Mechanical and Elecrical System

CHAPTER 5 5.1 : ELECTRICAL DISTRIBUTION

1

Important terminology

Coulomb (C):

The basic unit used to measure electric charge.

Joule (J):

A joule is the work done by a constant 1-N force applied through a 1-m distance.

2

where N is the newton, m is the meter, kg is the kilogram, s is the

second, Pa is the pascal, and W is the watt.

Joule (J)

One joule can also be defined as:

The work required to move an electric charge of one

coulomb through an electrical potential difference of one

volt, or one '"coulomb volt" (CV). This relationship can be

used to define the volt.

The work required to produce one watt of power for one

second, or one "watt second" (Ws) (compare kilowatt

hour). This relationship can be used to define the watt.

3

Important terminology

Ampere (A): One ampere or amp is the current that flows when 1 Coulomb of charge passes each second (1 A = 1 C/s)

Volt (V): If a charge of 1 Coulomb may be moved between two points in space with expenditure of 1 Joule of work, 1 Volt is said to be a potential difference existing between these points (1 V = 1 J/C)

Watt (W): The rate at which work is done or energy expended. The watt is defined as 1 Joule per second (1 J/s).

4

Quantities and SI Units

SI UNITS used in electricity:

VOLTS (V): unit of potential difference, emf, or voltage

OHM (): unit of resistance

AMPS (AMPERES) (A): unit of current

COULOMBS (C): unit of charge (= the charge moved when one amp of current runs for one second).

WATTS (W): unit of power (power energy per unit time). In electrical circuits, one watt is produced when a current of one amp flows down a potential difference of one volt.

JOULE (J): unit of energy.

5

Quantities and SI Units

Six Basic SI unit used in electrical engineering field:

6

Electrical Simple Rules.

One watt is one joule per second.

One amp is one coulomb per second.

If you double the voltage the current will double.

If you halve the voltage the current will halve.

If you double the resistance the current will halve.

If you halve the resistance the current will double.

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8

Quantity

Basic unit

Symbol

length

Luminous

intensity

m

mass

kilogram

kg

time second

s

Electric current

ampere

A

Thermodynamic

temperature

Kelvin/ Celsius

K/C

Luminous

intensity

Candela

cd

Charge

9

-Electricity is any effect resulting from the presence and/or movement

of electrical charges. - Electrical charge is property of the atomic particles,

- measured in Coulomb (C)

Conducting wire

(atoms within)

Battery (source of electromotive force, emf)

+ +

+ Motion of charge

Electric Current

An electric current is the flow of electric charges.

Conventionally this is the flow of positive charge.

In a simple circuit such as that illustrated, the current in the wire is composed of electrons that flow from the negative pole of the battery (the cathode at the bottom of the battery) and return to the positive pole (the anode at the top of the battery, marked by a +).

10

Electric Current

Electric current is the time rate of change of

charge, measured in Amperes (A).

Mathematically, the relationship between current

i, charge q, and time t, is

Current is measured in amperes (A),

1 ampere = 1 coulomb/second

dt

dqi

11

Kirchhoffs Laws

The algebraic sum of all electric currents into and out of

any junction of an electric circuit is zero.

I = 0

I = I1 +I2 + + In

12

Electric Current

13

Two common types of current are;

Direct Current (dc) Alternating Current (ac),

A direct current (dc) is a current that remains constant with time.

The symbol I is used to represent such a constant current.

An alternating current (ac) is a current that varies sinusoidally with time.

A time-varying current is represented by the symbol i.

Voltage

Some work or energy transfer is required to move the electron in a conductor in a particular direction. This work is performed by an external electromotive force (emf), typically represented by the battery.

The emf is also known as voltage or potential difference.

Electric potential is the energy required to move a unit of electric charge to a particular place in a static electric field.

Voltage can be measured by a VOLTMETER.

The unit of measurement is the VOLT (V).

14

Energy and Power

Power is a certain amount of energy used in a certain length of time

P = energy/time = W/t

VIP

15

In direct current resistive circuits, electrical power is calculated using Joule's law:

where P is the electric power,

V the potential difference, and

I the electric current.

Energy and Power

P = power = voltage x current

P = E x I

Or,

P = (I x R) x I = I2R

Or,

P = E x (E/R) = E2/R

W = Energy = Power x time

= p x t

= I2 x R x t

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Energy and Power

Power can be delivered or absorbed as defined by the polarity

of the voltage and the direction of the current.

17

- +

V

Power delivered or supplied

by voltage source- +

V

Power delivered or supplied

by voltage source

I

+ -

V

Power absorbed by resistor

I

+ -

V

Power absorbed by resistor

Two polarity of the voltage and the direction of the current

Energy and Power

Ohms Law defines the relationship between

the three fundamental electrical quantities: current, voltage, and resistance .

When a voltage is applied to a circuit containing only resistive elements, current flows according to Ohm's Law, which is shown below;

18

Ohm's law states that the electrical current (I) flowing in a circuit is proportional to the voltage (V) and inversely proportional to the resistance (R).

If the voltage is increased, the current will increase provided the resistance of the circuit does not change.

Increasing the resistance of the circuit will lower the current flow if the voltage is not changed.

The formula current , I = V/R

Energy and Power

Ohms Law The formula can be reorganized so that the relationship can easily be

seen for all of the three variables.

V = I R or I = V/R or R = V/I

Where: I = Electrical Current (Amperes)

V = Voltage (Volt)

R = Resistance (Ohms)

When the current flows from a higher potential to a lower potential (v = iR). If current flows from a lower to high potential, then v = -iR.

19

Energy and Power

Resistor

A resistor is a two-terminal passive electronic component which implements electrical resistance as a circuit element.

When a voltage (V) is applied across the terminals of a resistor, a current (I) will flow through the resistor in direct proportion to that voltage.

It is usually made from metallic alloys and carbon compounds.

Resistance factor depend on cross-sectional area (A), length (l) and resistivity () of the material used as shown in the figure. Mathematically:

20

ARL

y,resistivit withmaterialA area, sectional-cross

l length,

Energy and Power

A material with low resistivity is a good conductor; examples are gold,

copper and aluminum.

An insulator like mica and paper has a very high resistivity.

21

Insulator3x10^12Teflon

Insulator10^12Glass

Insulator5x10^11Mica

Insulator10^10Paper

Semiconductor6.4x10^2Silicon

Semiconductor47x10^-2Germanium

Semiconductor4x10^-5Carbon

Semiconductor2.45x10^-8Gold

Conductor2.8x10^-8Aluminum

Conductor 1.72x10^-8Cooper

Conductor1.64 x 10^-8Silver

UsageResistivity (.m)Material


Insulator10^12Glass


Insulator10^10Paper









Table 2: Resistivity of common materials at 20o C

Energy and Power

Example; Calculate the electrical resistance per meter length at 20o C of a

cooper conductor of 2.5mm2 cross section area.

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Insulator10^12Glass


Insulator10^10Paper










Insulator10^12Glass


Insulator10^10Paper










Calculate the electrical resistance per meter length at

20o C of a gold conductor of 3.5mm2 cross section area.


Insulator10^12Glass


Insulator10^10Paper










Insulator10^12Glass


Insulator10^10Paper










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Energy and Power

Conductance -the ability for electricity to flow a certain path

Reciprocal of resistance is conductance and denoted by G

It measures of how well an element will conduct electric current.

The unit for conductance is Siemens (S), and previously called mho () - ohm spelled back-ward.

24

R

1G

Measurement Equipment

25

ammeter

voltmeter

ohmmeter

megger

multimeter

wattmeter Watt-hour

meter

Circuit Design (series)

A series circuit is a circuit which provides only one path for current to flow

between two points in a circuit so that the current is the same through

each series component. The total resistance of a series circuit is equal to

the sum of the resistances of each individual resistor.

NeqequivalentT RRRRRRR ...321

:units

26

+ V1 - + V2 -

Vs

R1 R2

+ V3 - + VN -

R3 RN

+ V -

Vs

Rseries

(a) (b)

+ V1 - + V2 -

Vs

R1 R2

+ V3 - + VN -

R3 RN

+ V1 - + V2 -

Vs

R1 R2

+ V3 - + VN -

R3 RN

+ V -

Vs

Rseries

+ V -

Vs

Rseries

(a) (b)

T

S

R

VI:Current

Circuit Design (parallel) and Current

Division Resistors in a parallel configuration are each subject to the same

potential difference (voltage), however the currents through them add.

The conductance of the resistors then add to determine the

conductance of the network.

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Vs

+ V -

Vs

Rparallel

(a) (b)

I

+V1-

R1+V2-

R2+VN-

RN

I

I1 I2 IN

Vs

+ V -

Vs

Rparallel

+ V -

Vs

Rparallel

(a) (b)

I

+V1-

R1+V1-

R1+V2-

R2+V2-

R2+V2-

R2+VN-

RN+VN-

RN+VN-

RN

I

I1 I2 IN

Circuit (parallel) and Current Division

The equivalent resistance (Req) of the network can be computed:

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N321 I...IIII

1

N321

T

N321equivalentT

R

1...

R

1

R

1

R

1R

R

1...

R

1

R

1

R

1

R

1

R

1

Current:

Exercise

Calculate: Total resistance RT

Total current , I

V1, V2 and V3

Solutions:

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15105

321 RRRRT

AV

R

VI

T

s 530

150

29

150V

R 1 = 5

R 2 = 10

R 3 = 15

3015105321 RRRRT

R

VI

N

N

R

VI VVxIxRV 255511

VxV

VxV

75155

50105

3

2

Circuit Design (combination)

A resistor network that is a combination of parallel and series

connections can be broken up into smaller parts that are either one or

the other,

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Assignment

One 18 watt lamp and two 60-watt light bulb are plugged into a 120V circuit. For either DC or AC, the two bulbs are connected each other in parallel and in series with the lamp in the same circuit. Calculate;

i. the current flow through each light

ii. the total resistance of the circuit,

iii. the total energy consumed in a year,

the cost of electrical energy for the year (assume 365 days per year) if the lights have been used for 8 hour per day (based on $0.286/kWh).

answer

i. the current flow through each light (0.15A,05A,0.5A)

ii. the total resistance of the circuit, (RT=920)

iii. the total energy consumed in a year, (402.96kW)

iv. the cost of electrical energy for the year (assume 365 days per year) if the lights have been used for 8 hour per day (based on $0.286/kWh). ($115.25)

Exercise 2

One 100W lamp and one 200W lamp are plugged into a

120V circuit. For either DC or AC. The two lamps are

connected in parallel. Calculate the current flow through

each lamp, the total resistance of the circuit, the total

energy consumed in a month (30 days x 12 hours per

day), and the cost of electrical energy for the year (based

on current TNB rates).

Exercise 2: Calculate the following

current flow through each lamp,

the total resistance of the circuit,

the total energy consumed in a month,

the cost of electrical energy for month

Mechanical and Elecrical System

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