Download 1. Ohm`s law doesn`t apply to all non metallic

UNIT I - BASIC CIRCUIT ANALYSIS
PART A
1. State Ohm’s law
Ohm’s law states that the voltage (v) across a resistor is directly proportional to the
current (i)
flowing through the resistor, at constant temperature. ie, v α i ,v = iR, where R is the resistance (Ω).
2. State the Limitation of Ohm’s law
1. Ohm’s law doesn’t apply to all non metallic conductors 2. Doesn’t apply to nonlinear
devices like Zener diode, Voltage regulator, tubes etc., 3. It is not applicable for the metallic
conductors which changes with temperature
3. An Electric iron is rated 1000W, 240V. Find the current drawn & resistance of the
heating element.
P=V2/R ; R= 2402/1000 = 57.6Ω and I= V/R =240/57.6 = 4.166 A
4. Define i) charge ii) electric current iii) power iv) network & v) circuit.
i) Charge: Charge is an electrical property of the atomic particles of which matter consists,
measured in coulombs(C ).
ii) Electric current is the time rate of change of charge, measured in amperes(A). i = dq/dt
A direct current (DC) is a current that remains constant with time.
An alternating current (AC) is a current that varies sinusoidally with time
iii) Power is the time rate of expending or absorbing energy, measured in watts(w). p = dw/dt pPower in watts(w); w- energy in joules (J); t - time in seconds (S); (or) p = v i , v - Voltage in
volts(V); i - current in amperes(A);
iv) Network: The inter connection of two or more simple circuit elements forms an electrical
network .
v) Circuit : If the network contains at least one closed path, it is an electric circuit.
5. State Kirchoff’s Current law.
KCL (Kirchoff’s Current Law) states that the algebraic sum of currents entering a node
(or a closed boundary) is zero. (or)The sum of the currents entering a node is equal to the sum of the
currents leaving the node.
6. State Kirchoff’s Voltage law.
KVL (Kirchoff’s Voltage Law) states that the algebraic sum of all voltages around a closed path
(or loop) is zero. (or) Sum of voltage drop = Sum of voltage rise.
7. The total charge entering a terminal is given by q=5t sin 4πt, mC. Calculate the current at
t=0.5 seconds.
Given, Charge, q = 5t sin 4πt, mC = 5t sin 4πt x 10-3 C;
Time, t = 0.5 s
Current, i = q/t = 5t sin 4πt x 10-3/t = 5 sin 4πt x 10-3 = 0.5472 x 10-3 ,A i = 0.5472 mA
8. How much energy does a 100W electric bulb consume in two hours?
Power = Energy/Time => Energy = P*t = 100*2*3600 = 720000 = 720 KJ
9. A stove element draws 15 A when connected to a 120V line. How long does it take to consume
30KJ .
Time = Energy
, t = w = 30*103 = 16.67 sec
Power
p
120*15
9. Give the voltage- current relations for i) resistance ii) inductance and iii) capacitance.
i) Resistance,R: v=iR ii) Inductance,L: v = L di/dt iii) Capacitance: v=1/C ∫i dt
10. What do you meant by Active elements? Give examples.
The element which is capable of generating or supplying energy is called an Active element.
Example: Generators, Batteries, Operational Amplifiers etc.,
11. What do you mean by passive elements? Give examples.
The Passive elements are those, which are capable only of receiving power. Eg: Inductors and
Capacitors.
12. Define: Node (OR) Junction
A Node is a point in the network where two or more circuit elements are connected.
13. Define: Tree
A Tree is a complete path including all the nodes.
14. Define: Branch
A branch is a part of the circuit which lies between two junction points.
15. What do you meant by series and parallel circuit?
When the resistors are connected in series, such that the same current passes through all of them,
then they are said to be in series.
When the resistors are connected across one another such that the same voltage is applied to each,
then the are said to be in parallel.
16. What are the concepts of series circuit?
1. Current flow in all part of the circuit is the same. 2. Voltage across the different elements will
depend upon the resistance of the elements 3. Voltage drops are additive 4. Resistances are additive
5. Powers are additive 6. Applied voltage equals to the sum of different voltage drops.
17. What are the disadvantages of series circuit?
1. If a break occurs at any point in the circuit no current will flow and the entire circuit
becomes useless. 2. Series circuit is not practicable for lighting circuits 3. Electrical devices
have a different current ratings, they cannot be connected in series for efficient operation.
18. What are the concepts of Parallel circuit?
1.Same voltage across all elements. 2. All elements will have individual currents, depending upon
the resistance of element. 3. The total resistance of a parallel circuit is always less than the smallest
of the resistances. 4. If ‘n’ resistances of each of R are connected in partallel then 1/RT= 1/R1 + 1/R2
+........n terms = n/R (OR) RT= R/n 5. Powers, conductances and branch currents are additive
19. What are the advantages of Parallel circuit.
1. The electrical appliances rated for the same voltage but different powers (and hence currents) can
be connected in parallel without affecting each other’s performance. 2. If a break occurs in any one
of the branch circuits it will have no effect on the other branch circuits.
20. The current flowing through a resistor is 0.8A when a potential difference of 20V is applied.
Determine the value of Resistor?
From Ohm’s law, V=IR; R=V/I =20/0.8 =25 Ω
21. A voltage source of 20 sin π t v is connected across a 5 k Ω resistor .Find the current through
the resistor and the power dissipated.
i = v/R= 20 sin πt = 4 sin πt ,mA ; P = v i = 80 sin2 πt ,mW
5*103
22. Define power and energy. Give the expression for electrical power and energy.
Power is the rate of doing work and its unit is Watt. The unit of electric power is defined in terms
of the joule per second. One joule per second is the work done when one coulomb of electricity is
moved through a potential difference of one volt in one second. Power P = EI = I2R = E2/R Watts.
Energy is the product of power and time. If the power remains constant at P during the period of
time t seconds, the energy equals Pt Watt-sec or Joules. Energy W = Pt = EIt = I2Rt = E2t/R J.
23. Define AC.
Any quantity whose magnitude & direction changes with respect to time.
24. Define RMS value of an ac voltage signal.
The effective value of an AC is defined as that value of DC which on passing through a resistance
R ohms for a given time T seconds, produces the same heat as the AC passing through R for the
same time T.Mathematically,
2
2
2
2
(i1  i2  i3  ....  in )
(OR) I RMS  Area under the squared curve
Period
n
25. Define Average value of an ac voltage signal.
This is some kind of the average of the instantaneous values taken over one complete cycle of the
wave. Mathematically,
Area under the curve
i  i  i  .....  i n
(OR) Iav 
Iav  1 2 3
Base
n
26. Define form factor.
The ratio between RMS value and average value is known as form factor. For sine wave signal the
value of form factor is 1.11.
27. Define peak factor.
The ration between Maximum value and RMS value is known as peak factor. For sine wave signal
the value of peak factor is 1.414.
28. What is meant by sinusoidal AC Voltage?
Voltage varying with sine function of time; The sinusoidal voltage is, E=Em sinωt
29. What is meant by Sinusoidal AC Current?
Current varying as sine function of time; The sinusoidal current is, I= Im sinωt
30. What is meant by time period?
The time taken to complete one cycle is called the time period of quantity.
31. Define Frequency.
I RMS 
32.
33.
34.
35.
36.
The number of cycles completed by an alternating quantity per second is known as its frequency. It
is denoted by f and it is measured in cycles / second which is known as Hertz, denoted as Hz.
f=1/T Hz
What is meant by Amplitude?
The maximum value of positive or negative of the alternating quantity is called amplitude.
Write down the expression of equivalent resistance for ‘n’ – number of
resistors in series
connection.
For ‘n’ resistors connected in series, the equivalent resistance is given by,
Req=R1+R2+R3+………..+Rn
Write down the expression of equivalent resistance for ‘n’ - number of resistors in parallel
connection.
For ‘n’ resistors connected in parallel, the equivalent resistance is given by,
1
1
1
1
1



 ......... 
Re q R1 R 2 R3
Rn
Write the Algorithm for Nodal Analysis.
Select a node as the reference node. Assign voltages V 1,V2,…Vn-1 to the remaining
n-1 nodes.
Apply KCL to each of the n-1 nodes. Solve the resulting simultaneous equations to obtain the
unknown node voltages.
Write the Algorithm for Mesh Analysis.
Assign mesh currents i1,i2,….in to the n meshes. Apply KVL to each of the n meshes. Solve
the resulting n simultaneous equations to get the mesh currents.
37. Apply KVL and solve (ans: I=3.54)
38. Write the Mesh equation for the circuit shown in figure.
Ans: 7I1 – 2I2 =10
2I1-12I2=0
39. Distinguish between a Loop & Mesh of a circuit (DEC, ’10)
The closed path of a network is called a Loop. An elementary form of a loop which cannot be further
divided is called a mesh. In other words Mesh is closed path does not contain an other loop within it.
40. How are the following affected by change of frequency? a)Resistance b)Inductive reactance
(DEC, 10)
Resistance will not be affected by change of frequency. Inductive reactance will increase by
increasing frequency and vice versa
41. State Kirchoff’s law applied to A.C circuits.
(JUNE,’11)
KCL (Kirchoff’s Current Law) states that the vector sum of currents entering a node (or a closed
boundary ) is zero. (or)The vector sum of the currents entering a node is equal to the vector sum of
the currents leaving the node.
KVL (Kirchoff’s Voltage Law) states that the Vector sum of all voltages around a closed path (or
loop) is zero.
42. What are the advantages of node voltage method of solving electrical network? (JUNE,’11)
In the node voltage method it is necessary to recognize the junction nodes in the network with refer to
one junction node the other junction node voltage are assumed as independent variables.
PART- B
1. In the circuit shown in fig. calculate (i) the current in other resistors (ii) the value of unknown
resistance ‘X’ (iii) the equivalent resistance across AB.
Ans: (i)I30=1A,I15=2A,IX=2A
(ii) X=15ohm (iii) R=3ohm
2. Determine the power dissipated by 5 ohm resistor in the circuit shown in figure. (Ans:124.77 W)
3. Find the nodal voltages (ans:V1=13.06V,V2=-34.65V,V3=17.15V)
4. A parallel network consist of three resistors of 4, 8 &32 ohms. If the current in the 8ohm resistor
is 2A.what are the currents in the other resistors. (Ans 4A,0.5A)
5. Find the nodal voltages VA and VB by nodal analysis.
6. Determine the current through 47 Ω resistor for the circuit shown in figure using mesh analysis.
7. Find the current through 3 Ω resistor in the network shown in the figure
i3
i1
i2
8. State and prove kirchoff’s Laws.
9. If “n” number of resistor are connected in (i) series&(ii) parallel, Derive the expression for Req?
10. Determine ‘i’ in the circuit.
Ans: -5-40i-5-5i-5=0
-45i-15=0
i=15/45
=0.33333 A
11. For the circuit shown in figure, write the nodal equation.
Ans: 0.166V1 – 0.066V2 = 2
0.066V1 - 0.266V2 = -4
12. Using Ohm’s law and Kirchoffs’ laws, find the currents and voltages in the given circuit.
i1
i3
 1 
 i2
 3 
V2
13. Find V1 and V2 using Nodal analysis for the circuit given
 j5 
1
1 O0 , A
2
j10

 j10 
 0.5
j5 
90 0 , A
14.Find the branch currents I1, I2 and I3 using Mesh analysis for Figure
I2
I1
 I3
15.For the circuit shown in the figure, Determine the value of V2 such that the current through
(3+j4) Ω impedance is zero.
j4
20 0
0
j3

 j5

16.Find the Voltage Vab in the network shown in the figure.
a
V2
y



x
b
17.Determine the current in the 5Ω resistor for the circuit shown in Fig using nodal analysis
18. In the circuit shown in fig, find(i)the total current drawn from the battery, (ii) voltage across
2ohm resistor and (iii) current passing through 5ohm resistor
(JUNE,’11)
Ans: It= 1.6901A, V2Ω =3.3802,
I5Ω= 0.9859A
19. Use nodal analysis, Determine the voltage across 5ohm resistance and current in the 12V source.
Ans; Va=6.353v, Vb= 11.765v, Vc= 25.882v. (JUNE,’11)
UNIT II- NETWORK REDUCTION AND NETWORK THEOREMS FOR DC & AC CIRCUITS
PART- A
1. Define Lumped circuit.
The circuit in which the elements are separated physically like resistors, capacitors and inductors.
2. State division of current rule for a two branch parallel network.
R1 and R2 are connected in parallel, Let I be the total current, I1 be the current through R1, I2 be the
current through R2 Then I1 = I * R2/(R1+R2);
I2 = I * R1/(R1+R2)
3. State division of voltage rule for a circuit with three resistors in series.
R1 and R2 are connected in series, Let V be the total voltage, V1 be the voltage across R1, V2 be the
voltage across R2, Then, V1 = V * R1/(R1+R2);
V2= V * R2(R1+R2)
4. Write down the formulae for converting Star to Delta.
Rab=(RaRb+RbRc+RcRa) / Rc ;
Rbc=(RaRb+RbRc+RcRa) / Ra
Rca =(RaRb+RbRc+RcRa) / Rb
5. Define Node and super node.
A node is the point of connection of two or more branches.
A super node is formed by enclosing a voltage source connected between two nodes.
6. Define mesh and super mesh.
A mesh is a loop, which does not contain any other loops within it.
A super mesh results when two meshes have a current source in common.
7. State Superposition theorem.
The superposition theorem states that in any linear network containing two or more sources, the
response in any element is equal to algebraic sum of the responses caused by individual sources acting
alone, while the other sources are non operative; that is, while considering the effect of individual
sources, other ideal voltage sources and ideal current sources in the network are replaced by short
circuit and open circuit across their terminals.
8. What is the limitation of super position theorem.
Super position theorem can be applied for finding the current through or voltage across a particular
element in a linear circuit containing more than two sources. But this theorem cannot be used for the
calculation of the power.
9 State Thevenin's theorem .
Thevenin’s theorem states that any circuit having a number of voltage sources, resistances and open
output terminals can be replaced by a simple equivalent circuit consisting of a single voltage source in
series with a resistance(impedance), where the value of the voltage source is equal to the resistance
seen into the network across the output terminals.
10. State reciprocity theorem.
(JUNE,’11)
According to this theorem in a linear, bilateral network if we apply some input to a circuit which
consists of resistors, inductors, capacitors and transformers, the ratio of response in any element to the
input is constant even when the position of input and output are interchanged. This is called the
Reciprocity Theorem.
11. Is reciprocity theorem applied to the circuit having resistors, capacitors and diodes? Give your
reason.
No. Reciprocity theorem is applicable only for linear circuits.
12. State Substitution theorem.
The substitution theorem states that any impedance branch of a circuit can be substituted by a new
branch without disturbing the voltages and current in the entire circuit, provided the new branch has
same set of terminal voltage and current as that of original circuit.
13. State Maximum power transfer theorem.
For a given Thevenin equivalent circuit, maximum power transfer occurs when R L = RTH, that is,
when the load resistance is equal to the thevenin resistance.
14. State Norton's theorem.
Norton’s theorem states that any circuit with voltage sources, resistances (impedances) and open
output terminals can be replaced by a single current source in parallel with single resistance
(impedance), where the value of current source is equal to the current passing through the short circuit
output terminals and the value of the resistance (impedance) is equal to the resistance seen into the
output terminals.
15. Where and why maximum power transfer theorem is applied.
In a certain applications it is desirable to have a maximum power transfer from source to load. The
maximum power transfer to load is possible only if the source and load has matched impedance.
Eg: TV/Radio receiver
16. What is the condition to obtain maximum power when an ac source with internal impedance is
connected to a load with variable resistance and variable reactance.
Maximum power transferred from source to load, when the impedance is equal to complex conjugate
of source impedance.
17. What are the limitation of Thevenin’s Theorem?
The limitation of Thevenin’s theorem are, 1. Not applicable to the circuits consisting of nonliner
elements. 2. Not applicable to unilateral networks. 3. There should no be magnetic coupling between
the load and circuit to be replaced by Thevenin’s theorem.4. In the load side, there should not be
controlled sources, controlled from some other part of the circuit
18. Define Corollary.
If pure resistance is to be connected as load for maximum power transfer then its value must be equal
to the absolute magnitude of Z eq. RL = Zeq for Pmax when load is purely resistive.
19. A 10A current source has a source resistance of 100Ω. What will be t he equivalent voltage
source?
Ans: 1000V, R= 100Ω.
20. A 1V Voltage source has an internal resistance of 1Ω, Calculate the Maximum power that can
be delivered to any load.
Ans: Maximum power transferred to the load = Vs2RL / ( Rs + RL)2 = ¼ =0.25 W.
21. State the maximum power transfer theorem for AC circuit.
Maximum average power is transferred to a load when the load impedance is the complex conjugate
of the Thevenin’s impedance as seen from the load terminals, Z L = ZTh*
22. Determine the voltages V1 and V2 in the circuit shown in fig.
V1 = 10 x
V2 = 10 x
(
(
=5V
)
=5V
)
23. What is the equivalent resistance across A – B in the network shown in figure?
RAB  5 
3 6
 7
3 6
24. Write the expressions for resistance of a star network in terms of known delta values.
(JUNE,’11)
Ra = ( Rab Rbc )/( Rab+ Rbc+ Rca) ; Rb = ( Rbc Rca )/( Rab+ Rbc+ Rca) ; Rc = ( Rca Rbc )/( Rab+ Rbc+ Rca)
PART-B
1. Obtain the expression of equivalent star resistance in terms of delta resistance.
2. Obtain the expression of equivalent delta resistance in terms of star resistance.
3. Find the magnitude of total current, if R1&R2 are in parallel. R1 and R2 are 10 & 20ohm
respectively and V=50V(ans: It=7.5A,I1=5A,I2=2.5A)
4. For the circuit shown obtain the equivalent current source b\w the terminals XY (Ans:
I=3A,R=2/3ohm)
5. Calculate Vx using the method of Source transformation for Figure.
5
20  90 0 , V
4
3

+
j4
6. Find Rab in the circuit shown in figure.
7. Find the equivalent resistance between A and B.
8. Find the equivalent resistance between A and B
 j13
Vx

10
9. Find Rab in the circuit shown in figure.
.
10. Use star – delta transformation to find the input resistance of the given network
20
8
a
Rin
5

20
9
2
18
b
1
11. Verify the Reciprocity theorem for the network shown in Fiure.
I
1. 428A
12. Obtain the Thevenin’s equivalent circuit at terminals a-b for the figure given
d
 j6 
120 75 v
o
e
a
b
c
j12
f
13.Use the Superposition theorem to find i for figure given
i

14. Obtain the equivalent resistance Rab and then find the current i for Figure given

i
oa
12.5
120
5
V
10
30
15
20
15. Find the equivalent resistance between A& B of the circuit shown in the fig.
16. Find the Norton’s equivalent circuit for the network shown in the figure.


17. In the circuit find I3 and verify the reciprocity theorem.
I2
I3
I1
18. Convert the circuit show in Fig. to single voltage source with series resistance
19. Find equivalent resistance and current drawn by the source for the circuit shown
20. Use delta – star conversion to find resistance between terminals A and B of the circuit shown in
fig Ans: R equivalent = 6.244Ω
(JUNE,’11)
21. In the circuit shown in fig below, find the value of adjustable resistor R for maximum power
transfer to R. Also calculate the maximum power.Ans: Vth = 40V, Rth = 26Ω
(JUNE,’11)
UNIT III – RESONANCE AND COUPLED CIRCUITS
PART- A
1. Define Impedance.
Impedance is defined as the opposition of circuit to flow of alternating current. It is denoted by Z and
its unit is ohms.
2. Define Resonance.
Resonance is defined as a phenomenon in which applied voltage and resulting current are in-phase. In
other words, an AC circuit is said to be in resonance if it exhibits unity power factor condition, that
means applied voltage and resulting current are in phase.
3. Define Q - factor or Figure of Merit, Q.
The quality factor, Q of a resonant circuit is the ratio of its resonant frequency to its bandwidth.
The Q - factor of a circuit can also be defined as,
Q = 2 
Maximum energy stored in the circuit
Energy dissipated per cycle in the circuit
4. Show that in a series RLC circuit, f1f2 = fr2 where fr is the resonant frequency and f 1, f2 are the
half power frequencies.
R
1  
2L
 R  2
1 
  

LC 
 2L 
2
R
2 

2L
2
 R  2
1 
  

LC 
 2L 
2
1 R 
1  1 
R 
2
1 2    
-  
 
   r
LC  2L 
LC  LC 
 2L 
2
Hence, f1 f 2  f r
5. Define Conductance.
It is defined as the ratio of the resistance to the square of the impedance. It is measured in the unit
Siemens and it is denoted by G.
6. Define Susceptance.
It is defined as the ratio of the reactance to the square of the impedance. It is measured in the unit
Siemens and it is denoted by B.
7. What is a Resonant frequency?
The frequency at which resonance occurs is called resonant frequency. i.e. X L=XC.
8.What are the resonant condition?
i) The total impedance Z is minimum and is equal to R. ii) The circuit will be purely resistive circuit.
iii) Power factor of the circuit is unity. iv) Circuit element, Imax= V/R. v)Power at resonance, Pr=I^2R.
9. What is the series resonance?
The inductive reactance increases as the frequency increases (X L=ωl) but the capacitive reactances
decreases with frequency(XC=1/ωc). Thus inductive and capacitive reactances have opposite
properties. So, for any LC combination there must be one frequency at which Xl=Xc. This case of
equal and opposite reactance is called series resonance.
10. What is a parallel resonance?
The parallel circuit is said to be in resonance, when the power factor is unity. This is true when the
imaginary part of the total admittance is zero.
11. Define Bandwidth, half power frequencies?
The difference between the half power frequencies f1 and f2 at which power is half of its maximum is
called bandwidth
B.W.= f2-f1
It can be observed that at two frequencies f 1 and f2 the power is half of its maximum value. These
frequencies are called half power frequencies. Out of the two half power frequencies, the frequency f 2
is called upper cut-off frequency while the frequency f1 is called lower cut-off frequency.
12. Define Selectivity.
The selectivity is defined as the ratio of the resonant frequency to the bandwidth.
Selectivity = fr/B.W.
13. What are coupled circuits?
The two circuits are said to be coupled circuits if all or part of the electrical energy supplied to one
circuit is transferred to the other circuit, without having any electrical connection between them
14. Define self Inductance.
The property of the coil which opposes any change in current passing through it is called self
inductance of the coil. L = N/I
15. What is meant by Mutual Induction?
When two inductors (or coils) are in a close proximity to each other, the magnetic flux caused by
current in one coil links with the other coil, thereby inducing voltage in the latter. This phenomenon is
known as ‘Mutual Induction’.
M =N112/i = N212/i2
16. Define Mutual Inductance, M.
Mutual Inductance is the ability of one inductor to induce a voltage across a neighboring inductor,
measured in henrys (H).
17. State Dot convention.
(i) If a current enters the dotted terminal of one coil, the reference polarity of the mutual voltage in
the second coil is positive at the dotted terminal of the second coil. (ii) If a current leaves the dotted
terminal of one coil, the reference polarity of the mutual voltage in the second coil is negative at the
dotted terminal of the second coil.
18. Write the total inductance of two coils connected in series aiding and opposing.
Series - aiding connection : Leq = L1 + L2 + 2M
Series - opposing connection :
Leq = L1 + L2 - 2M
19. Define Coefficient of coupling, K.
(JUNE,’11)
The fraction of the total flux produced by one coil linking a second coil is called the Coefficient of
coupling, K.Thus, K = Ф12 / Ф1 = Ф21/ Ф2 K= M/L1L2
Since Ф12 < Ф1 or Ф21<Ф2, the value of K is always less than or equal to 1.
20. Two inductively coupled coils have self - inductances L1 = 50 mH and L2 = 200 mH. If the
coefficient of coupling is 0.5 (i) find the value of mutual inductance between the coils, and (ii) what
is the maximum possible mutual inductance?
(i) M = K L1 L2 = 0.5 (ii) M is max when K=1.M = L1 L2 = 50  10 3  200  10 3 = 100 mH
21. Two coils connected in series have an equivalent inductance of 0.4H when connected in aiding,
and an equivalent inductance of 0.2H when the connection is opposite. Calculate the mutual
inductance of the coils.
Series aiding,
Leq = L1 + L2 + 2M = 0.4 ---------------- (1)
Series opposing,
Leq = L1 + L2 - 2M = 0.2 ----------------- (2)
Solving equations (1) and (2),
4M = 0.2;
M = 0.05 H
22. What is the relation between the mutual inductance and self inductance of coils.
23. State dot rule.
The sign of the mutual induced voltage depends on direction of the winding of the coil. For
convenient, dot conventions are used for purpose of indicating direction of winding.
Rules for dot convention
If a current enters a dot in one coil, then mutually induced voltage is positive at the dotted end.
If a current leaves a dot in one coil, then mutually induced voltage is negative at the dotted end.
24.What are the application of tuned circuits.
Tuned circuits are used in communication systems, Radio receivers, in defence
25. Define an ideal transformer.
An ideal transformer is a transformer with no losses and having a core with infinite permeability,
which results in perfect coupling with no leakage flux.
26. A series RLC circuit has a resonant frequency of 12KHz. If R= 5 Ω and X1 at resonance is 300 Ω
Find the Bandwidth.
B.W = fr R/X1 = 12* 103 * 5/ 300 = 200Hz.
27.Find the resonant frequency in the ideal parallel LC circuit shown below
27. Determine the power factor of a RLC series circuit with R=5ohm, XL=8ohm and XC=12ohm.
(JUNE,’11)
=
=
+( −
)
= .
PART- B
1. Derive the relation between coefficient of coupling & the self inductance & mutual inductance.
2. Derive an expression for equivalent inductance of two coupled coils in (i) Series aiding.(ii) series
opposing,(iii)parallel aiding,(iv) parallel opposing
3. In an RLC series circuit, if ω1& ω2 are two frequencies @ which the magnitude of the current is the
same & if ωr is the resonant frequency. Prove that ωr= ω1 ω2.
4. (a) Derive the formula for the resonant frequency of series resonant circuit.
(b) Derive the formula for the resonant frequency of parallel resonant circuit
5. Explain & derive the relationship for bandwidth & half power frequencies of RLC series circuit.
6. Determine the quality factor of a coil of R=10ohm, L=0.1H, C=10μf (Ans: Q=10)
7. A series RLC circuit has Q=75 and a pass band (b\w half power frequencies) of 160Hz. Cal the
resonant freq & upper & lower Freq of the bass band.(Ans: fr=12KHz,f1=11920Hz,f2=12080Hz)
8 A series resonant circuit has BW=2000 Hz & Q=100. It uses a capacitor of 50pf. Calculate the constant
of the circuit. If an AC voltage of 1v is connected to this circuit what will be the voltage across inductor,
capacitor, & resistor at resonance? (Ans:R=159.4ohm, L=12.67mH, VL=100V, Vc=100V & VR=1V)
9. A series RLC circuits consist of R = 1000 ohm, L=100mH & C=10 x 10-12f, the applied voltage across
the circuit is 100V. calculate
(i) the resonant freq of the circuit (0.159x106Hz)
(ii) the Q-factor of the circuit at resonant frequency (100)
(iii) At what angular velocities do the half power points occur? [995x103 & 1005x103 r/sec]
(iv) Compute the BW of the circuit (10x103 r\sec)
10. A series RLC circuit has a resistance of 20 ohm, inductance of 0.05H & cap of 10μf. Find resonant
frequency B.W & Q of the circuit. (Ans: ω0=1414 r\sec, BW=400 r\sec, Q=3.54)
11. Derive the transfer function and maximum voltage amplification of a single tuned circuit.
12.In a RLC series circuit prove that resonant frequency is equal to geometric mean of half power
frequencies.(ωr = √( ω 1ω2))
13. Derive the expression for maximum amplification factor for a single tuned system. Also plot the
variation of amplification factor or output voltage with co- efficient of coupling.
14. Two coupled coils have a co-efficient of coupling of 0.85. N1 =100, N2 = 800 turns with coil 1 open
and a current of 5A in coil 2. The flux in coil 2 is 0.35mwb. Find self and mutual inductances of the coil.
15. A coil having an inductance of 100mH is magnetically coupled to another coil having an inductance
of 900 m H. The Coefficient of coupling between the coils is 0.45. Calculate the equivalent inductance if
the two coils are connected in Series aiding, Series opposing parallel aiding & Parallel opposition
16. Determine the value of capacitance C in order that the circuit resonates at a frequency of 6366Hz
17. In the parallel RLC circuit, calculate resonant frequency, bandwidth, Q-factor and power dissipated at
half power frequencies.
18. The no. of turns in two coupled coils are 600 and 1200 respectively. When a current of 4A flows in
the coil 1, the total flux in coil 1 is 0.5 wb and the flux linking coil 2 is 0.4 mwb, determine the self
inductances of the coils and mutual inductance between them. Also calculate the coefficient of coupling.
19. In RLC series circuit, R=30Ω, L=80mH, C=80 µF. Under resonant condition, find the i) resonant
frequency ii) voltage across each element iii) current iv) power. If the applied voltage is 150V.
20. Obtain the expression for resonant frequency for the circuit shown
21. A series RLC circuit shown in fig with R=60ohm, L=0.5H and C=40µF is connected across an AC
variable frequency supply of 200V. Calculate the resonant frequency and lower and upper half power
frequencies.
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22. Derive an expression for total inductance of two coupled coils connected in: Series aiding mode and
Series opposing mode
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UNIT IV- TRANSIENT RESPONSE FOR DC CIRCUITS
PART- A
1. Define the term time constant of a circuit.
In a circuit in which the current is increasing to a final steady value, the time(T) taken to reach
63.2% of the final value is called the time constant of the circuit.
2. Define time constant of a decaying circuit.
For a decaying circuit, the time constant is defined as the time required to reach 36.8% of the
initial value.
3. Draw the current curve of a RL transient connected to a DC source.
4. Write down the voltage equation of a series RLC transient circuit excited by a dc source, E.
Applying KVL to the circuit, the voltage equation becomes,
Ri  L
di 1

idt  E
dt C 
5. Define transient state and transient time.
In a network containing energy storage elements, with change in excitation, the currents and voltage
change from one state to another state. The behaviour of the voltage or current when it is changed
from one state to another state is called the transient state.
The time taken for the circuit to change from one steady state to another steady state is called the
transient time.
6. Define damping ratio. Give the damping ratio of RLC series circuit.
Damping ratio 
value of resis tan ce in the circuit
Re sis tan ce for critical damping
For RLC series circuit,  
R
2 L
C
7. Give the natural frequency n and damped frequency β of a series RLC circuit.
Natural frequency  n 
1
LC
Damped frequency    n2   n2 2 =  n 1   2
8. Write the condition for different cases of damping in a series RLC circuit.
If damping ratio,  = 1, it corresponds to critical damping;  >1, it corresponds to over damping
&  < 1, it corresponds to under damping.
9. A DC voltage is applied to a series RL circuit by closing a switch. The voltage across L is 100
volts at t=0 and drops to 13.5 volts at t = 0.02 sec.If L = 0.1 H, find the value of R.
eL = E e-Rt/L
At t = 0, eL = E e-0 = E = 100
At t = 0.02, eL =100 E e-0.02R/0.1 = E = 13.5 ; 100e-0.2 R = 13.5
Taking natural logarithm on both sides,
ln e-0.2R = ln 0.135;
-0.2 R = - 2;
R = 10 Ω
10. Write down the voltage equation of a series RLC circuit excited by an source.
11. Define Laplace transform.
The Laplace transform is an integral transformation of a function f(t) from the time
domain
into the complex frequency domain, giving F(s). Given a function f(t), its Laplace transform, denoted by
F(s) or L[f(t)], is given by
Where s is a complex variable given by s = σ + jω
12. What is meant by resistance?
The resistance of a circuit is the property by which it opposes the flow of current. It measures by
ohms.
13. Define Inductance?
When a time varying current passes through a circuit varying flux is produced. Because of this
change in flux, a voltage is induced in the circuit proportional to time rate of change of flux or current i.e.
emf induced α di/dt= Ldi/dt.
Where L, the constant of proportionally has to be called as self inductance of the circuits.
14. Define Capacitance.
A capacitor is a circuit element that, like the inductor, stores energy during periods of time and
returns the energy during others. In the capacitor, storage takes place in an electric field unlike the
inductance where storage is in a magnetic field.
15. Define Natural response or source free response.
The response of the circuit due to the stored energy in the circuit elements (independent of
sources) is called natural response.
16. Define forced response.
The response of the circuit due to the external source is called forced response
17. Define the term Rise time (tr) & Delay time (td).
The time taken by the response to reach 100% of the steady state value for the first time is known
as Rise time
The time taken by the response to reach 50% of the steady state value for the first time is known
as Delay time
18. Draw the transient response of a first order circuit with a forcing function.
19. Define transient response.
The response or the output of the circuit from the instant of switching to the attainment of steady
state is known as transient response.
20. Define the time constant of RL circuit
(JUNE,’11)
Time constant of RL circuit is defined as time taken to reach 63.2% of final value( steady state)
21. In circuits excited by DC source when there is no stored energy at initial state _capacitance_
behave at short circuit and Inductance behave as open circuit.
(JUNE,’11)
PART- B
1. Explain the solution, methodology of calculating the transient response of RLC series circuit with step
input?
2. A series RLC circuit with R=20Ω, L=10H and C=5f has a constant voltage V=100 volts applied at t=0.
Find the current response in the circuit . assuming zero initial condition. Ans: i(t)=5.05{e-0.01t –e-1.99t}
3. In the circuit shown in figure, switch S is in position 1 for a long time and brought to position 2 at time
t=0. Determine the circuit current.
4. Derive an expression for transient current, voltage & the energy stored in inductor of a RL transient
circuit excited by a DC Source.
5. Derive the transient current Expression for RL series circuit with input of V mSinωt.
6. A DC voltage of 100V is applied in the given circuit and the switch K is open. The switch K is closed
at t=0. Find the complete expression for the current.
7. Derive an expression for transient current, voltages & the energy stored in inductor of a RC transient
circuit excited by a DC source.
8. A series RLC circuit with R=300ohm, L=1H & c=100μf has a constant voltage of 50V applied to it at
t=0. Find the maximum current value. Assume zero initial condition (ans: i max=0.1377A)
9. Derive an expression for transient current of a RL decay transient excited by a DC source
10. Derive an expression for transient current of a RC decay transient excited by a DC source.
11. A circuit has a resistance of 1000ohm and a capacitance of 0.1µF. At t=0 it is connected to a12V
battery. Find (i) The current at t=0 (ii) Rate of change of current at t=0
12. For the circuit shown in figure, find the voltage across the resistor 0.5Ω when the switch, S is opened
at t=0. Assume that there is no charge on the capacitor and no current in the inductor before switching.
13. In the RC circuit shown in fig, the capacitor has an initial charge of Q0=100μc when the switch is
closed at t=0, find the time taken for the capacitor voltage to drop from 80 to 10 volts. (Ans: time
taken=207.94μsec)
14. For the source free RLC series circuit, the initial voltage across the Capacitor is 10V and the initial
current through the Inductor is zero. If R= 100 Ω, L= 20mH, C= 0.5μF. Evaluate i(t).
15. The switch shown in circuit is closed on position 1 @ t=0 and then moved to position 2, after one time
constant. Determine the current for t>0. Also Sketch the transient waveform.
16. A series RLC circuit with R= 5ohm and L=1H and C= 1/6 F has a constant voltage source of 50V
applied across it at time t=0. Obtain the equation for the current I in the circuit assuming all initial
conditions as zero. Also find the time when current in the circuit is maximum. Also find the maximum
value of current.
(JUNE,’11)
17. A sinusoidally varying voltage of V=50sin10t is applied to a series RC circuit shown in fig at time
t=0. R=2ohm, and C=0.25F. Find the equation for the current in the circuit assuming initial charge on
capacitor be zero
(JUNE,’11)
UNIT V- ANALYSING THREE PHASE CIRCUITS
PART- A
1. What are the three types of power used in AC circuits?
i) Real or Active or True power P=EI cosθ ii) Reactive power Q=EI sinθ iii)Apparent power S=EI
2. Define Real power.
The actual power consumed in an AC circuits is called real power. And P=EI cosθ
3. Define Reactive power.
The power consumed by the pure reactance (Xl or Xc) in an AC circuit is called reactive power. The
unit is VAR. and Q=EI sinθ
4. Define Apparent power and Power factor.
The Apparent power (in VA) is the product of the rms values of voltage and current. S = Vrms Irms
The Power factor is the cosine of the phase difference between voltage and current. It is also the cosine
of the load impedance. And Power factor = cos φ
The pf is lagging if the current lags voltage (inductive load) and is leading when the current leads
voltage (capacitive load).
5. What is meant by Complex power?
Complex power (in VA) is the product of the rms voltage phasor and the complex conjugate of the rms
current phasor. As a complex quantity, its real part is real power, P and its imaginary part is reactive
power, Q. and S = P + jQ
6. What are the advantages of 3 phase circuits over single phase circuits?
1. Generation, transmission and distribution of 3 phase power is cheaper 2. More efficient 3. Uniform
torque production occurs
7. State the relationship between line voltage & phase voltage and line current & phase current of a
3 phase delta connected system.
Vph = VL ; Iph = IL / 3
8.State the relationship between line voltage & phase voltage and line current & phase current of a
3 phase star connected system.
Vph = VL / 3; Iph = IL
9.Write the expression for the instantaneous values of emfs in a 3 phase circuit.
VR = Vm sin wt; VY = Vm sin (wt-1200); VB = Vm sin (wt-2400)
10.Give the expressions for Wattmeter readings in terms of Voltage, Current and Power factor
angle in Two – Wattmeter method.
W1 = VL IL cos (300+ );
W2 = VL IL cos (300- )
11.Give the expressions for finding Power factor of the load for Wattmeter reading in Two –
Wattmeter method.
cos  = cos {tan-1[3(W2 –W1 ) / (W2 +W1 )] }
12.Give some method available for measuring three-phase power.
i. Single wattmeter method. 2. Two-wattmeter method. 3. Three-wattmeter method.
13.A star connected load has 6+j8 ohm impedance per phase. Determine the line current if it is
connected to 400V, three phase, and 50Hz supply. Ans: Zph=10Ω/ph, I ph= 23.094A=IL. (JUNE,’11)
14. Define power factor.
Power factor is defined as the cosine of angle between voltage and current. If φ is the angle between
voltage
and current then cos φ is called as the power factor.
15. What are the advantages of two-wattmeter method?
The principal advantages is that the algebraic sum of the readings of the two wattmeters indicates the
total power regardless of,
(i) Load impedance;(ii)Source impedance; (iii)Difference in wattmeters; (iv) Phase sequence
16. Two wattmeters are used to measure the total power in a three phase, three wire balanced load.
One wattmeter reads zero. What is the power factor of the load?
The power factor of the load is 0.5
17. When the power is 0.5 for a balanced three-phase circuit, what will be the reading of one of the
wattmeter of the two watt meters used to measure three phase power?
One wattmeter reads zero. Other wattmeter reads the total power.
18. Write the expression for the power measured by two watt meters used in 3- phase balanced
load, in terms of voltage, current and power factor.
(JUNE,’11)
W1 = VLILcos(30 + ); W2 = VLILcos(30 - )
19. Write the expression for power factor in two wattmeter method of power measurement
=
√3
20. What are the disadvantages of two-wattmeter method?
i) Not applicable for three phase, 4 wire system. ii) the signs of w1 and w2 must be identified and noted
down correctly otherwise it may lead to the wrong results
21. Define Symmetrical System.
It is possible in polyphase system that magnitudes of different alternating voltage are different. But a
three phase system in which the three voltages are of same magnitude and frequency and displaced
from each other by 120° phase angle is defined as symmetrical system.
22. Explain the concept of balanced load.
The load is said to be balanced when magnitudes of all impedances Z ph1, Zph2 and Zph3 are equal and
the phase angles of all of them are equal and of same nature either all inductive or all capacitive or all
resistive.
23. What is phase sequence?
The order in which the voltage in the three phases reach their maximum positive values is called the
phase sequence.
24. Define Phasor and Phase angle.
A sinusoidal wave form can be represented or in terms of a Phasor. A Phasor is a vector with definite
magnitude and direction. From the Phasor the sinusoidal wave form can be reconstructed.
Phase angle is the angular measurement that specifies the position of the alternating quantity relative
to a reference.
25. What are the advantages of 3Φ system?
1.Constant power 2. Higher rating 3. Power transmission economics
26. While measuring power in a circuit by two wattmeter method, under what condition the two
wattmeter reading will be equal and why?
When the power factor is unity or when the load is purely resistive, then the two wattmeter reading
will be equal.
27. Which type of connection of 3Φ system is preferred at the point of utilization? Why?
Three phase , 4 wire system are used in utilization system so that either single phase or three phase
load can be connected.
PART- B
1. Explain the two wattmeter method of measurement of 3 phase power & p.f with neat phasor diagram
2. A three phase delta connected load having (3+j4)ohm imp/phase is connected across a 400volt 3 phase
source. Calculate the magnitude of line current through the load?
3. An unbalanced four wire star connected load has a balanced supply voltage of 400volts. The load imp
are ZR=(4+j8)ohm, Z=(3+j4)ohm & ZB=15+j10 ohm. Calculate the line currents, neutral currents & total
power? And also draw the phasor diagram.
(JUNE,’11)
4. Determine the power & P.f, if the two wattmeters read 1000 watts & 2000 Watts respectively.
5. In the balanced three phase system, the power is measured by two-wattmeter method & the ratio of two
meter reading is 2:1. Determine the power factor of the system.
6. S.T the total power is √ 3 VL IL cosΦ in a balanced 3 phase star or delta connected circuit, where V L,IL,
cosΦ are the line voltage, line current & P.f of the circuit.
7. A balanced star connected load having 4+j3 ohm imp per phase is connected across a 400V, 3 phase,
50V source. Calculate the magnitude of line current, P.f, power, reactive volt ampere & total volt ampere?
8. A balanced 3 phase star connected load with impedance 8+j6ohm per phase is connected across a
symmetrical 400v 3phase, 50HZ supply. Determine the line current, P.f of the load & the total power.
9. A delta load connected with Zab=100ohm, Zbc=-j100ohm, Zca=70.7+j70.7 ohm is connected across
the three phase 400V supply. Determine the line currents.
10. Three resistance of 25ohm each are connected in delta across a 500V, 3phase AC supply. Calculate (i)
Line & phase currents (Ans: 34.4A,20A); (ii) Phase voltage (Ans: 500V); (iii) Power consumed (Ans:
30W)
11.Three resistance of 50ohm each are connected in delta across a 300V, 3phase AC supply.
Calculate (i) Line & phase currents (ii) Phase voltage (300V) (iii) Power consumed
12.A balanced star connected load of (20+j15)ohm per phase is connected in star across a
400V,3 phase supply. Calculate (i) Line current (9.24A) (ii) The P.f (0.8 lag) (iii) The total
power in KW (5.12)
13.A 3 phase , 4wire symmetrical 440V,RYB Sstem supplies a star connected load in which
ZR=10∟0`ohm,Z y=10∟26.8`ohm, & ZB=10∟-26.8`ohm . Find the line current, the neutral currents &
the load power.
14. A 3phase ,400V, 50HZ supply has a delta connected load with ZAB=55∟0`ohm,
ZBC=35∟60`ohm,ZCA=40∟30`ohm. Determine phase & line currents & draw the phasor diagram. Take
the phase sequence as ABC.
15. A star load with Za=3+j0 ohm,Zb=2+j3 ohm,Zc=2-j0 ohm connected to a 3 phase, 4 wire, 100V
system. find the neutral currents.
16. A star connected load has impedance of 3+j4 ohm in each phase and is connected across a
balanced 3 phase delta connected alternator having line voltage of 120V. Obtain line current of
both the load and generator and also calculate real power, reactive power and total power.
17. A 3 phase star connected system with 400V line is connected to 3 loads 250o, 11-20o and
1516o. Find the line current , power and the current in the neutral of the system.
18. A balanced star connected load of (20+j15)ohm per phase is connected in star across a 400V,3 phase
supply. Calculate (i)Line current (Ans: 9.24A) (ii) P.f (Ans: 0.8 lag) (iii)The total power in KW (Ans:
5.12 KW)
19. A 3phase ,400V, 50HZ supply has a delta connected load with ZAB=15∟0`ohm,
ZBC=25∟60`ohm,ZCA=10∟30`ohm. Determine phase & line currents & draw the phasor diagram. Take
the phase sequence as ABC.
20. Calculate the total power input and readings of the two wattmeter connected to measure power in a
three phase balanced load, if the reactive power input is 15 KVAR and the load power factor is 0.8. Also
compute load KVA.
(JUNE,’11)