Module3 Electrical

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BASIC ELECTRICALENGINEEINGNotes

CURRICULUM DEVELOPMENT CENTRE,KALAMASSERY


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Basic Electrical Engineering

3.1.0 Basic Elec!ical Ci!c"i

A basic electric circuit contains a source of electrical energy, a load which changes

electrical energy into a useful form of energy and a switch to control the energy delivered to the

load.

3.1.1. S#"!ce$% Source is the device which furnishes the electrical energy used by the load. It

may consist of a simple dry cell, a storage battery, or a power supply.

L#a&$% The load is any device through which an electrical current flows and which

changes this electrical energy into a more useful form. Some common eamples of loads are a

bulb which changes electrical energy into light energy! an electric motor which changes

electrical energy into mechanical energy, spea"er in a radio which changes electrical energy into

sound.

S'ic($% It permits control of the electrical device, interrupts the current delivered to the

load.

Ci!c"i &ia)!a*$%

#e energised

$nergised


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The bulb does not glow when the switch is open. There is no complete path for current %I&

through the circuit. 'ut when the switch is closed, current flows in the direction of the arrows

from the (ve terminal to the )ve terminal of the battery, through the switch, lamp and bac" to the

)ve terminal of the battery. *ith the switch closed the path for current is complete. +urrent will

continue to flow until the switch is moved to the open position or the battery is completely

discharged.

3.1.+ Elec!ic ci!c"i

An electric circuit is a conducting path through which either an electric current flows or is

intended to flow. It can be divided into four categories.

. +losed circuit

-. pen circuit

/. Short circuit

0. $arth or lea"age circuit

1. Cl#se& Ci!c"i

It is the complete path or flow of electric current through the load. $g1 The glowing of a bulb

+. Oe- ci!c"iIf any one of the supply wires is disconnected or the fuse burns out, then current will not flow

through the circuit, it is called open circuit.

$g1) The circuit in which the switch is in off position.

3. S(#! ci!c"i

If the supply wires are connected directly by any means without any load, then the value of

current will be very high and this circuit is "nown as short circuit. The fuse may blown off

during short circuit.

. Ea!( #! lea/a)e ci!c"i

If any wire of the supply touches the body of an appliance, then it is "nown as earth or lea"age

circuit.

#epending upon the type of current flowing in the circuit it may be further classified as,

. #+ +ircuit

-. A+ +ircuit


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Se!ies ci!c"is

*hen the resistors are connected end to end, so that they form only one path for the flow of

current, then resistors are said to be connected in series and such circuits are "nown as series

circuits.

2et resistors 3, 3- and 3/ be connected in series and potential difference 4 volts applied

between A 5 # to cause flow of current of I Ampere through all the resistors

Now according to ohms law voltage drop across 3i.e. 47I3

Similarly 4-7I3-

4/7I3/

Total voltage 74(4-(4/

7I3(I3-(I3/

7I%3(3-(3/&

or 7 3(3-(3/

Thus when a number of resistors are connected in series, the e8uivalent resistance is given by

the arithmetic sum of their individual resistances.

i.e. 37 3(3-(3/

Series circuits are common in electrical e8uipment. The tube filaments in small radios are

usually in series. +urrent controlling devices are wired in series with the controlling e8uipment.

9uses are in series with the e8uipment they protect. A thermostat switch is in series with the

heating element in an electric iron. Automatic house heating e8uipment has a thermostat, electro

magnetic coils and safety cut out in series with a voltage source. 3heostats are placed in series in

large motors for motor current control. Ammeters are always connected in series with the circuit.


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Mai- c(a!ace!isics # a se!ies ci!c"i

. Same current flows through all parts of the circuit.

-. #ifferent resistors have their individual voltage drops.

/. Applied voltage is e8ual to the sum of voltage drops.

0. 4oltage drops are additive

:. 3esistors are additive.

6. Powers are additive.

Pa!allel ci!c"is

*hen a number of resistors are connected in such a way that one end of each of them is ;oined to

a common point and the other ends being ;oined to another common point. Then the resistors are

said to be connected in parallel and such circuits is "nown as parallel circuits. In these circuits

current is divided into as many paths as the number of resistances.

2et the resistances 3, 3- and 3/are connected in parallel and the potential difference of 4 volts

be applied across it. The potential difference across each resistor is same and e8ual to potential

difference applied to the circuit ie. 4

According to ohms law

+urrent in resistor 3is I 7

similarly I- 7

I/7

Adding the above e8uations,

I(I-(I/7


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7 4

I 7 I(I-(I/ 7 4

or 7

7 where 3 is the e8uivalent resistance of the whole circuit

7

Power P 7 4I watts

7 I3I

7 I- 3

7

Thus when a number of resistors are connected in parallel, the reciprocal of the e8uivalent

resistance is given by the arithmetic sum of the resistances parallel circuits are very common in

use. 4arious lamps and appliances in a house are connected in parallel, so that each one can be

operated individually.

C(a!ace!isics # a!allel ci!c"is

. Same voltage acts across each resistor

-. #ifferent resistors have their individual currents.

/. Total circuit current is e8ual to sum of individual currents

0. 'ranch currents are additive

:. Powers are additive

Diisi#- # c"!!e- i- a!allel ci!c"i


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Two resistances are ;oined in parallel across a voltage 4. The current in each branch, as given by

ohms law is,

I 7

I- 7

7


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i& $8uivalent resistance of the circuit, 373( 3-( 3/ ( 30

7 /(:(=(- 7 /= >

Potential #ifference applied across the circuit 47-= 4

ii& +urrent flowing through the circuit , I 7

7 70A

iii& 4oltage drop in / >resistance 47I3

70/7-4

4oltage drop in : >resistance 4-7I3-

70:7-=4

4oltage drop in = > resistance 4/7I3/

70=70=4

4oltage drop in - > resistance 407I3

70-70?4

P!#2le* +A circuit consists of four ==w lamps connected in parallel across a -/=4 supply. 9ind the

current which will flow through each lamp.

4I+R

4

== 7

3 7 :-@


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P!#2le* 3+alculate the effective resistance of the following combination of resistances and the voltage

drop across each resistance when a potential difference of 6=4 is applied. 9ind the circuit current

when :> resistor is removed.

3esistance between A and +7 7 ->

3esistance of branch A+# 7 ?(-7-=>

Now there are two parallel paths between points A and # of resistance -=> and :>.

3esistance between A and '70(?7->

Total circuit current 7 7 :A

+urrent through :> resistor 7 7 0A

+urrent in branch A+# 7 7 A

P# across /> and 6> resistors 7 - 7-4

P# across ?> resistor 7 ? 7?4

P# across :> resistor 7 :07-=4

P# across ?> resistor 7 ?: 70=4


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when :> is removed,

$8uivalent resistance 7

7 -(?(?7 -?>

+urrent in this case 7 7 -.0/A

P!#2le*

A resistance of -.- > is connected in series with a parallel circuit comprising - resistors -> and

?> respectively. +alculate the total power dissipated in the circuit when the applied voltage is -

volts.

P 7 4I

I 7

$8uivalent resistance of the parallel combination at -> 5 ?> 7 7 0.?>

$8uivalent resistance of the circuit 7 -.- ( 0.?


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7 B>

I 7 7 7 /A

Power P 7 -/ 7 6/*

P!#2le* 5

9our resistances are connected in series across a -:=4 supply. If the value of first three, resistors

are =>, -=> and /=> respectively, find the value of the fourth resistor when the power

consumed by the circuit is 6-:*.

P 7 6-:w

P 7 4I

I 7 7 7 -.: A

$8uivalent resistance 3 7 7 7 == >

$8uivalent resistance of the first / resistors 7 = ( -= ( /= 7 6= >

the fourth resistor 7 ==) 6= 7 0=>

P!#2le* 6Three resistors are connected in series across a -4 battery. The first resistance has a value of -

>, second has a voltage drop of 04 and third has a power dissipation of -*. +alculate the value

of the circuit current.


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P!#2le* 7

A circuit consists of three resistors />, 0> and 6C in parallel and a fourth resister 0> in series. A

battery of -4 is connected across the circuit. 9ind the total current in the circuit and the voltage

across the fourth resistor of 0>.


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3.1. POER

Power is defined as the rate of doing wor" or the amount of wor" done in unit time. Dnit of

power is EwattF or E;ouleGsecondF. ie. one watt of power consumed in one second. The output

power capacity of electrical e8uipments is epressed in watt. 9or commercial purposes the ma;orunits of power and energy are used.

Aa!e- #'e! VA #! KVA

The product of rms value of current and voltage is "nown as apparent power. The pf of the load

is not ta"en into account in this case. It is measured in volt)ampere%4A& or Hilo4olt)ampere

%H4A&. The losses of transformers and A+ generators are depending on 4oltage and current

which it supply. So the output capacity of transformers and generators are rated in H4A.

Kil# a

Hilo watt is the widely accepted commercial unit of power. The output capacity of motors,

heaters etc are epressed in Hilo *att .

I H* 7 === *

Me)a a

ega watt is normally used as the higher unit of electric power. The generating station capacity

is epressed in ega *att .

ega watt7 ===H* 7 =6watts

Kil# 'a%8#"! 9K(:

Hilo *att)


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3.1.5 E-e!); C#-s"*i#- a-& c#s

$lectric energy used by a consumer is measured in Hilo watt )hours. The charges are

made on the basis of number of "ilo watt) hours %units& used during a particular period.

Jenerally the period is ta"en as one month. Total cost the energy consumption in a given periodis given by the e8uation.

+ost + 7 cost per H*h number of units used

E)$% 91:A 6= * lamp is connected to -0=4 supply.


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7 /6=L- 7 3s. B-=G)

E)$% 93:A factory has a -/=4 supply from which the following loads are ta"en,

. 2ighting1) == nos. of :=*

:== nos. of :*

-. 9an1) := nos. of 0=*

:= nos. of 6=*

/.


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An alternator is a machine which converts mechanical energy into electrical energy. The output

voltage of an alternator is always A+. Alternators are widely used for bul" power generation. A+

single phase and three phase supply can be obtained from alternators.


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AC


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current is given as,

i 7 Im. Sin wt 7 Im. Sin -.ft

The following are some of the important and regularly used terms in alternating circuits.

ae#!*$ The shape of the instantaneous values of the voltage or current plotted on M ais

against the time on L ais. The waveform varies sinusoidally.

I-sa-a-e#"s al"e$ The value of any alternating 8uantity %voltage or current& at any particular

instant is called the instantaneous value and is designated by a small letter, EeF or EiF

e 7 $m. Sin -.ft

C;cle$ It signifies the repetition of a set of positive and negative instantaneous values of the

alternating 8uantity. ne cycle consist of two halves ie, (ve and ve half.

3.+.0 Ci!c"i Pa!a*ee!s

I-&"ca-ce 9L:$ It is the property of a coil to oppose the change in current in an alternating

circuit. It is denoted by the symbol E2F and its SI unit is EhenryF %


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is inversely proportional to the supply fre8uency EfF and the capacitance E+F. It is denoted by L +

and is measured in EohmF%&.

ie. L+7 , where EfF in hertO and E+F in farad.

I*e&a-ce$ It is the effective opposition to an alternating current in a circuit. All alternating

current circuits are made up of combinations of resistance 3, inductance 2 and capacitance +.

The circuit elements 3, 2 and + are called circuit parameters. The effect of inductive reactance

L2is to oppose the effect of capacitive reactance.


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4ector #iagram

9ig. shows a circuit containing a resistance 3 connected across a sinusoidal voltage 4. The vector

diagram for current, I and voltage 4 %both rms value& can be drawn as shown. 4oltage and

current in this circuit are in phase with each other.

In the circuit, I 7

P"!el; i-&"cie ci!c"i

+ircuit #iagram

4ector #iagram

9ig. shows a purely inductive circuit containing only one inductor, 2 connected to an a.c. source,

voltage with fre8uency, f

The inductive reactance L27 -.f2

The current, I 7 7

It is found that the phase difference between voltage and current is @==. If the phase difference is

measured from the voltage phasor, 7 )@==. ie. in a purely inductive circuit, current I is said to be


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lagging the voltage E4F by @==.

P"!el; caaciie ci!c"i

+ircuit #iagram

4ector #iagram

9ig. shows a purely capacitive circuit containing only one capacitor, + connected to an a.c.

source, voltage 4 with fre8uency EfF

The capacitive reactance, L+7

The current, I 7 7 -.f+.4

It is also found that the phase difference between voltage 4 and current I is @==. If the phase

difference is measured from the voltage phasor, 7 (@==1 ie., in a purely capacitive circuit

current leads the voltage by @==or voltage lags behind current by @==.

3.+.+ Se!ies R.L.C. ci!c"i


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A circuit containing 3, 2, and + in series is called a general series circuit. +urrent is used as

reference vector in the series circuit since it is common to all the elements in the circuit.

4oltage across 3, 43is in phase with I

4oltage across 2, 42is leading with I by @==

4oltage across +, 4+is lagging with I by @==

Total voltage 4 is the vector sum of 43, 42and 4+. Since 42and 4+are in opposite direction,

the resultant of 42and 4+is the arithmetical difference between them.

4oltage triangle

4- 7 43- ( %42 L+&

-

7 %I3&-( %IL2 IL+&-

7 I-Q3-( %L2 L+&-R


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ie. 4 7 I

If the total impedance in the circuit is given by EF, 4 7 I

I 7 I

or 7

9rom, this e8uation the impedance triangle for a series 32+ circuit can be drawn as shown

The power factor of the circuit, +oscan be found from the Impedance Triangle

+os7 7

P!#2le* 1

A coil has an inductance of -:m< and negligible resistance. +alculate its reactance at :=


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P!#2le* +

+alculate the reactance of a -9 capacitor at a fre8uency at :=


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7 60B

%b& +apacitive reactance, L+7

7

7

7 0==

%c& Impedance in the circuit, 7

7

7 /??.6

%d& +urrent in the circuit, I 7

7

7 =.60/A

%e& Power factor, +os 7

7

7 =.BB-

P!#2le* 5

A circuit consists of a resistor of :, a coil of resistance 0 and inductive reactance 6 and a

capacitor of reactance @ connected in series across a -0=4, :=


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7 @.0@

The circuit current, I 7

7

7 -:./A

P!#2le* 1

A resistance of -=, an inductance of =.-< and a capacitance of ==9 are connected in series

across --=4, :=


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%iii& Three phase ) four wire system

The most commonly used system for the ordinary domestic consumer is the -)wire system or the

/)phase, 0)phase system. In the case of /)phase, 0)wire system, domestic consumers are supplied

between one of phases and neutral conductor, thus giving -/=4, :=


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Mi-ia"!e Ci!c"i B!ea/e! 9MCB:

iniature circuit brea"er %+' is connected& is the circuit to prevent the accidents due to short

circuit or over current. Short circuit is prevented by tripping unit which consist of a relay.Thermal overload protector %bimetal& to prevent over current.

Now day miniature circuit brea"ers are used for domestic and commercial wiring instead of

fuses. +' can be put EnF or EffF by moving the handle EupF and EdownF. +' with different

current carrying capacity is available.

3.3.+. Ea!(i-)

$arthing means connections of the neutral point of a supply system or the non current carrying

parts of electrical apparatus, such as metallic frame, metallic sheathing of cables, motor frame,

stay wires etc. to the general mass of earth in such a manner that at all times an immediate

discharge at $arthing is done electric energy ta"es place without danger.

%& To ensure Oero potential an all non current carrying parts of an apparatus.

%-& To avoid the electric hoc" to the human beings.

%/& To protect e8uipments using lea"age circuit brea"er.

Li)(-i-) A!!ese!

A lightening arrester is a device used on electrical power system to protect the insulation on the

system from the damaging effect of lightening. etal oide varistors %4S& have been used

for power system protection. 2ightening arrester is also "nown as surge arrester. *hen a surge

occurs due to lightening the arrester provides a path to it to the earth through its ground terminal.

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Module3 Electrical