M. Electricity 1. Electric Charge · 2020-04-08 · charge is zero and the body as a whole is...

M. Electricity

1. Electric Charge

• Electric charge is a fundamental attribute of particles.

• Electrostatics are defined as the interactions between electric charges that are at rest (or nearly

2005 Pearson Education South Asia Pte Ltd

so).

• The figure shows some experiments used to demonstrate electrostatics.

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1. Electric Charge


Fig. 21.1

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1. Electric Charge

• Electrostatics experiments show that there are exactly two kinds of electric charge, negative and positive.

• Two positive charges or two negative charges repel each other. A positive charge and a


repel each other. A positive charge and a negative charge attract each other.

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1. Electric Charge

• CAUTION– “Like charges” only mean that two charges have

the same algebraic sign (both positive or both negative).

– “Opposite charges” means that the electric


– “Opposite charges” means that the electric charges on both objects have different signs (one positive and the other negative).

• A technological application is in a laser printer; the figure shows a schematic diagram of such a printer in operation.

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2005 Pearson Education South Asia Pte Ltd Fig. 21.2

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1. Electric Charge

Electric Charge and the Structure of Matter• The atomic structure consists of three particles: the

negatively charged electron , the positively charged proton , and the uncharged neutron .


• Protons and neutrons make up the nucleus while electrons orbit it from a distance.

• The figure shows how changes in the atomic structure of lithium determines its net electric charge.

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1. Electric Charge

Electric Charge and the Structure of Matter


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1. Electric Charge

Electric Charge and the Structure of Matter• Atomic number is defined as the number of

protons or electrons in a neutral atom of an element.


• A positive ion is formed by removing one or more electrons from an atom; a negative ion is one that has gained one or more electrons. This process is called ionization .

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1. Electric Charge

Electric Charge and the Structure of Matter• When the total number of protons equals the total

number of electrons in a macroscopic body, its total charge is zero and the body as a whole is electrically neutral.


• When we speak of the charge of a body, we always mean its net charge.

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1. Electric Charge

Electric Charge and the Structure of Matter• The Principle of Conservation of Charge: The

algebraic sum of all the electric charges in any closed system is constant.


• In any charging process, charge is not created or destroyed but merely transferred from one body to another.

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1. Electric Charge

Electric Charge and the Structure of Matter• The magnitude of charge of the electron or

proton is a natural unit of charge.

• Every observable amount of electric charge on any


• Every observable amount of electric charge on any macroscopic body is always either zero or an integer multiple (positive or negative) of this basic unit, the electron charge – quantization of charge.

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2. Conductors, Insulators, and Induced Charges

• Conductors of electricity are materials that permit electric charge to move easily through them; Insulators do not.

• Most metals are good conductors while most non-


• Most metals are good conductors while most non-metals are insulators. Semiconductors are intermediate in their properties between good conductors and good insulators.

• The figure shows the use of copper as a good conductor, and glass and nylon as good insulators.

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2. Conductors, Insulators, and Induced Charges

• In a metallic conductor, the mobile charges are always negative electrons.

• In ionic solutions and ionized gases, both positive and negative charges are mobile.


and negative charges are mobile.

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• Coulomb’s Law states that:

The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance

3. Coulomb’s Law


proportional to the square of the distance between them.

• The directions of the forces the two charges exert on each other are always along the line joining them, as shown in the figure.

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3. Coulomb’s Law

2005 Pearson Education South Asia Pte LtdFig. 21.9

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3. Coulomb’s Law

• Coulomb’s Law is usually written as:


where

229

0

22120

/100.94

1

/10854.8

CmN

mNC

•×=∈

•×=∈ −

π

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3. Coulomb’s Law

• The most fundamental unit of charge is the magnitude of the charge of an electron or proton, denoted by e, where

e = 1.602176462(63) x 10-19 C


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Example 21.4 Vector addition of electric forces in a plane

In Fig. 21.12, two equal positive point charges q1

= q2 = 2.0 µC interact with a third point charge Q = 4.0 µC. Find the magnitude and direction


magnitude and direction of the total (net) force on Q.

Fig. 21.12

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21.4 Electric Field and Electric Forces

• The electric field at a point is defined as the electric force experienced by a test charge q0 at the point, divided by the charge q0.

• That is, the electric field at a certain point is equal to the electric force per unit charge experienced by

Er

0Fr


a charge at that point:

• SI unit is 1 newton per coulomb (1 N/C).

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• The figure shows how a charged body creates an electric field in the space around it.


Fig. 21.13

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• The electric field that a charged body produces exists at all points in the region around itself.

• The electric force is an “action-at-a-distance” force that acts across empty space without needing any


matter to transmit it through the intervening space.

• The electric force on a charged body is exerted by the electric field created by other charged bodies.

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• The figure shows the electric force exerted by an electric field on a point charge.

EqFrr

= (21.4


EqFrr

00 = (21.4)

Fig. 21.14

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• The electric field , or electric force per unit charge, is useful because it does not depend on the charge of the body on which the electric force is exerted.

• CAUTIONThe electric force experienced by a test charge q0

Er


The electric force experienced by a test charge q0can vary from point to point, so the electric field can also be different at different points. For this reason, Eq. (21.4) can be used only to find the electric force on a point charge, not on large bodies where the electric field may vary with different locations on the body.

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• The source point S is the location of the point charge that is producing the electric field we are investigating.

• The field point P is the location where we are determining the field.


• The unit vector denotes the direction along the line from source point to field point.

• The figure illustrates these terms.

r

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Fig. 21.15


Fig. 21.15

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• The magnitude and direction of the electric field can be given by the vector equation:

vector field

Er


• The vector field is thus the infinite set of vectors associated with every point in space in an electric field.

• The figure shows how a point charge produces an electric field at all points in space.

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Fig. 21.16

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• The field vectors point outwards from the charge for positive charges, and inward for negative charges.

• When the magnitude and direction of the field (and hence its vector components) are the same


everywhere throughout an electric field, the field is uniform.

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Example 21.7 Electron in a uniform field


Fig. 21.18

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Example 21.8 An electron trajectory

If we launch an electron into the electric field of Example 21.7 with an initial horizontal velocity v0 (Fig. 21.19), what is the equation of its trajectory?


equation of its trajectory?

Fig. 21.19

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21.5 Electric-Field Calculations

• In most realistic situations that involve electric fields and forces, charge is distributed over space.

• Thus, the principle of superposition of electric fields is used to find the total electric field at a


given point P, set up by the individual electric fields produced by each point charge in the field:

Lrrr

rr

+++== 3210

0 EEEqF

E

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Example 21.9 Field of an electric dipole

Fig. 21.20


Fig. 21.20

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Example 21.10 Field of a ring of charge

A ring-shaped conductor with a radius a carries a total charge Q uniformly distributed around it (Fig. 21.21). Find the electric field at a point P that lies


field at a point P that lies on the axis of the ring at a distance x from its center.

Fig. 21.21

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Example 21.11 Field of a line of charge

Positive electric charge Qis distributed uniformly along a line with length 2a, lying along the y-axis between y = -a and y = +a. (This might represent


+a. (This might represent one of the charged rods in Fig. 21.1.) Find the electric field at point P on the x-axis at a distance x from the origin.

Fig. 21.22

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Example 21.12 Field of a uniformly charged disk

Find the electric field caused by a disk of radius R with a uniform positive surface charge density (charge per unit area) σ, at a point along


area) σ, at a point along the axis of the disk a distance x from its center. Assume that x is positive. Fig. 21.23

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21.6 Electric Field Lines

• An electric field line is an imaginary line or curve drawn through a region of space so that its tangent at any point is in the direction of the electric-field vector at that point.


• This is illustrated by the following figure.

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Fig. 21.25

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• They show the direction of at each point, and their spacing indicates the corresponding magnitude.

• At any particular point, the electric field has a unique direction, so field lines never intersect.

Er


• The figure shows the field maps of the electric field lines for three different charge distributions.

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Fig. 21.26

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23.1 Electric Potential Energy

• Potential Energy U is the work done when a conservative force acts on a particle to move it from one point to another.


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Electric Potential Energy in a Uniform Field• The force on a test charge that moves from one

point to another is constant and independent of its location.

• The work done by this force is also independent of


• The work done by this force is also independent of the particle’s path, as shown in Fig. 23.1.

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Electric Potential Energy of Two Point Charges• The concept of electric potential energy can also be

applied to a point charge in any electric field caused by a static charge distribution.

• This is shown in Fig. 23.4 where displacement is


• This is shown in Fig. 23.4 where displacement is along a radial line in the electric field set up by a single, stationary charge.

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• The potential energy U when the test charge q0 is at any distance r from charge q is thus


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• Potential energy is always defined relative to some reference point where U = 0.

• It is a shared property of the two charges q and q0

because it is a consequence of the interactions(attractive or repulsive) between these two bodies.


• Fig. 23.6 is the graphical illustration of how U varies with these interactions.

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The total electric field at each point is the vector sum of the fields due to the individual charges, and the total work done on the charge q during


on the charge q0 during any displacement is the sum of the contributions from the individual charges.

Fig. 23.7

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• For every electric field due to a static charge distribution, the force exerted by that field is conservative.

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23.2 Electric Potential

• Generally, potential is potential energy per unit charge.

• SI units: volt (1 V).• Vab, the potential of a with respect to b, is the work

done by the electric force when a UNIT charge


done by the electric force when a UNIT charge moves from a to b. In other words, it is also the work that must be done against the electric force to move a UNIT charge slowly from b to a.

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23.2 Electric Potential


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25.2 Resistivity

• Resistivity ρ is described by Ohm’s law :


• SI units: ohm-meter , Ω·m.

• Conductivity – the reciprocal of resistivity, with units as (Ω·m)-1.

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25.2 Resistivity


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25.2 Resistivity

• Over a small temperature range (up to 100°C or so), the resistivity of a metal can be represented approximately by the equation


• Fig. 25.6 illustrates this relationship graphically.

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25.2 Resistivity


Fig. 25.6

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25.3 Resistance

• In a conductor with resistivity ρ, the direction of the current is always from the higher-potential end to the lower-potential end.


the lower-potential end.

Fig. 25.7

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25.3 Resistance

• The resistance R of a particular conductor is related to the resistivity ρ of its material by


• Generally,

• SI units: ohm , Ω1 Ω = 1 V/A

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25.3 Resistance

• A circuit device made to have a specific value of resistance between its ends is called a resistor .


Fig. 25.8

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25.3 Resistance


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25.3 Resistance


Fig. 25.9

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25.4 Electromotive Force and Circuits

• For a conductor to have a steady current, it must be part of a path that forms a closed loop or complete circuit .


circuit .• If the circuit is

incomplete, the current flows for only a very short time.

Fig. 25.11

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• Fig. 25.13 is a schematic diagram of an ideal source of emfthat maintains a potential difference between conductors a


between conductors a and b, called the terminals of the device.

Fig. 25.13

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• Fig. 25.14 is the schematic diagram of the same ideal source of emf in a complete circuit.


Fig. 25.14

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Example 25.5 A source on open circuit

Figure 25.16 shows a source (a battery) with an emf ξof 12 V and an internal resistance r of 2 Ω. (For comparison, the internal resistance of a commercial 12-V lead storage battery is only a few thousandths of an ohm.) The wires to the left of a and to the right of the ammeter A are not connected to anything.


the ammeter A are not connected to anything. Determine the readings of the idealized voltmeter V and the idealized ammeter A.

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Example 25.5 A source on open circuit


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Example 25.6 A source in a complete circuit

Using the battery in Conceptual Example 25.5, we add a 4-Ωresistor to form the complete circuit shown in Fig. 25.17. What are the


Fig. 25.17. What are the voltmeter and ammeter readings now?

Fig. 23.17

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Example 25.7 Using voltmeters and ammeters

The voltmeter and ammeter in Example 25.6 are moved to different positions in the circuit. What are the voltmeter and ammeter readings in the situations shown in a) Fig. 25.18a and b) Fig. 25.18b?


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Example 25.7 Using voltmeters and ammeters

2005 Pearson Education South Asia Pte LtdFig. 23.18

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Example 25.8 A source with a short circuit

Using the same battery as in the preceding three examples, we now replace the 4-Ω resistor with a zero-resistance conductor, as shown in


conductor, as shown in Fig. 25.19. What are the meter readings now?

Fig. 25.19

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• The net change in potential energy for a charge qmaking a round trip around a complete circuit must be zero.

• Hence the net change in potential around the circuit must also be zero.


• Fig. 25.20 is a graph showing how the potential varies as we go around the complete circuit of Fig. 25.17.

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Fig. 25.20

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25.5 Energy and Power in Electric Circuits

• In electric circuits we are most often interested in the rate at which energy is either delivered to or extracted from a circuit element.

• The time rate of energy transfer is power, denoted by P:


• Units: watt , W1 W = 1 J/s

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• The power input to the circuit element between a and b is P = (Va – Vb)I = VabI.


Fig. 25.21

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• If the circuit element is a resistor, the rate of transfer of electric potential energy into it is


• The internal energy of the material will increase and energy (heat) will be dissipated in the resistor at a rate I2R.

• Every resistor has a power rating, the maximum power the device can dissipate without becoming overheated and damaged.

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Power Output of a Source


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Power Input to a Source


Fig. 25.23

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26.1 Resistors in Series and Parallel


Fig. 26.1 Four different ways of connecting three resistors

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• When several resistors R1, R2, R3,…are connected in series, the equivalent resistance Req is the sum of the individual resistances.

• The same current flows through all the resistors in a series connection.


• In general:

• The equivalent resistance of any number of resistors in series equals the sum of their individual resistances and is greater than any individual resistance.

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• When several resistors are connected in parallel, the reciprocal of the equivalent resistance Req is the sum of the reciprocals of the individual resistances.

• All resistors in a parallel connection have the same potential difference between their terminals.

• In general:


• In general:

• The equivalent resistance is always less than any individual resistance.

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• For the special case of two resistors in parallel:

• Because , it follows that

21

21

RR

RRReq +

= (two resistors in parallel) (26.3)

2211 RIRIVab ==21 II = (two resistors in parallel) (26.4)


2

2

1

1

R

I

R

I = (two resistors in parallel) (26.4)

• Currents carried by two resistors in parallel are inversely proportional to their resistances. More current goes through the path of least resistance.

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Example 26.1 Equivalent resistance

Compute the equivalent resistance of the network in Fig. 26.3a, and find the current in each resistor. The source of emf has negligible internal resistance.


Fig. (26.3)

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Example 26.1 (SOLN)

• The 6-Ω and 3-Ω resistors are in parallel with an equivalent resistance of 2Ω. The remaining series combination of the 2-Ω resistor with the 4-Ω resistor is reduced to 6Ω.


4-Ω resistor is reduced to 6Ω.

• To find the current, reverse the steps used to reduce the network. (Fig. 26.3)

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Example 26.2 Series versus parallel combinations

Two identical light bulbs are connected to a source with ε=8V and negligible internal resistance. Each light bulb has a resistance R=2Ω. Find the currentthrough each bulb, the potential difference across each bulb and the power delivered to each bulb


each bulb and the power delivered to each bulb and to the entire network if the bulbs are connected a) in series, b) in parallel c) Suppose one of the bulbs burns out (filament breaks and no current can flow through it) What happens to the other bulb in the series case? Parallel case?

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Example 26.2 Series versus parallel combinations


Fig. 26.4 Circuit diagrams for two light bulbs (a) in series and (b) in parallel

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Example 26.2 (SOLN)

Identify and Set up

• Simple series and parallel connections are involved. Use Eq.(25.18) to find the power delivered to each resistor:

Execute

RVRIP /22 ==


Execute

• (a) Potential difference across each of the identical bulbs is the same:

•

VAIRVV bcab 4)2)(2( =Ω===

WPPtotal

WARIP

162

8)2()2( 22

===Ω==

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Example 26.2 (SOLN)

Execute

• (b) Similarly,

WV

RV

P

AV

R

VI

de

de

322

)8(

428

22=

Ω==

=Ω

==


• For the parallel case, the value of Req is less, thus is greater.

R 2Ω

eqtotal RVP /2=

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Example 26.2 (SOLN)

Execute

• (c) In the series case there will be no current at all in the circuit and neither bulbs will glow.

• In the parallel case the potential difference across either bulb remains equal to 8V even if


across either bulb remains equal to 8V even if one of the bulbs burns out.

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26.2 Kirchhoff’s Rules

• Kirchhoff’s junction rule is based on conservation of charge. This states that the algebraic sum of the currents into any junction must be zero.


• Kirchhoff’s loop rule is based on conservation of energy and the conservative nature of electrostatic fields. It states that the algebraic sum of potential differences around any loop must be zero

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• Kirchhoff’s loop rule is based on conservation of energy and the conservative nature of electrostatic fields. It states that the algebraic sum of potential differences around any loop must be zero.


• Careful use of consistent sign rules is essential in applying Kirchoff’s rules.

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• A junction in a circuit is a point where three or more conductors meet. Junctions are also called nodes or branch points.

• A loop is any closed conducting path.

Fig. 26.7 Kirchhoff’s


Fig. 26.7 Kirchhoff’s junction rule states that as much current flows into a junction as flows out of it

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Fig. 26.6 Two networks that cannot be reduced to simple series-parallel combinations of resistors

M. Electricity 1. Electric Charge · 2020-04-08 · charge is zero and the body as a whole is...

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