed by windings contains magnets

field.

(d)Wrong Field lines due to a solenoid at its ends and

outside cannot be so completely straight and confined;

such a thing violates Ampere’s law. The lines should

curve out at both ends and meet eventually to form

closed loops.

91. (d) The pole near the geographic North-pole of the earth is

called the North magnetic pole. Likewise, the pole near

the geographic South-pole is called the South magnetic

pole.

92. (a)

93. (b)

94. (a) Dip is the angle that the total magnetic BE of the earth

makes with the surface of the earth.

95. (d) Angle of dip, tan = E E

E E

Z H

H H = 1

∴ = 450

96. (b)

97. (a) Electrons in an atom orbiting around nucleus posses

orbital angular momentum. These orbiting electrons are

equivalent to current-carrying loop and thus posses

orbital magnetic moment. Diamagnetic substances are

the ones in which resultant magnetic moment in an atom

is zero.

98. (b) The most exotic diamagnetic materials are

superconductors (meissner effect).

99. (c) Electrons in an atom orbiting around nucleus posses

orbital angular momentum. These orbiting electrons are

equivalent to current-carrying loop and thus possess

orbital magnetic moment. Diamagnetic substances are

the ones in which resultant magnetic moment in an atom

is zero.

100. (b) the phenomenon of perfect diamagnetic in super-

conductors is called meissner effect.

101. (d) Superconducting magnets are used for running

magnetically levitated superfast trains.

102. (b)

103. (b) In some ferromagnetic materials the magnetization

persists. Such materials are called hard magnetic

materials or hard ferromagnets. Alnico, an alloy of iron,

aluminium, nickel, cobalt and copper, is one such

material.

104. (a) The magnetic susceptibility of a material is a measure of

the ease with which a specimen of that material can be

magnetized in a magnetizing field. For a diamagnetic

substance, magnetic susceptibility (xm) is independent of

temperature.

105. (a) Ferromagnetism decreases with rise in temperature. If

we heat a ferromagnetic substance, then at a definite

temperature, the ferromagnetic property of the

substance suddenly disappears and the substance

becomes paramagnetic. The temperature above which a

ferromagnetic substance becomes paramagnetic is called

the curie temperature of the substance.

106. (c) The correct measure of hardness of a material is its

coercivity; i.e., the field strength required to be applied in

opposite direction to reduce the residual magnetic of the

specimen to zero.

107. (b) liquid oxygen is paramagnetic because its atoms possess

permanent magnetic dipole moment.

108. (b) If a diamagnetic substance is brought near the North or

South-pole of a bar magnet, it is feebly repelled by both

the poles of magnet such as antimony, copper, gold and

silver.

109. (c) At Curie temperature, ferromagnetic becomes

paramagnetic.

110. (a) Substance which at room temperature retain their

ferromagnetic property for a long period of time are

called permanent magnets.

61




111. (a) The material should have a high permeability. Steel is

one favoured choice. It has a slightly smaller retentivity

then soft iron but this is outweighed by the much smaller

coercivity of soft iron. Other suitable materials for

permanent magnets are alnico, cobalt, steel.

112. (a)

113. (c) Core of electromagnets are made of ferromagnetic

materials which have high permeability and low

retentivity. Soft iron is a suitable material for

electromagnets.

114. (d) In certain applications, the material goes through an AC

cycle of magnetization for a long period. This is the case

in transformer cores and telephone diaphragms. The

hysteresis curve of such materials must be narrow. The

every dissipated and the heating will consequently be

small. The material must have a high resistivity to lower

eddy current losses.

115. (c) Permanent magnet should have large coercivity and

large retentivity. Therefore, the hysteresis cycles of the

material should be tall and wife.

116. (c) Electromagnets are made of soft iron because soft iron

has high permeability and low retentivity.

117. (d) Area of hystereis loop is proportional to net energy

absorbed per unit volume by the material, as it taken

over a complete cycle of magnetization.

For electromagnets and transformers energy loss should

be low.

i.e., this hysteresis curves.

Also B = 0, when H = 0 and |H| should be small when B =

0.

118. (b)

119. (a, c, d)

120. (b) If a wire loop is rotated in a magnetic field, the frequency

of change in the direction of the induced emf is twice per

revolution.

121. (c) The phenomenon in which electric current is generated

by varying magnetic fields is called electromagnetic

induction.

122. (d) The pioneering experiments of Faraday and Henry have

led directly to the development of modern day

generators and transformers.

123. (d) Electromagnetic induction is utilized in the functioning

of mouth piece of a telephone now-a-days.

124. (a) Faraday demonstrated that electric currents were

induced in closed coils when subjected to changing

magnetic fields.

125. (a) Moving magnet produce electric current in closed coil.

62




126. (d) The discovery and understanding of electromagnetic

induction are based on a long series of experiments

carried out by Faraday and Henry.

127. (d) When the north pole of a bar magnet is pushed towards

the coil, the pointer in the galvanometer deflects,

indicating the presence of electric current in the coil.

Current is induced in the coil.

128. (c) The galvanometer inductor deflects in the opposite

direction, when the magnet is pulled away from the coil.

129. (c) Current will be larger, when the magnet is pushed faster

towards the coil, also current is large when magnet is

pulled faster away but not it is in opposite direction.

130. (a) The galvanometer shows a momentary delfection when

the tapping key K is pressed.

131. (c) An emf is induced in a coil when magnetic flux through

the coil changes with time. This emf causes electric

current in closed coil.

132. (d) Emf, observations indicate that if circuit is open, then

opposite charges accumulate on opposite ends of

conductor.

When conductor PQ moves downward (in figure)

positive charge accumulates at Q and negative charges at

P. so, emf across PQ is induced. Flow of charge (current)

is induced in closed circuit only. Emf is induced in both

open and closed circuits.

133. (d) The magnitude of the induced emf in a circuit is equal to

the time rate of change of magnetic flux through the

circuit. Mathematically, the induced emf is given by

=- Bd

dt

The negative sign indicates the direction of and hence

the direction of current in a closed loop.

This is statement of Faraday’s law of electromagnetic

induction. Fleming’s rules, Newton’s third law deal with

forces and their directions.

134. (b)

135. (a) Changing magnetic flex cheats emf or potential

difference which creats electric field. Electric field of can

credit force of stationary change.

A changing magnetic field can exert a force on the

stationary charge.

136. (b) The statement of Lenz’s law is ‘the polarity of induced

emf is such that it tends of produce a current which

opposes the change in magnetic flux that produced it’.

Faraday’s law gives magnitude of induced emf. Fleming’s

rules give force on charged particle in field.

137. (a) An emf is induced across the open ends of the circuit.

The direction of the induced emf can be found using

Lenz's law. For conductor CD, C is at positive potential.

We shall use lenz's law to find polarity.

When S-role of magnet goes away from coil it induces N-

pole at C and S- pole at D so that movement of magnet is

prevents. Creation of N-pole at C induces anti clockwise

current at C or + ve polarity at C. It c and c are foiled lay

wire current will flow from C to D through the wire.

North polarity creates anti clock wise current.

138. (d) Suppose that the induced current was in the direction

opposite to the one depicted. In that case, the south-pole

due to the induced current will face the approaching

north-pole of the magnet.

139. (c) In this situation, the bar magnet experience a repulsive

force due to the induced current. Therefore, a person has

to do work in moving the magnet. Where does the

energy spend by the person go? This energy is dissipated

by Joule heating produced by the induced current.

140. (b) Case I Closed coil is moving inside constant electric field.

Case II Closed coil is fully inside constant electric field.

No current is induced in either case. Current cannot be

induced by changing the electric flux.

141. (c) By Lenz’ law the direction of induced current in the ring

is such as to oppose the falling of N-pole of the magnet.

So, the direction of induced current will be anti-

clockwise, because the induced current makes the ring a

magnetic dipole, with its N-pole upward which opposes

(repel) the N-pole of falling magnet. Hence, the direction

of the current in the ring will be anti-clockwise

63




142. (b) According to Lenz’s law of electromagnetic induction, the

relative motion between the coil and magnet produces

change in magnetic flux.

143. (a) As the shape of loop is changing and hence, the flux

linked with the loop changes. There will and induced emf

and hence induced current in the coil. As circle has

maximum area, for given perimeter.

So, magnetic flux through the coil is increasing. Induced

emf opposes it by giving induced current in anti-

clockwise direction.

144. (b) Conductor.

145. (c) For a closely wound coil of N turns the magnetic flux

linked with all turns is same. When the flux B through

the coil changes, each turn contributes to the induced

emf.

146. (b) Mutual inductance of the pair of coils depends on

distance between two coils and geometry of two coils.

147. (b) Self inductance is that phenomenon in which a change in

electric current in a coil produces an induced emf in the

coil itself.

148. (d) The self-induced emf always opposes any change

(increase or decrease) of current in coil.

149. (c) One method to induce an emf or current in a loop is

through a change in the loop’s orientation or a change in

its effective area.

As the coil rotates in a magnetic field B, the effective area

of the loop (the face perpendicular to the field) is A cos θ,

where, θ is the angle between A and B.

This method of producing a flux change is the principle

of operation of a simple AC generator. An AC generator

converts mechanical energy into electrical energy.

150. (a) From Faraday’s law, the induced emf for the rotating coil

of N turns is them,

= N Bd

dt

= - NBA

d

dt(cos t)

Thus, the instantaneous value of the emf is

= NBA sin t

Where, NBA is the maximum value of the emf, which

occurs when sin t = + 1. If we denote NBA as 0, then

= 0 sin t

151. (d) E = E0 Sin wt

Emax when Sin = max

So = 90°, 270°

152. (a) Bd

dt

= - NBA sin t, change of flux is greatest for t = θ

= 900, 2700, θ = 900, 2700.

153. (d) Relative motion between the magnet and the coil that is

responsible for induction in the coil.

154. (d) An AC generator cosists of a coil mounted on a rotor

shaft. The axis of rotation of the coil is perpendicular to

the direction of the magnetic field. The coil (called

armature) is mechanically rotated in the uniform

magnetic field by some external means.

The rotation of the coil causes the magnetic flux through

it to change, so an emf is induced in the coil. The ends of

the coil are connected to an external circuit by means of

slip rings and brushes.

155.(a, b, c)

SSC CDS

BANKrAILWAY



Physics



1999 to till date

C L A S S E S

Chapter - 07

(AC Circuits)

1




AC CURRENT AND RLC Transient Currents

Such electric currents which vary for a small finite time, while growing from zero to maximum value or while decaying from

maximum value to zero value are called transient currents.

Amplitude

Alternating

Current can be represented in sine or cosine function.

I = Io sin t

Instantaneous

value of current

maximum value of current

angular frequency

time period

Frequency = no. of waves passing through a point in one second.

Frequency = 1

time period

And E.M.F. can be represent as

E = E0 sin wt

Where E = IR = V if (E = V) or I = E/R

Alternating current or voltage or e.m.f. can be of many forms. Some of them are shown in Figure.

O V O V O V t t t

Polarity is never marked in the symbol of A.C. source as it keeps on reversing itself.

Mean Value or Average Value of Alternating Current

The mean value or average value of a.c. over any half cycle is defined as that value of steady current which would send the same

amount of charge through a circuit in the time of half cycle (i.e. T/2) as is sent by the a.c. through the same circuit, in the same time.

Im = 0

2I

= 0.637 I0

Mean or average value of a.c. over positive half cycle is 0.637 times the peak value of a.c., i.e., 63.7% of the peak value.

2




3




Similarly, Em = 0

2E

= 0.637 E0 = 63.7% E0

Average value of alternating e.m.f. over the full cycle = zero.

Note that ordinary d.c. ammeter and d.c. voltmeter cannot measure alternating currents/voltages. When used in a.c. circuits,

they record zero reading because average value of alternating current/voltage over a full cycle is zero.

Root Mean Square Value of Alternating Current

The root mean square (r.m.s.) value of a.c. is defined as that value of steady current, which would generate the same amount of heat

in a given resistance in a given time, as is done by the a.c., when passed through the same resistance for the same time.

I = 0I

2 = 0.707 I0

The r.m.s. value or effective value or virtual value of a.c. is 0.707 times the peak value of a.c., i.e. 70.7% of the peak value of a.c.

Similarly, E = 0E

2

R.M.S. value of alternating e.m.f. is 0.707 times the peak value of alternating e.m.f.

Alternating currents/voltages are measured by a.c. ammeter/voltmeter respectively. These instruments are called hot wire

instruments and they measure only virtual values of alternating currents/voltages. The values of alternating voltages/currents

quoted anywhere are virtual values only.

RESISTOR INDUCTOR CAPACITOR

Symbol

Function To dissipate heat energy To store energy in magnetic field

form when electric current flows

through it.

To store charge

Resistance (R)

Hindrance in the path of charge

Inductance (L)

the property of an electric conductor

or circuit that causes an

electromotive force to be generated

by a change in the current flowing.

Capacitor (C)

Capacity to store charge

Unit Ohm () Henry (H) Farad (F)

RAS

Resistor add in series

LAS

Inductor add in series

CAP

Capacitor add in Parallel

Series

Combination

RS = 1 + 2 = 3

LS = 1 + 2

= 3 1 1 11

2 2sC

Parallel

combination

1 1 1 1

4 4 2PR

1 1 1 1

4 4 2

PL

2

2

CP = 2 + 2 = 4

4




5




A.C. Circuit Containing Resistance, Inductor and capacitor Only

Resistor Inductor Capacitor

Current and voltage are is same

phase

I

E

I = E

R

So value of current is somewhat

less than value of E.

R = E

I

I = Io sin t

E = o sin t

Current lags behind E by 90°

E

I

90°

E = eo sin t

I = Io sin (t – 90°) and

I = L

E

X = Voltage Resistance

Here XL = Inductive Reactance

It represents the effective resistance offered by Inductance

XL = L = 2L

E = eo sin t

I = Io sin (t + 90°) and

I = C

E

X

XC = Capacitive Resistance It represents the effective

resistance offered by Capacitance

XC =1/C =1/ 2C

I

E

I = Io sin t

E = Eo sin t

I

E

Io

Eo I = Io

sin t

E = Eo

sin t

Io Eo

Eo

Io

Current leads voltage by 90°

Pure inductance offers zero resistance to DC ?

The inductive reactance limits the current in a purely inductive circuit in the same way as resistance limits the current in a purely

resistive circuit. Clearly, the inductive circuit in the same way as resistance to the inductance (L) and also to the frequency () of

the alternative current.

In dc circuit, = 0. XL = 0

i.e. a pure inductance circuit offers zero resistance to dc. it means a pure inductor cannot reduce dc.

XL is measured in ohm.

The dimensions of inductive reactance are the same as those of resistance.

Capacitor blocks DC ?

6




The capacitive reactance limits the amplitude of current in a purely capacitive circuit in the same way as the resistance limits the

current in a purely resistive circuit. Clearly, capacitive reactance varies inversely as the frequency of a.c. and also inversely as the

capacitance of the condenser.

In a d.c. circuit, = 0, XC = i.e., a condenser will be block d.c.

Hence XC is measured in ohms, just like resistance R. The dimensions of capacitive reactance are the same as that of resistance.

It should be clearly understood that the physical processes involved in capacitive and resistive circuits are quite different. In a

resistive circuit, the resistance is due to the obstruction to the passage of electrons. But in a capacitive circuit, resistance to the flow

of current is offered by the charged capacitor.

A.C. Circuit Containing Resistance, Inductance and Capacitance in Series (RLC Circuit)

90°

90°

VL

I

VR

I

VC

I

R L C

VR VL VC

VR

C

Y'

O

B'

B

Y

X IO A 90°

K

90° OE

VC

VL

(i) The maximum voltage across R is R 0V I R

RV is in phase with current

(ii) The maximum voltage across L is L 0V I XL

As voltage across the inductor leads the current by 90°.

(iii) The maximum voltage across C is C 0V I XC

As voltage across the capacitor lags behind the alternating current by 90°.

As the voltage across L and C have a phase difference of 180°, the net reactive voltage is L CV V , assuming that L CV V .

OK = 2 2OA OB'

7




E0 = 2 2 22

R L C 0 0 L 0 CV V V I R I X I X

E0 = 22

0 L CI R X X

The total effective resistance of RLC circuit is called Impedance of the circuit. It is represented by Z.

Z = 220

L C

0

ER X X

I

It is clear that in an a.c. circuit containing R,L,C, the voltage leads the current by a phase angle , where

tan = L C 0 L 0 C

R 0

AK OB' V V I X I X

OA OA V I R

tan = L CX X

R

The alternating e.m.f. in the RLC circuit would be represented by

E = E0 sin ( t + )

Cases:

(i) When XL> XC, tan is positive. Therefore, is positive. Hence voltage leads the current by a phase angle . The a.c. circuit is

inductance dominated circuit.

(ii) When XL< XC, tan is negative. Therefore, is negative. Hence voltage lags behind the current by a phase angle . The a.c. circuit

is capacitance dominated circuit.

Impedance Triangle

The total effective resistance offered by the RLC circuit is called Impedance. It is represented by Z.

From the three phasors, R OV I R ;

L O LV I X and C O CV I X , we obtain, what is known as Impedance Triangle.

The impedance (Z) of the a.c. circuit Z = 22

L CR X X . AOK = is the phase angle by which voltage leads the current in the

circuit, where tan = L CX X

R

.

The reciprocal of reactance is called susceptance of the a.c. circuit

The reciprocal of impedance is called admittance of a.c. circuit.

Both, the susceptance and admittance are measured in mho, i.e., ohm–1 or Siemen.

A.C. Circuit containing Resistance and Inductance

Z = 2 2

LR X

tan = L O L

R O

V I X

V I R

tan = LX

R

A.C. Circuit containing Resistance and Capacitance

Let a source of alternating e.m.f. be connected to an ohmic resistance R and a condenser

of capacity C, in series.

Z = 2 2

CR X

8




VR

I

R C

VR VC

90°

VC

I

Note that in all a.c. circuits, the relation that holds is E

I

= Z, where

Z = R, in case of a.c. circuit containing R only,

Z = XL, in case of a.c. circuit containing L only,

Z = XC, in case of a.c. circuit containing C only,

Z = 2 2

LR X , in case of a.c. circuit containing R & L, in series

Z = 2 2

CR X , in case of a.c. circuit containing R & C, in series

Z = XL – XC, in case of a.c. circuit containing L & C, in series

Z = 22

L CR X X , in case of a.c. circuit containing R, L & C in series.

The phase relation between alternating voltage and current in any a.c. circuit is given by

tan = L CX X

R

Analogy between Mechanical and Electrical Quantities

S. No. Mechanical System Electrical System

1.

2.

Mass m

Force constant k

Inductance L

Reciprocal capacitance 1/C

9




3.

4.

5.

Displacement x

Velocity, = dx

dt

Mechanical energy, E = 2 21 1kx m

2 2

Charge q

Current, i = dq

dt

Electromagnetic energy, U = 2

2q 1LI

2C 2

Q Factor of Resonance Circuit or Sharpness of Resonance

The Q factor of series resonant circuit is defined as the ratio of the voltage developed across the inductance or capacitance at

resonance to the impressed voltage, which is the voltage applied across R.

Q =

voltage across L voltage across Cor

applied voltage voltage across R applied voltage voltage across R

Q = 1 L

R C

Q is just a number having no dimensions.

Higher the value of Q, the narrower and sharper is the resonance.

Power Factor of an A.C. Circuit

Power factor an a.c. circuit is defined as the ratio of true power to apparent power of the circuit.

P = E I cos

P is called true power and (E I) is called apparent power or virtual power.

Power factor =

true power P

apparent power E I

= cos

=

22

L C

R R

Z R X X

Power factor = cos = R Resis tance

Z Impedance

Power Factor is always positive, but less than one or at the most equal to one.

Average Power Associated with Resistance or Non-Inductive Circuit

Average power over a complete cycle of a.c. through the resistor is the product of virtual voltage and virtual current.

P = EI

Average Power Associated with An Inductor

Average power over a complete cycle of a.c. through an ideal inductor is zero.

Average Power Associated with A Capacitor

Average power supplied to an ideal capacitor by the source over a complete cycle of a.c. is also zero.

Average Power in RLC Circuit (or Inductive Circuit)

P = E I cos = E

E

Z

cos

Average power over a complete cycle in an inductive circuit is the product of virtual e.m.f., virtual current and cosine of the phase

angle between the voltage and current.

10




So,

(i) In RL circuit, Z = 2 2

LR X and cos =R

Z

(ii) In RC circuit, Z = 2 2

CR X and cos =R

Z

(iii) In LC circuit, Z = XL – XC and = 90°

(iv) In RLC circuit, Z = 22

L CR X X and cos =R

Z

In all a.c. circuits, I = E

Z

Resonance

It is a condition in which Natural frequency of the system = frequency of the signal applied on the system from outside

At resonance, the amplitude of the signal becomes very high.

Real life Examples

• When a loud humming noise is heard from a loudspeaker,

At this condition

The natural frequency of oscillation of membrane of loudspeaker = frequency of signal supplied as Input to it.

• Large Bridges sometimes collapse., Due to Resonance during Earthquake.

As natural frequency of oscillation of Bridge = frequency of signal due to Earthquake.

Condition for Electrical Resonance. An electrical signal has resonance.

When

XL = XC

11




Inductive Reactance = Capacitive Reactance

When

XL = Land XC = 1

C

So, L = 1

c

or 2 = 1

LC =

1

LC

2 = 1

LC

or

= frequency of oscillation

= 1

2 LC

• TV Antenna's (Receiver) receive signal only when frequency matches and this frequency matches at Resonance

At resonance, XL = XC and = 0°.

cos = cos 0° = 1

Therefore, maximum power is dissipated in a circuit at resonance.

Further, note that whatever the circuit, power dissipation is always through resistance R.

At resonance, L = 1

C Z = R

i.e., at resonance, series LCR circuit is equivalent to a purely resistive circuit. Hence current and voltage are in phase.

Wattless Current or Idle Current

The current which consumes no power for its maintenance in the circuit is called wattless current or Idle current.

Advantages and Drawbacks of A.C. Over D.C.

(a) Advantages of a.c. over d.c. are:

(i) Generation, transmission and distribution of a.c. is much more economical than d.c.

(ii) The a.c. voltages can be easily varied using transformers.

(iii) The a.c. can be easily converted into d.c.

(iv) The magnitude of a.c. can be reduced using a choke coil, without involving loss of energy.

12




(v) A.C. travels on the surface of the conductor. Therefore, for long distance transmission of a.c., we often save costly conducting

materials using inner core of cheaper material. For example, ACSR (i.e., aluminium conductor steel reinforced) is widely used for

electric supply lines.

(vi) A.C. machines are often small sized, easy to use and have longer life.

(b) Drawbacks of a.c. are:

(i) It is more dangerous to work with a.c. at high voltages. The moment the insulation is faulty, one gets a severe shock.

(ii) The shock of a.c. is attractive, whereas that of d.c. is repulsive.

(iii) There are certain phenomena like electroplating, electro-refining, electrotyping etc. where a.c. cannot be used. In such case, d.c.

is needed.

(iv) The a.c. is transmitted more from the surface of conductor than from inside. Therefore, several fine insulated wire (and not a

single thick wire) are required for the transmission of a.c.

The a.c. can be converted into d.c. with the help of a rectifier, while d.c. can be converted into a.c. with the help of an inverter.

The a.c. can be stepped up or down with the help of a transformer.

13




Practice Questions 1. Which current do not change direction with time?

(a) DC current (b) AC current


2. The electric mains supply in our homes and offices is a

voltage that varies like a sine function with time. Such a

voltage is called ….. and the current driven by it in a

circuit is called the …. .

(a) DC voltage, AC current

(b) AC voltage, DC current

(c) AC voltage, DC voltage

(d) AC voltage, AC current

3. Potential difference between two points is called

(a) AC current (b) Voltage

(c) DC current (d) resistor

4. When the current changes continuously in magnitude

and periodically in direction, several times per second,

the current is known as the

(a) direct current

(b) induced current

(c) displacement current

(d) alternating current

5. Which of the following graphs shows, in a pure resistor,

the voltage and current are in phase?

6. The sum of instantaneous current values over one

complete cycle is

(a) negative (b) positive

(c) zero (d) Both (a) and (b)

7. When AC current passes through a resistor there is

dissipation of

(a) joule heating (b) electrical energy

(c) power (d) Both (a) and (b)

8. To express AC power in the same form as DC power, a

special value of current is defined and used, is called

(a) root mean square current (lrms)

(b) effective current

(c) induced current


9. The household line voltage of 220 V is a rms value with a

peak voltage of

(a) 310 V (b) 311 V

(c) 307 V (d) 302 V

10. In a purely resistive AC circuit, the current

(a) lags behind the emf in phase

(b) is in phase with the emf

(c) leads the emf in phase

(d) leads the emf in half the cycle behind it in the other

half

11. In order to show phase relationship between voltage and

current in AC circuit, we use the notion of

(a) phasors (b) sine function


12. What will be the phase angle between the voltage and

the current in resistive AC circuit?

(a) π/2 (b) π/4

(c) π/3 (d) Zero

13. Voltage and current in an AC circuit are given by

V = 5 sin (100 πt – π/6)

and I = 4 sin (100 πt + π/6)

(a) voltage leads the current by 300

(b) current leads the voltage by 300

(c) current leads the voltage by 600

(d) voltage leads the current by 600

14. Alternating current cannot be measured by DC ammeter,

because

(a) AC cannot pass through DC ammeter

(b) average value of current in complete cycle is zero

(c) AC is virtual

(d) AC changes its direction

15. The inductive reactance is directly proportional to the

(a) inductance (b) frequency of the currents

(c) Both (a) and (b) (d) amplitude of current

16. Which of the following figure shows that the current

phasor I is π/2 behind the voltage phasor V?

14





17. In a purely inductive AC circuit, the current reaches its

maximum value later than the voltage by

(a) one-fourth of a period

(b) half of a period

(c) three by fourth of a period

(d) complete a period

18. Which of the following graphs represents the correct

variation of inductive reactance XL with angular

19. In an AC circuit, the current lags behind the voltage by

π/2. The components of the circuit are

(a) R and L (b) L and C

(c) R and C (d) only R

20. Current I across the capacitor in a purely capacitive AC

circuit is

(a) im sin (t + π/4) (b) im sin (t + π/2)

(c) imcos(t + π/4) (d) im cos (t + π/2)

21. Which of the following is called capacitive reactance and

is denoted by XC?

(a) C (b) 1/C

(c) 2/C (d) C/R

22. The dimension of capacitive reactance is the same as that

of

(a) current (b) inductance reactance

(c) voltage (d) resistance

23. Capacitive reactance is inversely proportional to

(a) frequency (b) capacitance

(c) voltage (d) Both (a) and (b)

15




24. Which of the following diagram shows that the current

phasor I is π/2 ahead of the voltage phasor V as they

rotate counter-clockwise?

25. Same current is flowing in two alternating circuits.

The first circuit contains only inductance and the other

contains only a capacitance. If the frequency of the emf of

AC is increased, the effect on the value of the current will

be

(a) increase in the first circuit and decrease in the other

(b) increase in both the circuits

(c) decreases in both the circuits

(d) decrease in the first circuit and increase in the other

26. Resonant circuits are used in

(a) the tuning mechanism of a radio

(b) TV set



27. In tuning, we vary the capacitance of a capacitor in the

tuning circuit such that the resonant frequency of the

circuit becomes nearly equal to the frequency of the

radio signal received. When this happens, the ……A……

with the frequency of the signal of the particular radio

station in the circuit is maximum. Here, A refers to

(a) resonant frequency

(b) impedance

(c) amplitude of the current

(d) reactance

28. In an AC circuit, the average power dissipated depends

(a) on the voltage

(b) current

(c) cosine of the phase angle ϕ between them


29. Which of the following components of a L-C-R circuit,

with AC supply, do not dissipates energy?

(a) L, C (b) R, C

(c) L, R (d) L, C, R

30. A choke is preferred to a resistance for limiting current

in AC circuit, because

(a) choke is cheap

(b) there is no wastage of power

(c) choke is compact in size

(d) choke is a good absorber of heat

31. In an AC circuit the power factor

(a) is zero when the circuit contains an ideal resistance

only

(b) is unity when the circuit contains an ideal resistance

only

(c) is unity when the circuit contains a capacitance only

(d) is unity when the circuit contains an ideal inductance

only

32. Power factor is maximum in a L-C-R circuit when

(a) XL = XC (b) R = 0

(c) XL = 0 (d) XC = 0

33. Which of the following device, use the principle of

mutual induction?

(a) Dynamo

(b) Transformer

(c) Capacitor

(d) Voltmeter

34. The value of emf in the secondary coil depends on

(a) the number of turns

(b) material used

(c) voltage

(d) induced flux

35. If the transformer is assumed to be 100% efficient (on

energy losses), then

(a) the power input is equal to the power output

(b) the power input is less than the power output

(c) the power output is less than the power input


36. The large scale transmission and distribution of

electrical energy over long distances is done with the use

of

(a) dynamo

(b) transformers

(c) generator

(d) capacitor

16




37. If the secondary coil has less turns than the primary,

then it is called

(a) step-up-transformer

(b) step-down transformer

(c) ideal transformer


38. I. When a capacitor is connected to a voltage source in a

DC circuit, current will flow for the short time required

to charge the capacitor.

II. As charge accumulates on the capacitor plates, the voltage

across them increases, opposing the current.

III. A capacitor in a DC circuit will limit or oppose the

current as it charges.

IV. When the capacitor is fully charged, the current in the

circuit falls to zero.

Which of the above statements are incorrect? Choose the

correct option.

(a) I, II and III (b) II, III and IV

(c) I and IV (d) None of these

Matching Types

39. Match the following.

Column I Column II

A. VR 1. π/2 ahead of I

B. VC 2. Parallel to I

C. VL 3. π/2 behind I

A B C A B C

(a) 1 2 3 (b) 2 3 1

(c) 3 2 1 (d) 1 3 2

40. Match the following.

Column I Column II

A. VRm 1. imXL

B. VCm 2. imR

C. VLm 3. imXC

A B C A B C

(a) 1 2 3 (b) 3 2 1

(c) 1 3 2 (d) 2 3 1

41. As the frequency of an AC circuit increases, the current

first increases and then decreases. What combination of

circuit elements is most likely to comprise the circuit?

(a) Inductor and capacitor

(b) Resistor and inductor

(c) Resistor and capacitor

(d) Resistor, inductor and capacitor

ANSWER KEY 1 A 2 D 3 B 4 D 5 B 6 C 7 D 8 D 9 B 10 B 11 A 12 D 13 C 14 B 15 C 16 B 17 A 18 B 19 A 20 B 21 B 22 D 23 D 24 C 25 D 26 C 27 C 28 D 29 B 30 B 31 B 32 A 33 B 34 A 35 A 36 B 37 B 38 D 39 B 40 A 41 A,D

17




SOLUTION 1. (a)

2. (d)

3. (b)

4. (d)

5. (b)

6. (c)

7. (d) Joule heating is given by i2 R and depends on i2 (which is

always positive whether i is positive or negative) and not

on i. Thus, there is joule heating and dissipation of

electrical energy when an AC current passes through a

resistor.

8. (d)

9. (b) Vm = 2 V = (1.414) (220 V) = 311 V

10. (b)

11. (a)

12. (d)

13. (c) Phase difference Δϕ = ϕ2 – ϕ1 = π/6 – (- π/6) = π/3

14. (b)

15. (c) Inductive reactance XL = L = 2πfL

16. (b)

17. (a)

18. (b) Inductive reactance, XL = L ⇒ XL ∝

19. (a) When t = 0 due to large impedance of two inductor

current will flow only in 12Ω.

∴ Imin = 5/12.

After sometime current become is steady then R = 12Ω

will go out of circuit only r1 and r2 will be effective route

of current flow.

reff = 2Ω ⇒ Imax =5

2⇒ max

min

I

I= 6

20. (b) Current I across the capacitor is im sin (t + π/2).

21. (b) Xc = 1

WC

22. (d)

23. (d)

24. (c)

25. (d) For the first circuit, i = V V

Z L

So, increase in will cause a decrease in i.

For the second circuit, i = V

1/ C

Hence, increase in will cause an increase in i.

26. (c) Resonant circuit are used in Radio, Tv set.

27. (c) At resonance, current in the circuit is maximum.

28. (d) P = VI as

29. (b)

30. (b)

31. (b)

32. (a) In L-C-R circuit, in the condition of resonance XL = XCi.e.,

circuit behaves as resistance circuit. In resistive circuit

power factor is maximum.

33. (b)

34. (a)

35. (a)

36. (b)

37. (b)

38. (d) When a capacitor is connected to a voltage source in a DC

circuit, current will flow for the short time required to

charge the capacitor.

As charge accumulates on the capacitor plates, the

voltage across them increases, opposing the current.

That is, a capacitor in a DC circuit will limit or oppose the

current as it charges.

When the capacitor is fully charged, the current in the

circuit falls to zero.

39. (b)

40. (a)

41. (a, d) Reactance of an inductor of inductance L is, XL = 2vL

where, v is frequency of the AC circuit.

XC = Resistance of the capacitive circuit = 1

2 fC

On increasing frequency v, clearly XL increases and XC

decreases.

For and L-C-R circuit,

Z = impedance of the circuit

= 2

22 2L C

1R X X R 2 vL

2 vL

18




As frequency (v) increases, Z decreases and at certain

value of frequency known as resonant frequency (V0),

impedance Z is minimum that is Zmin = R current varies

inversely with impedance and at Zmin current is

maximum.

· 2020. 9. 10. · nd 3 1 Raja Sir Income Tax Inspector 14 Years’ teaching experience •CAT...

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