circuit theory - sri eshwar college of engineering · web viewohm’s law states the current...

Circuit Theory

Two Mark Question Bank

Question Bank – Circuit theory

UNIT – IBASIC CIRCUITS ANALYSIS

1. State Ohm’s Law.Ohm’s law states the current flowing through a conductor is directly

proportional to the voltage applied across that conductor at constant temperature.I ∞V

I=VR

2. What are the limitations of Ohm’s Law?i) It is not applicable to the nonlinear devices like diodes, zener diodes,

voltage regulators etc.ii) It does not hold good for non-metallic conductors such as silicon carbide.iii) It does not hold good for variable temperatures.

3. State Kirchoff’s laws.Current Law:

KCL states that the algebraic sum of the currents entering into a node or a junction is equal to the algebraic sum of currents leaving from that node.

In other words, the algebraic sum of currents at any node is equal to zero.Voltage Law:

KVL states that the algebraic sum of branch voltages around any closed path or loop is zero.

In other words, the algebraic sum of voltage rise is equal to the algebraic sum voltage drops around any closed loop.

4. What are active & passive elements?The elements which are capable of delivering power to the external devices are

called active elements. Example: Voltage & Current sources.The elements which are capable only of receiving power are called passive

elements. Example: Resistors, Capacitors & Inductors.5. What are independent & dependent sources?

The sources whose voltage & currents are not affected by the other parts of the circuit are called Independent Sources

The sources whose voltage & currents are not fixed and they dependent upon the voltage or current existing at some other part of the circuit are called Dependent Sources6. Define lumped & distributed elements

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Physically separable elements such as resistors, capacitors & inductors are called lumped elements.

The elements which are not separable for electrical purposes are called distributed elements. Example: Transmission line7. What are bilateral & unilateral elements?

The element in which the voltage – current relationship is same for the current flowing in either direction is called a bilateral element.

The element which has different voltage – current relationship for the different current direction is called a unilateral element.8. Distinguish between ideal & practical source

In an ideal voltage source, the internal resistance is assumed zero. But a practical voltage source consists of internal resistance.

The terminal voltage of ideal voltage source is constant & independent on the current. But the terminal voltage of practical voltage source varies with respect to its internal resistance.9. Find the equivalent resistance between A & B

Equivalent resistance between A & B,

RAB=[ (1 x1 )(1+1 )

+0.5]1RAB=[ (1 x1 )

(1+1 ) ]=0.5Ω10. Three fans are connected in parallel across 200 V. Each fan is rated at

100 W, 110 W & 120 W respectively. How much current flows through each fan & what is the total current?We know that, Power P = V x I.

I = P/VCurrent flowing through Fan 1 = 100 / 200 = 0.5 ACurrent flowing through Fan 2 = 110 / 200 = 0.55 ACurrent flowing through Fan 3 = 120 / 200 = 0.6 AThe total current is = 1.65 AVoltage across 12 Ω resistance = 12.16 x 12 = 146 V

11. Two capacitors C1 & C2 are connected in series. If C1 = 12 µF and equivalent capacitance is 3.33 µF, find C2.

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We know that the equivalent capacitance of two capacitors connected in series is,

C eq=C1C2

C1+C2

3.33=12C2

12+C2

C2=4.67 µF

12. Define Impedance.Impedance is the measure of the opposition that a circuit presents to the

passage of AC current when a voltage is applied. It is the vector sum of resistance & reactance expressed in Ohms.

Z=√R2+X2

13. A resistance R is connected in series with a parallel circuit comprising two resistances of 12 Ω and 8Ω. Total power dissipated in the circuit is 700 W when the applied voltage is 200V. Find the value of R.

The equivalent resistance of the circuit is,

Req=V 2

P=200

2

700=57.14Ω

Therefore,

57.14=( 12 x812+8 )+RR=52.34Ω

14. A resistance 100 Ω & capacitance –j150 Ω are connected in series. The applied voltage is 50 V. Determine the power factor.

Power Factor ,cosθ=RZ

Z=√R2+X2

Z=√1002+502Z=111.8Ω

cosθ= 100111.8

=0.894

15. Find the value of I in the figure shown below.

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Applying KCL at the node, 2 + (-3) + 5 = (-2) + I.Therefore, I = 6 A

16. Two circuits A & B are connected in parallel across 200 V, 50 Hz supply. Circuit A consists of 10 Ω resistance & 0.12 H inductance in series while circuit B consists of 20Ω resistance & 40 µF capacitance. Calculate the current in each branch.

X L=2πfL=2π∗50∗0.12=37.68Ω

Impedanceof branch A=√R2+XL2=√102+37.682=38.98Ω

Current∈branch A= 20038.98

=5.13 A

XC=1

2 πfC= 12 π∗50∗40∗10−6=79.6Ω

Current∈branchB= 20079.6

=2.51 A

17. Define power. What is the relation between power, voltage & current?Power is defined as the rate of doing a work or rate of change of energy. Its

unit is watts. One watt is the amount of power generated when one joule of energy is consumed in one second.

Power , P=V x I

18. Draw the power triangle & mention each side of it.

19. A voltage divider circuit of two resistors is designed with a total resistance of the two resistors equal to 50 Ω. If the voltage across one of the resistors is 10% of the input voltage, find the values of two resistors.

Totalresistance=R1+R2

Voltageacross R1=V i( R1R1+R2 )= 10

100V i

V i

R150

= 10100

V i

R1=5Ω∧R2=45Ω

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20. A 25 Ω resistance has a voltage V = 150 sin 377 t volts. Find the corresponding current & power.

Current=V rms

R

Current=

V m

√2R

=

150√225

=4.24 A

Power=I2 R=4.242∗25=450W

21. An Incandescent lamp is rated as 230 V, 230 W. Find the rated current & resistance of the filament.

Current through thelamp , I= PV

=230230

=1 A

Resistanceof the filament ,R=VI=2301

=230Ω

22. Define mesh analysis of a circuit.Mesh analysis is one of the methods to solve linear two terminal circuits. In this

analysis, kirchoff’s voltage equation is written for as many currents as the number of independent loops.23. Define form factor. What is the value of it in the case of sinusoidal

voltage?Form factor of a waveform is defined as the ratio of rms value to the average

value of the wave.

Formfactor=V rms

V avg

Formfactor of sine wave=

V m

√22V m

π

=1.11

24. Determine the current flowing a branch whose impedance is (3 + j4) Ω when a voltage of 200 V is applied.

Impedance=√R2+X2=√32+42=¿5Ω ¿

Current=VZ

=2005

=40 A

25. Write the current division rule.Current division rue is applied to a parallel circuit to find the current in each

branch.

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Current∈abranch=Incomingcurrent x Opposite ResistanceTotal Resistance

I 1=I S XR2

R1+R226. Draw the V – I characteristics of Ideal source.

27. The resistance of two wires is 25 Ω when connected in series & 6 Ω when connected in parallel. Calculate the resistance of each wire.

¿ series ,R1+R2=25−−−−−−−1

¿∥,R1 .R2R1+R2

=6

R1 . R225

=6

R1 .R2=150

R1=150R2

−−−−−−2

Substitute equation 2 in equation 1, 150R2

+R2=25

R2=15Ω∧R1=10Ω

28. A series RLC circuit has R = 25 Ω, L = 0.221 H & C = 66.3 µF with a frequency of 60 Hz. Find the power factor.

Power factor=RZ

Z=√R2+ (X L−XC )2

X L=2π fL=2∗3.14∗50∗0.221=83.27Ω7


XC=1

2 π fC= 12π∗60∗66.3∗10−6=2653Ω

Z=√252+ (83.27−2653 )2=2570Ω

Power factor= 252570

=¿

29. Determine the current through 1Ω & 4Ω resistor of the circuit shown below.

Current through10Ωresistor=1010

=1 A

Current through1Ωresistor=1∗41+4

=0.8 A

Current through4Ωresistor= 1∗11+4

=0.2 A

30. Write the equations of energy stored by an inductor and capacitor

Energy stored by an inductor is, W = LI2 / 2I is the Current flow through the inductor

Energy stored by a capacitor W = CV2 / 2V is the Voltage across capacitor

31. Define RMS voltage.It is defined as the DC equivalent of AC voltage that produces same heating

effect.32. Distinguish between mesh and loop of an electric circuit.

Mesh: It has got only one closed path.Loop: It has more than one closed path. It is a combination of meshes.

33. How are the following affected by the change of frequency?(a) Resistance(b) Inductive reactance

Resistance does not change with change in frequency.Inductive reactance changes directly proportional to the frequency.

34. Define nodal analysis of a circuit.

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It is method of analyzing an electric circuit where nodes are identified and equations at each node are written by applying Kirchhoff’s current law. Nodal analysis is used for analyzing the circuits having more number of current sources.

35. An electrical appliance consumes 1.2kWh in 30 mins at 120V. What is the current drawn by the appliance?

Current , I=1.2×10000.5×120

=20 A

UNIT – IINETWORK REDUCTION & NETWORK THEOREMS FOR DC & AC CIRCUITS

1. State Thevenin’s theoremAny linear two terminal network having number of voltage sources, current

sources & resistances can be replaced by an equivalent circuit consists of a voltage source and a resistor in series with it.

2. State Norton’s theorem.Any linear two terminal network having number of voltage sources, current

sources & resistances can be replaced by an equivalent circuit consists of a current source and a resistor in parallel with it.

3. State Superposition theorem.In any linear two terminal network having more than one source, the response

in any element is equal to the algebraic sum of the responses caused by individual sources acting alone with other sources non operative.

4. State Maximum Power Transfer theoremIn any linear two terminal network, the maximum power is delivered to the

load when the load resistance is equal to the source resistance (or thevenin’s resistance).

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5. State Reciprocity theoremIn any linear bilateral network, the ratio of response to excitation is same even

if the response & excitation are interchanged.

6. What is the condition for maximum power transfer in AC & DC circuits?In DC circuits

Load resistance should be equal to source or thevenin’s resistance. i.e RL

= RS

In AC circuitsLoad impedance should be equal to conjugate of source impedance.

7. Find the equivalent current source for the network shown below

8. Transform the given delta network into star network

9. Calculate the value of RL so that maximum power is delivered to the load

RTH=10∗1010+10

=5Ω

Therefore, RL should be equal to RTH = 5 Ω for the maximum power to be transferred to the load

10. Calculate the current through 50 Ω & 100 Ω resistors in the circuit shown below

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Equivalent resistanceof the circuit is=100∗50100+50

+4=37.33Ω

Current delivered by the10V source= 1037.33

=0.2679amps

Current through100Ωresistor=0.2679∗50100+50

=0.08929amps

Current through50Ωresistor=0.2679∗100100+50

=0.1786amps

11. Why do you short circuit the voltage source and open circuit the current source when you find Thevenin’s resistance of a network?

To find Thevenin’s resistance, it is required to replace the voltage and current sources by their internal impedances. The internal impedance of voltage is zero and hence it is short circuited (impedance is zero in short circuit). The internal impedance of current source is infinity and hence it is open circuited.

12. State the voltage division principle for two resistors in series.

V R1=Applied voltage× Same resistanceTotalresistance

V 4 Ω=10×4

100+4=0.38V

13. State the current division principle for two resistors in parallel.Current division rue is applied to a parallel circuit to find the current in each branch.

Current∈abranch=Incomingcurrent x Opposite ResistanceTotal Resistance

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For the circuit shown,

I 1=I S XR2

R1+R2

14.Find the equivalent current source for a voltage source of 100 V with series resistance of 2Ω.

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UNIT – IIIRESONANCE AND COUPLED CIRCUITS

1. Write the condition for resonance in series RLC circuits.

Resonance occurs when a) The inductive reactance is equal to the capacitive reactance,b) The circuit is purely resistive. i.e Z = R,c) The power factor of the circuit is unity,d) The current in the circuit is maximum

2. Define Bandwidth of a resonant circuit.

It is the range of frequencies for which the value of current is 70.7 % of its value at resonance.

3. Define quality (Q) factor.

It is the ratio of reactance to the resistance of a coil. The quality factor (or Q) of an inductor is the ratio of its inductive reactance to its resistance at a given frequency, and is a measure of its efficiency. The higher the Q factor of the inductor, the closer it approaches the behavior of an ideal, lossless, inductor.

4. What is effect of Q factor on band width?

Bandwidth of a resonant circuit is less when the Q factor is more and the bandwidth is wide when the Q factor is small.

5. Give any two comparisons how the circuits respond during series and parallel resonance.

Series Resonance Parallel ResonanceResonance occurs when XL = XC

i.e Z = RResonance occurs when B = 0i.e Y = 1 / R

Impedance at resonance is minimumZ = R

Impedance at resonance is maximumZ = L/CR

Current is maximum Voltage is maximumIt magnifies voltage It magnifies current

6. A series RLC circuit with Q = 250 is resonant at 1.5 MHz. Find the frequencies at half power points and bandwidth.

B.W = fr/Q = 1.5 x 106/ 250 = 6000 Hzf1 = 1.5 MHz – 3000 Hz = 1.2 MHzf2 = 1.5 MHz + 3000 Hz = 1.8 MHz

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7. What is selectivity of a resonant circuit?

Selectivity of a resonant circuit is its ability to differentiate between the signals having desired frequency and the undesired signals

8. Define resonant frequency in term of half power frequencies.

f r=f 1+R4 πL

f r=f 2−R4 πL

9. What are the half power frequencies?

The frequencies at which the power is half of the value at resonance are called half power frequencies.

10. Define Self Inductance

It’s the ability of one coil to produce emf in the same coil when it is excited by a voltage.

Self-inductance of a coil is defined as the Weber turns in one coil per ampere current in the same coil. Its measured in henrys.

11. Define Mutual Inductance

It’s the ability of one coil to produce emf in the other coil when they are kept in close proximity.

Mutual inductance between two coils is defined as the Weber turns in one coil per ampere current in the other coil. It is measured in henrys.

12. Find the maximum possible value of mutual inductance of two inductively coupled coils with self-inductance L1 = 25 mH & L2 = 100 mH

The maximum possible mutual inductance can be obtained when K = 1.Mmax=K √L1L2

Mmax=1√25∗10−3∗100∗10−3

Mmax=50mH

13. Define co-efficient of coupling

The amount of coupling between the two coupled coils is expressed in terms of coefficient of coupling.

K= M√L1L2

14. State dot rule for coupled circuit14


It states that if a current enters the dotted terminal of one coil, then the emf induced in the second coil will be positive at its dotted terminal.

15. What are the types of tuned circuits and where it is used?

a) Single tuned circuitsb) Double tuned circuits

16. What is meant by ideal transformer?

Ideal Transformer is characterized by assuminga. Zero power dissipation in the primary & secondary windingsb. The self-inductances of primary & secondary are extremely largec. The coefficient of coupling is unity

17. Two coupled coils L1 = 0.9H, L2 = 2.5H having a coupling coefficient k=0.8. Find the mutual inductance M and turns ratio N2/N1.

M=K √L1L2M=0.8√0.9 X 2.5

M=1.2H

18. Determine the quality factor of a coil for the series resonant circuit consisting of R = 10Ω, L = 0.1 H and C = 10µF.

19. Give the applications of tuned circuits.

RF amplifiers

UNIT – IVTRANSIENT RESPONSE FOR DC AND AC CIRCUITS

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1. Define transient time

The time taken for the circuit to change from one steady state to other steady state is called transient time. Time taken by the current to reach its final value from initial value.

2. Compare steady state & transient response

A circuit having constant sources is said to be in steady state if the voltage & current do not change with time.

The response of a network when the voltage or current change from one state to the other is called transient state response

3. Write the transient current equation of series RL & series RC networks applied with step voltage of V volts

Transient current equation for RL circuit is,

i (t )=VR

(1−e−RL t )

Transient current equation for RC circuit is,

i (t )=VR

(e−tRC )

4. What is the significance of initial condition? Write a short note on initial condition for the basic circuit elements.

Initial conditions of a network are the values of current & voltages just before switching.

5. Define damping ratio of RLC circuit

The ratio of resistance in the circuit to the resistance for critical damping is called damping ratio.

6. What is the condition to be present in a series RLC circuit to make the circuit critically damped?

Condition for critical damping is,

( R2L )

2

= 1LC

7. How does the capacitor act at t = 0 and t = ∞

A capacitor will act as a short circuit at t = 0+ and will act as open circuit at t = ∞.

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8. How does an inductor act at t = 0 and t = ∞

An inductor will act as open circuit at t = 0+ and will act as a short circuit at t = ∞.

9. A series RL circuit with R = 100 Ω & L = 20 H has a DC voltage of 200 V is applied through a switch at t = 0. Assuming the initial current through the inductor at t = 0 is zero, find the current at t = 0.5 sec.

The transient current equation for RL circuit is,

i (t )=VR

(1−e−RL t )

i (t )=200100

(1−e−10020 t )=5 (1−e−5 t)

Current at t=0.5 sec is,i (t )=5 (1−e−5×0.5 )

i=1.83 A

10. Define time constant of transient response

The time constant of RL series circuit is defined as the period during which the current rises to 63.22% of its final value.

The time constant of RC series circuit is defined as the period during which the current falls to 36.8% of initial current.

11. Write the time constant for RL and RC network.

Time constant for RL, τ = L / RTime constant for RC, τ = RC

12. What is meant by zero input response or free response or natural response?

When a circuit contains storage elements which are independent of the sources, the response depends on the nature of the circuit. Therefore, the response due to the internal energy stored in the passive elements in the circuit is called natural or free or zero input response.

13. What is meant by forced response?

When a circuit contains active elements (sources), the response is due to the nature of those sources. Therefore, the response of a circuit due to application of external energy is called forced response.

14. Compare steady state and transient response.

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A circuit having constant sources is said to be in steady state if the currents & voltages do not vary with time.

In a circuit containing energy storage elements, with change in input, the voltage & current changes from one state to the other. The behavior of the voltage or current when it is changed is called transient state.

15. Draw the transient response of RL and RC network (or) Sketch the transient current i(t) Vs t graph for a series RL circuit.

Transient response of RL Transient response of RC

16. Why transient occurs in electrical circuits?

If a circuit containing one or more energy storage elements (L or C) is excited by a source which abruptly changes its value, the energy state of the circuit is disturbed. This disturbance or transient is due to the variation of storage elements or due to the switching conditions.

The inductance does not allow sudden change in current and the capacitance does not allow sudden change in voltage. Hence in inductive and capacitive circuits transient occurs during switching operation

17. Find the time constant of RL circuit having R = 10 Ω and L = 0.1 H.

τ= LR

=0.110

=10msec

18. An RLC series circuit has R = 10 Ω and L = 2 H. What value of capacitance will make the circuit critically damped?

Condition for critical damping is,

( R2L )

2

= 1LC

R2

4 L= 1C

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C=4 LR2

=4×2102

=0.08 F

UNIT – VANALYSING THREE PHASE CIRCUITS

1. A 3Φ balanced star connected load has 500 V line to line voltage & 10 A line current. Determine the phase voltage & phase current.

In star network,

V ph=V L

√3=500

√3=289volts

I ph=I L=10amps

2. A 3Φ balanced delta connected load has 500 V line to line voltage and 10 A line current. Determine the phase voltage and phase current.

In Delta network,

I ph=I L

√3= 10

√3=5.77amps

V ph=V L=500volts

3. Draw the phasor diagram of phase & line voltage & currents in a balanced delta connected load.

4. Draw the phasor diagram of phase & line voltage & currents in a balanced star connected load

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5. Write the expression for power factor in a balanced 3Φ circuit

Power factor=cos [ tan−1√3(W 1−W 2

W 1+W 2 ) ]6. Compare balanced and unbalanced network

Let the three phase circuit consists of loads Z1, Z2 & Z3. If all the loads are equal both in magnitude & phase angle and connected to a balanced supply, it is called a balanced network.

If all the loads are different, it is called an unbalanced network even if the supply system is balanced.

7. State the advantages of three phase system.a. All electric power generated and distributed is in 3 Φ, 50 HZ. So when 1 Φ or

2 Φ supply is required, they can be taken from 3 Φ system rather than generating independently.

b. For the same amount of power to be produced, the 3 Φ system is more economical than 1 Φ system.

c. 3 Φ motors are easily started than 1 Φ motors.d. 3 Φ motor or 3 Φ generator produces more output than 1Φ motor or 1 Φ

generator.e. To transmit a given amount of power over a given length, 3 Φ transmission

circuit requires less conductor size than 1 Φ system.8. What will be the readings of the two wattmeters used for the

measurement of power in a three phase circuit at unity power factor?

W 1=√32

V L I L

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W 2=√32V L I L

i.e Both the wattmeters readings are equal and each will read half of the total power

9. Write the relation between phase & line quantities in a delta connected system

In Delta network,I L=√3 I phV ph=V L

10. Write the relation between phase & line quantities in a delta connected system

In star network,V L=√3V ph

I ph=I L11. When do the two wattmeters read equal in the two wattmeter method

of three phase power measurement?Both the wattmeters in the two wattmeter method of power measurement will

read equal values when the power factor is unity.

12. How can a wattmeter be used to measure reactive power?In case of balanced 3 Φ circuit, the reactive power can be determined by using

one wattmeter. The current coil of the wattmeter is connected in one line and its pressure coil is connected across the other two lines.

Let the reading of wattmeter be Wr,Then thetotal reactive power=√3W r

13. When does one wattmeter read zero in two wattmeter method of 3 Φ power measurement?

One of the wattmeter read zero in two wattmeter method of 3 Φ power measurement when the power factor is 0.5.

14. Give the expression for three phase power in terms of line valuesTotal average power=√3V L I LcosΦ

Where VL = Line voltage,IL = Line current,Cos Φ = Power factor

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15. A 3 – phase 440 V supply is given to a balanced star connected load of impedance (6 – j8) Ω in each branch. Find the magnitude of the line current.

16. Define power factor of a circuit.It is the cosine of the angle between current and voltage in a circuit. It is also

the ratio of real power to apparent power in a circuit.17. What is phase sequence of a 3-phase system?

Phase sequence in a 3 phase system is the order in which the three voltages reach their peak value. The two possible phase sequences are RYB and RBY.

18. A delta connected load has (30 – j 40) Ω impedance per phase. Determine the phase current if it is connected to a 415 V, 3 phase, 50 Hz supply.

I ph=V ph

30− j 40= 41530− j 40

=4.98+ j 6.64

I ph=8.3 A

19. Write the effect of power factor in energy consumption billing.A penalty in terms of money for any decrease in p.f below a certain value will

be posed to the consumers by the electricity board.

20. Distinguish between unbalanced source and balanced load.Unbalanced source: All the three voltages will have different magnitudes and are displaced unequal angles.Balanced load: Loads connected to all the phases are equal and draw same currents.

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circuit theory - sri eshwar college of engineering · web viewohm’s law states the current...

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