EE6201 CIRCUIT THEORY (COMMON TO EEE,ECE,EIE) QUESTION ...

EE6201 CIRCUIT THEORY

(COMMON TO EEE,ECE,EIE)

QUESTION BANK

UNIT-I

BASIC CIRCUITS ANALYSIS

PART-A

1. State Kirchoff’s Laws for electric circuits.

2. Calculate the equivalent resistance of the following combination of resistor and source

current.

3. Define power factor.

4. A resistance of 120Ω and a capacitive reactance of 250Ω are connected in series across

a AC voltage supply. If a current of 0.9 A is flowing in the circuit find out the power

factor.

5. A bulb is rated as 230V, 230W. Find the rated current and resistance of the filament.

6. State Ohm’s law and its limitations.

7. Define active elements and passive elements.

8. A 9Ω resistor is connected in parallel with a series combination of resistors of 5Ω and

13Ω. If the drop across 5Ω is 10V. Find the total applied voltage and total current.

9. The lamps in a set of Christmas tree lights are connected in series. If there are 20

lamps and each lamp has resistance of 25 Ω, Calculate the total resistance of the set

of lamps and hence calculate the current taken from supply of 230 volts?

10. Find the equivalent conductance Geq of the circuit shown below.

11. How are the following affected by change of frequency?

a) Resistance b) Inductive reactance.

12. Two identical resistors connected in series across a voltage source dissipate 10W

Power. What will be the power dissipated if they are connected in parallel across

the same source?

13. Two inductances L1=3mH and L2=6mH are connected in parallel. Find Leq.

14. Determine the power factor of a RLC series circuit with R= 5Ω,XL=8Ω and XC=12Ω.

15. Define Circuit, electrical network, active network, node, branch.

16. Find the magnitude of currents in the Ammeter of resistance 10Ω.

40 ohms

16 ohms

20 v olts

4 ohms

6 ohms

12 ohms

www.Vidyarthiplus.com


.

17. Draw the phasor diagram for pure inductance, pure capacitance and pure resistance.

18. An 1Φ 50 Hz ac supply system has the RMS values of 100V, 10 A. Determine the

instantaneous value of voltage and current.

19. Find the value of R1 and R2 when they are parallel with the following conditions. The

current in R1 is twice the current flowing through R2 and the equivalent resistance of the

parallel combination is 10/3Ω.

20. Determine the power absorbed by each of the elements in a given circuit.

PART-B

1. (a) Determine the current delivered by the source shown in the circuit below.

(b)For the network shown below,]\ obtain the current ratio (I1/I3) using mesh analysis.



2. (a) Obtain the voltage Vx using mesh current method for the circuit shown in figure

(b)For the circuit shown below a) Find the equivalent resistance between P&Q b)

Total current from 240V source c) The current through 18Ω resistor

3. (a) In a circuit consisting of two elements in series, the equations for voltage and

current are i=28sin(314+60º) and e=180 sin 314t find a) the RMS value of the voltage

and current b) the frequency c) the power factor d) the power e) the values of circuit

constants.

(b) For the circuit shown below find the node voltages, and currents I1, I2 ,I3.



4. (a) Using mesh analysis, determine the current through 1Ω in the given figure.

(b) Find Rab in the circuit shown in the figure.

5. (a)Obtain currents through various elements in the circuit using nodal method.



(b) Find loop currents by mesh analysis.

6. (a) In the circuit find Rab.

(b) Determine IL using nodal analysis.



7. (a)Find the current in 5Ω resistor and the voltage across it in the network using mesh

analysis technique.

(b)Compute V1 and V2 in the circuit using nodal analysis.

8. (a) Find the source current and load current in the circuit using Kirchoff's laws.



(b)Determine Vx and ix in the given circuit.

9. (a) Determine the value of unknown node voltages.



(b) Using mesh analysis, find loop currents.

10. Determine the power consumed by 10Ω resistor in the circuit by nodal method analysis.



UNIT-II

NETWORK REDUCTION AND NETWORK THEOREMS FOR DC & AC

CIRCUITS

PART A

1. Determine the current flowing through the resistors R1 and R3 if current through R2 is 1A.

2. Write the objective of star delta transformation.

3. State the voltage division principle for two resistors in series and the current division

principle for two resistors in parallel.

4. Given a delta circuit having resistors, write the required expressions to transform the

circuit to a star circuit.

5. Given a star circuit having resistors, write the required expressions to transform the circuit

to a delta circuit.

6. Three equal value resistors of value 5Ω are connected in star configuration. What is the

resistance in one of the arms of equivalent delta network?

7. State Thevenin’s theorem.

8. State Norton’s theorem.

9. Explain the concept of current division in a circuit.

10. Write the importance of source transformation and convert the practical voltage source

into current source.

11. Three resistors A,B and C are connected in parallel and takes 2.5 A,IB=2IC Calculate(a) IB

and IC (b)the line voltage and (c)RB and RC.

12. State Linearity principle theorem.

13. State Maximum power transfer theorem.

14. Define Reciprocity theorem.

15. Determine the maximum power that can be delivered by a 10V battery with an internal

resistance of 1 Ω.



16. What is the condition for maximum power transfer in D.C.and A.C.circuits?

17. Calculate the value of RL,so that maximum power is transferred to load.

18. Is reciprocity theorem applied to the circuit having resistors, capacitors and diodes? Give

your reason.

19.Using superposition theorem ,find i in the circuit.

20. Write down the steps to solve the circuit using Norton’s theorem.

PART-B

1.Obtain Thevenin,s equivalent circuit

.



2.Obtain Norton’s equivalent circuit

3. Using source transformation, replace the current source in the circuit shown below by a

voltage source and find the current delivered by the 50V source.

4. Convert the network shown below into an equivalent π-connected circuit.

5. Use source transformation, find the current through 1Ω resistor.



6.i) Find the current in branch AB having resistor in the given network using Thevenin's

theorem.

ii) ) Find the voltage drop across 12Ω resistor using Norton's theorem.

7. Obtain Thevenin's and Norton's equivalent between the terminals A and B and Calculate voltage drop across RL in the circuit.

8.i) Derive the expression for conversion of star into delta and delta into star with neat diagram.

ii)Use star to delta transformation to find resistance between terminals A and B.



9.i)For the circuit shown below, determine the voltage across (2+j5) Ω impedance by using

Superposition theorem.

ii) Prove that, in a pure resistive circuit,RL=RTh using Maximum power transfer theorem.

10. Determine the maximum power delivered to the load impedance ZL in the circuit shown

below.



UNIT-III

RESONANCE AND COUPLED CIRCUITS

PART-A

1. When do you say that a given AC circuit is at resonance?

2. Give the equation which relates self inductance, mutual inductance and coefficient of

coupling.

3. Two inductively coupled coils have L1=50mH and L2=200mH. If the coefficient of

coupling is 0.5. compute the value of mutual inductance between the coils.

4. In a series RLC circuit if the value of L and C are 100µH and 0.1µF respectively, find the

resonance frequency in Hz.

5. What is meant by coupling coefficient?

6. Define the term quality factor and State the significance of it .

7. State Dot rule for coupled circuits.

8. When the power is maximum in the series resonance circuits? Why ?

9. Define resonant frequency in terms of half power frequencies.

10. What is the range of frequencies for which the effective impedance is (a) capacitive (b)

inductive, in a series resonance circuit.

11. Define self inductance and mutual inductance.

12. What is the maximum possible mutual inductance of two inductively coupled circuits

with self inductance L1=25mH and L2=100mH.

13. What is a tuned circuit? Give its applications.

14. A coil is represented by a series of combination of L=50mH and R=15Ω. Calculate

quality factor at 10 KHz.

15. How are the applied voltage and resulting current of a series resonant circuit related in a

phasor diagram?

16. Compare the properties of series and parallel resonant circuits.

17. A circuit with a resistor, inductor and capacitor in series in resonance at fr –Hz. If all the

component values are now doubled, determine the new resonant frequency.

18. Calculate the resonant freq and quality factor for the circuit shown

100uF 90Ω

10 Ω

5H



19. For the circuit shown, find the voltage across the terminals A and B if the current changes

at the rate of

100A/s

20. Calculate the value of effective inductance for the circuit shown.

PART-B

1. Derive the expression for resonant frequency of a series RLC circuit.

2. (a) For the circuit shown determine the value of Rc for which the given parallel circuit

resonates.

(b) A series RLC circuit with R=10 Ω, L=10mH and C=1uF has an applied voltage of

200V at resonance frequency. Calculate the resonant frequency, the current in the circuit

and voltage across the elements at resonance. Find also the quality factor and bandwidth

for the circuit

RC -j12.5Ω

3Ω j12Ω

.

L2=2H

L1=1H

M=0.5H

B A

I

L2=2H . .

L1=1H M=2H



3. (a) The signal voltage in the circuit shown below is e(t) =0.01sin(2π455x10e3t)V. What

should be the value of C in order that the circuit would resonate at this signal frequency?

At this condition, find the values of I, Vc, Q and bandwidth of the circuit.

(b) (RL+j20)Ω and (20-j10)Ω are connected in parallel. Determine the value of RL for

resonance.

4. For the circuit shown, derive the expression for resonant frequency.

5. A series circuit with R=10 Ω, L=0.1H and C=50uF has an applied voltage V=50∟0 V

with variable frequency. Find (1) the resonant frequency (2) the values of frequency at

which maximum voltage occurs across inductor (3) the values of frequency at which

maximum voltage occurs across capacitor (4) the quality factor of the coil.

6. (a) For a parallel RLC circuit, discuss about the variation of impedance, voltage and

current with respect to frequency. Also derive the expression for quality factor and

bandwidth of the circuit.

(b) For the circuit shown determine the impedance at resonant frequency, 10Hz above

resonant frequency and 10Hz below resonant frequency.

7. In the coupled circuit shown below find the voltage across 5Ω resistor.

RC

C

RL

L

V

e

+

0.9Ω 15µH C

10Ω 0.1H 10µF

VS

50∠0

V

5Ω

-j4Ω

3Ω

j5Ω

j10Ω

I1 I2

K=0.8

Ω



8. (a) State dot rule for coupled circuits. Using this determine the equivalent reactance of the

coupled circuit shown in figure.

(b) For the coupled circuit shown in figure find the ratio V2/V1 which results in zero

current I1.

9. (a) In the circuit shown in figure, find the value of I1 and I2 and also the real power

supplied by each source.

(b) Calculate the voltage V for the coupled circuit shown. Repeat with the polarity of one

coil reversed.

10. Derive the relationship between self inductance, mutual inductance and coefficient of

coupling.

j3Ω j2Ω

j3Ω

j6Ω j5Ω

j4Ω

2Ω 5Ω

j2Ω

j2Ω

j2Ω

j2Ω

V2

+

-

V1

+

- I1 I2

4Ω 4Ω

j8Ω

j4Ω

j4Ω

j2Ω

I1 120∠0 V I1 120∠90 V

50∠0 V 5Ω

-j4Ω

3Ω

j5Ω

j10Ω

I1 I2

K=0.8

Ω

V

+

-



UNIT-IV

TRANSIENT RESPONSE FOR DC CIRCUITS

PART A

1. What is a Step function?

2. What is an initial condition?

3. What is a transient? Define the term time constant of a transient response.

4. What is steady state value?.

5. Define a time constant of a RC circuit.

6. Distinguish between free and forced response.

7. What is meant by Critical damping?

8.. Sketch the current given by I (t) = 5 – 4 e-20 t

.

9.Draw the equivalent circuit at t=0+ for a capacitor with initial charge of of q0.

10. Draw the equivalent circuit for inductor and capacitor at t=0+ when there is no initial

energy

11. Sketch the response of RC network for a unit step input.

12. Find the time constant of RL circuit having R=10Ω, L= 0.1 mH.

13. A coil having a resistance of 10 KΩ and inductance of 50mH is connected to a 10

volts,10KHz power

supply. Calculate the impedance.

14. A RLC series circuit has R=10Ω. L=2H. What value of capacitance will make the circuit

critically damped?

15. In a series RLC circuit, L=2H and C= 5uF. Determine the value of R to give critical

damping.

16. Distinguish between transient response and steady state response of a circuit.

17. A series RL circuit with R=10Ω and L=1H, has a 100 V source applied at t=0. Find the

current for t>0.

18. What is the condition to be present in a series RLC circuit to make the circuit critically

damped?

19. A series RL with R=100Ω and L=20H has a dc voltage of 200V applied through a switch

at t=0. Assuming the initial current through the inductor at t=0 is zero, find the current at

t=0.5sec.



20. Consider two cases of RC parallel circuit. First case when DC voltage is applied and

second case when AC voltage is applies. Compare how the capacitor gets charged in two

cases.

PART-B

1. Derive the step responses of RL and RC circuits. Compare their performances.

2. Derive the expression for current response of RLC series circuit with sinusoidal excitation.

Assume that the circuit is working in critical damping condition.

3. In the circuit given, the switch has been in position 1 for sufficient time to establish steady

state conditions. The switch is then moved to position 2. Find the current transient.

4. Derive the expression for current transient when series RL circuit is excited by a sinusoidal

source v=Vm (sin ωt) at t=0.

5. A series RLC circuit with R=50Ω, L=0.1H and C=50uF as a voltage of 100V applied to it

at t=0 through a switch. Find the expression for a current transient. Assume initially relaxed

circuit conditions.

6. In the circuit shown find the expression for current if the switch is closed at t=0 and the

value of current at t= 1ms. Assume initial charge on the capacitor is zero.

7. In the circuit shown find the expression for current if the switch is closed at t=0 and the

value of current at t= 1ms. Assume initial charge on the capacitor is zero.



8. Find the Z parameters for the circuit shown in fig.

9. Find Y parameters of network shown in fig.

10. Find the h parameters of the network shown in fig

UNIT-V

THREE PHASE CIRCUITS

PART-A

1. What is the difference between balanced and unbalanced circuits?

2. In the measurement of three phase power using two wattmeter method, when both the

wattmeter read same values, what is the value of power factor of the load?



3. Write the types of unbalanced load?

4. What are the main objectives of interconnection of the phases?

5. What are the types of interconnections?

6. Write the relation between phase voltage and line voltage in star connected system.

7. Write the relation between phase voltage and line voltage in delta connected system.

8. Write the condition for balanced star connected load

9. Draw the circuit diagram for balanced delta connected load

10. What are the four methods can be analyzed in unbalanced star connected load

11. Define three phase balance load

12. Explain balance supply system

13. Three inductive coils each having resistance of 16 ohm and reactance of j12ohm are

connected in start across 400V,3 phase, 50Hz supply. Calculated phase voltage.

14. A three phase motor can be regarded as balanced Y load. A three phase motor draws\

6.6kW when the line voltage is 220V and the line current is 18.2A.Determine the

power factor of the motor.

15. In two wattmeter power measurement method, if one wattmeter reads zero, what will

be the power factor of the circuit

16. What are the advantages of three phase system.

17. In a three phase balanced delta system, the voltage across R and Y is

400∟0˚V.What will be the voltage across Y and B? Assume RYB phase sequence.

18. Calculate the power factor if V(t)=Vmsinωt and i(t)=Im sin(ωt-45˚)?

19. Three inductive coils each having resistance of 16 ohm and reactance of j12ohm are

connected in start across 400V,3 phase, 50Hz supply. Calculated phase voltage.

20. A balanced star connected load of (3-j4ohm) impendence is connected to 400 V three

phase supply. What is the real power consumed?

PART-B

1. Explain three phase power measurement by 2 wattmeter method for star and delta

connected load and determine the power equation and draw the phasor diagram.

(16)

2. (a)Two wattmeter methods is used to measure power in a 3 phase load, the wattmeter

readings are 400 W and -35 W .Calculate (i) total active power (ii) power factor and

(iii) reactive power . (8)



(b) Derive the expression for balanced delta connected load and draw the phasor

diagram. (8)

3. (a) A balanced star connected load of (3-j4) Ω impedance is connected to 400 v three

phase supply. What is the real power consumed? (8)

(b) Derive the expression for balanced star connected load and draw the phaser

diagram. (8)

4. A balanced delta connected load takes a line current of 15 A when connected to a

balanced 3 phase 400 v system. A wattmeter with its current coil in one line and

Potential coil between the two remaining lines read 2000W. Describes the load

Impedance.

5. The two wattmeter methods produces wattmeter readings P1=1560W and P2=2100W

When connected to delta connected load. If the line voltage is 220V, Calculate (1) the

per phase average power (2) the per phase reactive power. (3) the power factor (4) the

phasor impedance.

6. Obtain the readings of two wattmeters connected to a three phase three wire 120V

system feeding a balanced delta connected load with load impedance of 12∟30˚Ω.

Assume either phase sequence. Find the phase power and compare the total power to

the sum of the wattmeter readings

7. A three phase four wire 120V ABC system feeds an unbalanced Y-connected load

with ZA=5∟0˚Ω, ZB=10∟30˚Ω and ZA=20∟60˚Ω.Obtain four line currents

8. Determine the line currents, power factor and total power when a 3 phase 400V

supply is given to a balanced load of impedance (8+j6) ohm in each branch is

connected in Star.

9. 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 15KVAR

and the load power factor is 0.8.Also compute load KVA

10. A balanced abc-sequence Y-connected source with Van=100∟10˚V is connected to

delta connected balanced load (8+j4) ohm per phase. Calculate the phase and line

currents.



EE6201 CIRCUIT THEORY (COMMON TO EEE,ECE,EIE) QUESTION ...

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