Electrical Circuits Course File

8/12/2019 Electrical Circuits Course File

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-----------------------------------------------------------------------------------Electrical Circuits

ELECTRICAL CIRCUITS

Objective:

The overall objective of teaching this semester course on Electrical Circuits is to

given the Under Graduate Engineer a through grounding of the fundamentals of electric

circuits for second year first semester EEE Students. At the end of the second year first

semester the student would develo an in deth !nowledge of circuit elements "active and

assive#$ their characteristics and their functioning when networ!ed .E%uied with this

!nowledge the student would be able to analy&e many engineering roblems by tracing

the various elements in the set rocesses in terms of the electrical e%uivalents.

The subject of Electrical Circuits would constitute a basic building bloc! for electrical

engineers $ in the understanding of electric ower and its steady state characteristics.

Such understanding would also hel the engineer to design his system after analy&ing the

circuit under all conditions.

Before commencement of the subject the student should have a knowledge of :

'ector calculus

Comle( arithmetic

'arious functions li!e trigonometric and e(onential etc.

)nowledge about solution of *ifferential e%uations in time domain and +alace

transform methods.

*ifferentiation and ,ntegration of different functions.

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UNIT IINTRODUCTION TO ELECTRICAL CIRCUITS

Objective:

The objective of this unit is to ma!e the students familiar with the basic fundamentals of

electrical circuits and introduce him1her in the following toics2

*ifferent circuit elements"$+ and C# and their characteristics.

Source Transformation of Electrical Circuit.

'oltage 3 Current relationshi for assive elements "for different inut signals-

s%uare$ ram$ saw tooth$ triangular#

Important points and definitions:

There are two tyes of networ! elements 0# Active elements 4# 5assive elements

,nter connection of two or more circuit elements is called a networ!

,f a networ! consists of a closed ath in which current can flow it is called a

circuit

Active elements are those which suly energy.

5assive elements are those which consume energy.

,n active elements there are two different tyes 0# 5ractical indeendent sources

4# *eendant sources.

There are three different assive elements.

o 0# esistors 4# ,nductor 6# Caacitor

Objective tpe !"estions:

0. Give different tyes of active elements.

4. 7ame different tyes of assive elements.

6. Give the difference between ideal voltage source and ractical voltage source. e8. Give the difference between ideal current source and ractical current source.

9. Give voltage current relationshi for esistor.

:. Give voltage current relationshi for ,nductor.

;. Give voltage current relationshi for Caacitor.

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4. /ind the e%uivalent resistance between the terminals A B in the following

networ!.

The students are further advised to solve different roblems in the Te(t oo!s mentioned.

#revio"s E%amination &"estions :

0. *etermine Currents and 'oltages of the resistances in the following networ!

using source transformation.

4. =rite the volt-amere relationshi of $ + and C elements.

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9

6

6 6

6

0

0

8


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6. E(lain the indeendent and deendent sources>

8. *escribe the source transformation techni%ue>

9. The current waveform for the ure inductance of 6m is shown in below

figure 0. *raw the voltage and ower wave forms.

:. *istinguish between ideal and ractical sources and draw their characteristics.

;. Calculate the value of D in the circuit shown in below figure 0$ if the ower

sulied by both the sources is e%ual.


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'oltage 3 Current relationshi for assive elements

Te%t boo's for Unit ( :

0. 7etwor! Theory by Sudha!ar B Schaum mohan

4. Engineering Circuit. Analysis by aith B )ymberly "/undamentals#

6. Electrical Technology "'ol-0# 3 .+. Theraja "Fagnetic C!ts.#

8. 7etwor! Theory 3 oga 7arasimham "Source transformation#

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0

64

6446

.

..... ++=

604604

4604

4

...

...

++

=

4

060660

++=

604604

6046

6

...

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++

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Fesh and 7odal analysis are two basic techni%ues used in finding solution of

electrical networ!s.

)'+ is used to form mesh e%uations in mesh analysis.

)C+ is used to form nodal e%uations in nodal analysis.

Essa Tpe !"estions and prob$ems:

0. E(lain about different Active and 5assive elements with their voltage current

relationshis.

4. State and e(lain )irchhoff laws.

6. State and e(lain star-delta Transformation

8. E(lain about 7odal Analysis9. E(lain about Fesh Analysis

#revio"s E%amination &"estions:

0. Use nodal analysis to find the ower dissiated in the : ohm resistor in the

following circuit.

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4. /ind the voltage to be alied across DA- in order to drive a current of 0@ A

into the circuit as shown in below figure 0 using star-delta transformation>

6. Jbtain the e(ressions for star-delta e%uivalence of resistive networ!>

8. Calculate the current in the 9K resistor using !irchoffs laws for the networ!

shown in below figure 4.

9.*etermine the current in the 9K resistor for the circuit shown in below figure 4.

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9. State and e(lain !irchoffs laws>

:. *etermine the resistance between the terminals DA- in the networ! shown in

below figure 0.

After completion of this unit the student should be able to know

)irchhoff laws

7etwor! reduction techni%ues

Series and 5arallel connection

Star-*elta Transformation.

7odal analysis

Fesh Analysis

Te%t )oo's for Unit + :0. 7etwor! Theory by Sudha!ar B Schaum mohan

4. Engg. C!t. Analysis by aith B )ymberly

6. Electrical Technology "'ol-0# 3 .+. Theraja

8. 7etwor! Theory 3 oga 7arasimham

9. Electrical Circuits 3 Schuam series

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A leading alternating %untity is one which reaches its ma(imum value earier as

comared to the other %uantity.

A lagging alternating %uantity is one which reaches its ma(imum value later than

the other %uantity.

The r.m.s value of an alternating current is given by that steady "dc# current which

when flowing through a given circuit for a given time roduces the same heat as

roduced by the alternating current . =hen flowing through the same circuit of

the same time.

Average value of an alternating current is e(ressed by that steady current which

transfers across any circuit the same charge as it transferred by that alternating

current during the same time.

The r.m.s. value of a eriodic wave of time eriod T is given by

410T

@

4

rms dtvT

0'

=

The average value of a eriodic wave of time eriod T is given by

=T14

@

dtvT14

0avgV "for symmetrical waveforms#

,f ac voltage is alied to an ure resistor voltage across it and current assing

through it are in hase with each other.

,f an ac voltage is alied to a ure inductor current assing through it lags by ?@ @

with resect to voltage across it .

,f an ac voltage is alied to a ure caacitor the current assing through it leads

the voltage across it by ?@@.

,f an ac voltage is alied to an -+ circuit$ current assing through the circuit

will lag the alied voltage by some angle greater than &ero and less than ?@@

deending on the values of and +.

,f an ac voltage is alied to an -C circuit$ current assing through the circuit

leads the alied voltage by some angle.

,n case of -+-C circuit current either lags or leads deending on the effect of

inductance and caacitance.

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,f inductive effect is more then current lags otherwise if caacitive effect is more

current leads.

Three tyes of owers are there in case of ac circuits. 0. Aarent ower 4. Active

ower 6. eactive ower.

The roduct of voltage and current in the circuit gives aarent ower "',#

The roduct of voltage and in hase comonent of current gives active ower

"', Cos #

The roduct of voltage and %uadrature comonent of current gives reactive ower

"', Sin #

Comle( ower is given by S L ',M

To reresent ac %uantities we use j notation.

S/ort Ans0er !"estions:

0. *efine FS value.

4. *efine average value.

6. Give the FS and average values$ form factor and ea! factor of sinusoidal ac

voltage$ half wave and full wave sinusoidal waves.

8. *efine ower factor.

9. =hat is comle( ower>

:. =hat is aarent ower>

;. =hat is reactive ower>

?. Give the difference between imedance and resistance.

0@. The ratio '$ , give in case of ac circuits.

00. =hat are ,nductive and Caacitive reactances>

04. *efine admittance.06. *efine suscetance.

Essa Tpe !"estions and prob$ems :

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0. An alternating current of fre%uency :@& has a ma(imum value of 04@A.

=rite down the e%uation for instantaneous value.

4. E(lain about hase and hase difference.

6. /ind FS and Average values of the following waveform.

8. /or the following wave find effective value.

9. A current of 9A flows through a non inductive resistance in series with

cho!ing coil when sulied at 49@'$ 9@&. ,f the voltage across the resistance

is 049' and across the coil 4@@'$ calculate a# imedance b# the ower

absorbed by the coil and the total ower.

:. ,n the following fig. ,f voltage meter reads :@'$ find reading of ammeter.

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#revio"s E%amination &"estions :

0. /ind form factor and ea! factor of a sinusoidal alternating voltage of

ma(imum value 'm.

4. A series +C circuit with L0@@$ + L @.9$ CL8@(0@-:/ has an alied

voltage of 0@@ @ with variable fre%uency. Calculate the resonance

fre%uency$ current at resonance voltage across +C. Also calculate the N-

factor$ uer and lower cutoff fre%uencies.

6. *etermine the branch and total active and reactive owers in the arallel

circuit shown.

8. E(lain the significance of j-oerator. =hat are the different forms of

e(ressing the sinusoidal %uantity in comle( form>

9. Comute the FS and average values of s%uare wave form shown in below

figure 4.

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:. *efine the FS value and obtain an e(ression for the FS value of

sinusoidal current>

;. *etermine the circuit current and .f for the following networ! shown in

figure 6.


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After completion of this unit the student should be able to know:

Concet of alternating voltages.

FS values$ Average values$ /orm factor$ 5ea! factor

Te%t )oo's for Unit + :

:. 7etwor! Theory by Sudha!ar B Schaum mohan

;. Engg. C!t. Analysis by aith B )ymberly


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+ocus diagram2 ,t is the curve in the comle( lane traced by a oint as one of the

arameter of the circuit is varied.

There are different tyes of locus diagrams2 0. ,medance locus diagram 4.

Admittance locus diagram 6. Current locus diagrams.

esonance2 the unity ower factor condition of comle( imedance circuit is

called resonance.

There are two tyes of resonance in electrical circuits2 0. Series resonance

4. 5arallel resonance

,n series resonance the imedance of the circuit is minimum and is e%ual to .

The current in the circuit is ma(imum under series resonance conditions.

The fre%uency of resonance is given by 2

+C4

0f@

=

and width2 and width of any system is the range of fre%uencies for which the

current or o1 voltage is ;@.;P of its value at resonant fre%uency.

and width of +C series circuit is given by

+4

.=

=

,t is also given by f43 f0=here f4L uer cutoff fre%uency

f0L lower cutoff fre%uency

04r fff =

the ratio of voltage develoed across + or C to the alied voltage is !nown as

N-factor.

'

Q,"or#

'

Q,N C+=

04

r

f-f

fN=


0. *efine N-factor.

4. *efine bandwidth.

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6. E(lain the rocedure to draw the locus diagram of -+ series circuit when +

is varying>

8. A series +C circuit has to be designed so that it has a band width of 64@ &

and inductance of the coil is @.4. ,t is has to resonate at 69@&$ determine

the resistance of coil and caacitance of condenser. ,f the alied voltage is

09@'$ determine the voltage across caacitor and coil>

9. *erive the e(ression for band width of +C series circuit>

:. A series circuit consisting of L 9@@K$ + L @.9 and C L 09 O/ is

connected to a variable fre%uency suly of 04@'. ,f the fre%uency is varied

through 8@ to


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Series and arallel resonance

+ocus diagrams for various series and arallel circuits.

Te%t )oo's for Unit + :


04. Engg. C!t. Analysis by aith B )ymberly

06. Electrical Technology "'ol-0# 3 .+. Theraja

08. 7etwor! Theory 3 oga 7arasimham

09. Electrical Circuits 3 Schuam series

UNIT41 2A,NETIC CIRCUITS

Objective :

The objective of this unit is to ma!e the students familiar with magnetic circuits

$/aradays laws and introduce him1her in the following toics 2

/aradays +a ws of Electro magnetic ,nduction

Self and Futual ,nductances

Fagnetic circuit analysis "series and arallel#

Important points and definitions :

Fagnetic circuit is defined as the ath which is followed by Fagnetic flu(.

The different terms we come across in magnetic circuits are 2 eluctance$ FF/$

5ermeance$ /lu( density$ Fagnetic field intensity$ Self inductance$ Futual

inductance$ dot convention$ coefficient of couling.

elation between magnetism and electricity "electromagnetic induction#.

/aradays laws of electromagnetic induction.

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/irst law states that whenever the magnetic flu( lin!ed with a circuit changes an

emf is always induced in it.

Second law states that the magnitude of induced emf is e%ual to the rate of change

of flu( lin!ages.

Objective tpe !"estions :

0. *efine dot convention.

4. *efine mutual inductance.

6. *efine Coefficient of couling.

8. Give the relationshi between FF/$ /lu( and eluctance.

Essa Tpe !"estions :

0. State and e(lain /aradays +aws

4. E(lain about dot convention.

6. *erive a relation for coefficient of couling in terms of self and mutual

inductances.#rob$ems:

0. A ring has a mean diameter of 40cm and cross sectional area of 0@cm4. The ring is

made u of semi circular sections of cast iron and cast steel with each joint having

a reluctance e%ual to an air ga of @.4mm. find the amere turns re%uired to

roduce a flu( of


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:@@O=b when an air ga of 0mm length is now cut in ring. Also determine the

flu( roduced if FF/ remains constant. Given relative ermeability of mild steel

is 04@@.

9. E(lain the imortance of dot convention in couled circuits.

:. A mild steel ring has a mean circumference of 0@@@ mm and a uniform area of

cross-section of :@@ mm4. Calculate the FF/ re%uired roducing a flu( of 9@@

n=b$ assuming ermeability of mild steel as 04@@. An air ga of 4 mm in length

is now cut in the ring. *etermine the flu( roduced$ if the FF/ remains

constant.

;. State and e(lain /aradays laws of electromagnetic induction.


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4. An iron ring has a mean length of 9@cm has an air ga of 0mm and a winding of

4@@ turns. ,f elative ermeability is 8@@ when a current of 0A flows in the

winding determine the flu( density. 7eglect lea!age and fringing.

6. A cast steel electromagnet has an air ga of length 4mm and an iron ath of length

6@cm /ind the FF/ needed to roduce a flu( density of @.


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Futual inductance roblems

Fagnetic circuits roblems

Te%t boo's for Unit ( :


4. Engg. C!t. Analysis by aith B )ymberly "/undamentals#

6. Electrical Technology "'ol-0# 3 .+. Theraja "Fagnetic C!ts.#

8. 7etwor! Theory 3 oga 7arasimham "Source transformation#

UNIT 1I NET5OR6 TO#OLO,7

Objective :

The objective of this unit is to ma!e the student familiar with grah theory$ various

networ! analysis techni%ues and duality of electrical networ!s. This unit introduces the

student with the following toics 2

,ntroduction to networ! toology a techni%ue used for analy&ing and solving large


+oo analysis and nodal analysis methods.

*uality and dual networ!s.

Important points and definitions:

7etwor! toology or grah theory deals with grah of networ! and rovides

information that hels in the formation of networ! e%uations.

eresentation of networ! with each element relaced by line segment with all

the nodes are in the networ! is called a grah.

A tree is a connected sub grah of networ! which consists of all the nodes of

original grah with no closed ath.

The branches of a tree are called twigs.

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The removed branches from the grah to form a tree is called cotree. The

branches of co-tree are lin!s.

An incidence matri( is one which gives the information about the interconnection

of various branches.

/or a given tree of a grah$ addition of each lin! between any two nodes forms a

loo called the fundamental loo or tie set.

A cut set is a minimum set of branches of a connected grah such that the removal

of these branches causes the grah to be cut into e(actly two arts.

A fundamental cut set is one which consists of only one tree branch and

remaining lin!s.

Fesh and 7odal analysis are two basic techni%ues used in finding solution of


)'+ is used to form mesh e%uations in mesh analysis.

)C+ is used to form nodal e%uations in nodal analysis.

A networ! is said to be dual to other networ! if mesh e%uations of first networ!

are same as the nodal e%uations of the other networ!.


0. A tree has

4. The no. of branches in a tree is the no. of branches in a grah.

6. The tie set schedule gives the relation between

8. Fesh analysis is based on

9. 7odal analysis is based on

:. =hat is the dual element for caacitor>

;. =hat is the dual element for current source>

?. =hat is the dual element of resistor>

Essa tpe !"estions and prob$ems:

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?. Use nodal analysis to find the ower dissiated in the : ohm resistor in the

following circuit.

0@. *raw the dual networ! for the following networ!.

.'..,.T. Course /ile ----------------------------------------------------------------------- 4

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Electrical Circuits Course File

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