DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING147201 –ELECTRIC CIRCUITS AND ELECTRON DEVICES (ELECTRICAL)

QUESTION BANK (Common to ECE, CSE, IT)

UNIT I - CIRCUIT ANALYSIS TECHNIQUES

PART A

1. Define active and passive element.The elements which can deliver energy are called active elements. E.g.: Voltage source

and current source. The elements which consume energy either by absorbing or storing are called passive elements. E.g. Resistor, Inductor and Capacitor

2. How much energy does a 100W electric bulb consume in two hours? Power = Energy Time Energy = P x t = 100*2*3600 = 720000 = 720 KJ

3. Define series and parallel connection.If two or more elements are connected such that the current through them are same, then

the connection is called series connection.If two or more elements are connected such that the voltage across them is same then the

connection is called parallel connection.

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 p- Power 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. 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*10 3 = 16.67 s Power p 120*15

6. What is an ideal and practical independent source? Give the circuit symbols.

1

An ideal independent source is an active element that provides a specified voltage or current that is completely independent of other circuit elements.

a. Constant current b. Constant Current c. Time varying d. Constant or Time Source Source current source varying voltage

Fig.1 Ideal independent sources

7. State Ohm’s law.Ohm’s law states that, at constant temperature, current passing through the conductor is directly proportional to potential difference between two ends of the conductor.

i.e., i α v , i = V/R, where R is the resistance (Ω).

8. Draw the characteristics of ideal and practical voltage sources.

9. Draw the characteristics of ideal and practical current sources.

VI

VI

+

-

E(V)

I (A)

Ideal

Practical

2

Is

(A)

V (V)

Ideal

10. 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 π t = 4 sin πt ,mA 5*103

P = v i = 80 sin2 πt ,mW 11. State Kirchoff’s current and voltage laws. 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 towards a node is equal to the sum of the currents leaving from the node.

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

12. 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, C: v=1/C ∫i dt

13. Find V3 and its polarity if the current in the circuit of Fig.3 is 0.40 A.

Fig.3Assume that V3 has the same polarity as V1

Applying KVL and starting from the lower left corners,V1-5I-V2-20I+V3 = 050-2-10-8+V3 = 0V3 = -30V

Terminal b is positive with respect to terminal a.14. Find the voltage between A& B in a voltage divider network shown in Fig.4.

3

Practical

1 K

5 K4 K

A

B100

+

-

Fig.4Voltage between A & B,

VAB= (5+4) *100 = 90V (5+4+1)

15. Determine the equivalent inductance of the three parallel inductors shown in Fig.5

Fig.5

1/Leq = 1/L1+1/L2+1/L3 = 1/10+1/20+1/20 = 5 mH

16. Convert the voltage sources shown in fig to current source.

E = 20v, Rs = 5 ΩIs = E/R = 20/5 =4 A

17. A 10A current source has a source resistance of 100ohm. What will be the equivalent voltage source?

A

B

5

20 V

+

-4 A 5

A

B

4

V =IR = 10 x 100 = 1000 V18. What is the equivalent resistance across A – B in the network shown in fig.

19. What will be the length of the copper rod having a cross – section of 1cm2 and a resistance of 1ohm? Take resistivity of copper as 2 x 10-8 ohm –m

20. What will be the inductance of the coil with 1000turns while carrying a current of 2A and producing a flux of 0.5mwb?

N= 1000, φ = 0.5mwb, I = 2AInductance, L = N/I = 1000 X 0.5 X 10-3/2= 0.25H

21. What will be the equivalent inductance across A – B in the network shown in fig.

100

A

B

10 A

A

B

100

1000 V

+

-

A

B

5

6

3

5

Leq = L1 + [L2L3 / (L2+L3)]

22. A steady current of 3A flows through an inductance of 0.2 H. What will be the energy stored in the inductance?

I = 3A, L = 0.2HEnergy stored in the inductance, W = LI2/2 = 0.2 X 32/2 = 0.9 J

23. What will be the equivalent capacitance across A – B in the network given below?

Ceq = (C2 + C3) C1 / (C1 + C2 + C3)

24. A 100microfarad capacitance is charged to a steady voltage of 500V. What is the energy stored in the capacitance?

C = 100μF, V = 500VEnergy stored in capacitance, E = CV2/2 = 100 x 10-6x 5002/2 = 12.5 J

25. Determine the currents I1 and I2 in the circuit as shown in figure.

A

B

C1

C3C2

A

B

6

I1 = Is x = 2.7273 A

I2 = Is – I1 = 2.28 A

26. Determine the voltages V1 and V2 in the circuit shown in fig.

V1 = 10 x = 5 V

V2 = 10 x = 5 V

27. 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

12

10

5 I1

I2

Is=5A

52.273V

5 5

10 V

V1 V2

7

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.

28. 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.

29. 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.

30. 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.

31. State Maximum power transfer theorem.For a given Thevenin’s equivalent circuit, maximum power transfer occurs when

RL = RTH, that is, when the load resistance is equal to the thevenin’s resistance.

32. 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.

8

33. 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.

E.g.: TV/Radio receiver

34. 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.

35. What are the limitations of Thevenin’s Theorem? The limitations of Thevenin’s theorem are,

1. Not applicable to the circuits consisting of nonlinear 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.36. Write down the formulae for converting Star to Delta.

37. Write down the formulae for converting Delta to Star.

COMPLEXACTIVE

NETWORK

A

B

Rth

Isc

A

BB

9

38. Draw the thevenin’s equivalent circuit for the given circuit.

Rth = = 2.5 Ω

I = = 1 A

Vth = V5 Ω = I x 5 = 1x5 = 5V

39. A battery of 120 volts having internal resistance of 2 ohm supplies a load resistor RL through a resistance of 1 ohm resistor in series. Find the value of RL so that the power delivered is maximum.

According to maximum power transformer maximum power will be delivered hen the load resistance equals internal resistance.

Hence RL = internal resistances = 1+2 = 3 Ω.

40. Find the Thevenin’s equivalent resistance for the given circuit.

A

B

5

10 V+

-

I

5

10

A

B

Vth= 5 V+

-

Rth = 2.5

Rth = =

Rth = 0.4545 Ω

PART – B

1) A 18Ω resistor is connected in parallel with a series combination of resistor of 10ohms and 26 ohms. If the drop across the 10 ohms is 50V, find the total applied voltage and the total current.Ans: 180V, 15A

2) Reduce the network of Fig.8 into a single resistance.Ans: R = ¾ = 0.75Ω

3) For the circuit shown in Fig.10, Find a) V1 and V2 b) the Power dissipated in the 3KΩ and 20KΩ resistors and c) the power supplied by the current source.Ans: a) 15V, 20V b) 75mW c) 200mW

4) In the circuit shown in Fig.11, determine vx and the power absorbed by the 12Ω resistor.Ans: 2V, 1.92W

5) Determine the power dissipated by 5 ohm resistor in the circuit shown in fig below.

5

+

-E 1 1

11

Req = + 5 = 10.464 Ω

Is = = 4.995 Ω

P5 Ω = IS2 R = (4.995)2 x 5 = 124.77 W

6) Using source transformation, find the power delivered by the 50V voltage source in the circuit shown in fig.

7) By using source transformation, source combination resistance combination converts the circuit shown in fig. into a single voltage source and single resistance.

20

5

10 Ω

52.273V

Is

30

+ -

2

2

1

2

+

-

+

-

5A

5A

10 V

5 V

12

8) Derive the expression for the energy stored in the capacitor and Inductor.

9) (a) Derive the expression for converting from Star connected resistance to Delta.10) (b)If resistance in each branch of delta is 30Ω, 25Ω and 40Ω, find the resistance in

each branch of star (6)

10) Find the current through the 23Ω resistance using superposition theorem. (16)

11) Find the power dissipated in R in the circuit shown using Norton theorem, if the value of R is 12Ω. (16)

4

2

4

5A

2A

2V

5V

Q P- +

-+

-+

47 Ω

4 Ω

20 A

23 Ω

27 Ω

200VΩ

13

12) Find the power dissipated in R in the circuit shown using thevenin’s theorem, if the value of R is 20Ω. (16)

13(a) Find the equivalent resistance between C and B (10)

13(b) Find the equivalent resistance between A and B (6)

14(a) Find the current through the 3Ω resistor by super position theorem (8)

9 Ω

9 Ω27Ω

27Ω

27ΩA

B

14

14(b) Find the value of R if it receive the maximum power and also find its maximum power. (8)

UNIT IITRANSIENT RESONANCE IN RLC CIRCUITS

PART - A1. 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 reaching 36.8% of the initial value.

3. 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,

4. 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.

5. Define damping ratio. Give the damping ratio of RLC series circuit.

15

For RLC series circuit,

6. Give the natural frequency and damped frequency β of a series RLC circuit.

Natural frequency

Damped frequency =

7. 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.

8. A DC voltage is applied to a series RL circuit by closing a switch. The voltage acrossL 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

9. What is the quality factor of a series RC circuit?Q = ωnL/R = 1 /R L/C

10. Write down the voltage equation of a series RLC circuit excited by a source.

m sin ωt

11. Define the following terms i) sinusoid ii) Time period iii) frequency iv) phasor A sinusoid is a signal that has the form of the sine or cosine functions The time taken for any wave to complete one full cycle is called the time period

(T). The frequency of the wave is defined as the number of cycles that a sine wave

completes in one second. A phasor is complex number that represents the amplitude and phase of a

sinusoid.

16

12. Find the amplitude .phase, time period and frequency of the sinusoid. v(t)=12cos(50t+15º)

We know, v(t)=Vmcos(ω t+Ф) v(t)= 12cos(50t+15º)

ω = 50 rad/sec Amplitude, Vm=12VPhase, Ф=15ºTime period, T=2π/ω = 2π/50 = 0.1257 secFrequency, f = 1/T = 7.958Hz

13. Define RMS value of a sinusoidal current. The effective or RMS value of an alternating current is given by the steady current (DC)

which, when flowing through a given circuit for a given time, produces the same amount of heat as produced by the alternating current which when flowing through the same circuit for the same time.

(Or) It is the effective value of a periodic current that delivers the same average power to a

resistor as the periodic current.

14. A 200volt ,50Hz source supplies a series RC circuit R=30ohms and C=79µF.Find a)the impedance, b)the current, c)power factor d)power

a) Z = (R2+XC2) = (302+402) = 50 ohms Xc = 1/2πfC = 40Ω

b) I = E/Z = 200/50 = 4A c) p.f = cos Ф = R/Z = 30/50 = 0.6 (leading capacitive current) d) Power = EI cos Ф = 200×4×0.6 = 480 watts

15. Find the reactance of a 0.2H inductor at 50Hz frequency, At what frequency is the reactance 500 0hms. XL=2πfL=2π×50×0.2=62.8318 0hms. When XL=500Ω, f’=? 500=2π f’L f’=500/(2π L)=500/(2π ×0.2)=397.887 Ω

16. 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.

17. 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 =

18. What is a resonant frequency? The frequency at which resonance occurs is called resonant frequency i.e. X L=XC.

19. What are the resonant conditions?

17

i) The total impedance Z is minimum and equal to R. ii) The circuit will be purely resistive circuit. iii) Power factor of the circuit is unity. iv) Circuit element, I max = V/R. v) Power at resonance, Pr = I2R.

20. What is the series resonance? The inductive reactance increases as the frequency increases (XL=ωl) but the capacitive reactance 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.

21. 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.

22. Define Bandwidth, selectivity, 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 f1 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 f2 is called upper cut-off frequency while the frequency f1 is called lower cut-off frequency.

The selectivity is defined as the ratio of the resonant frequency to the bandwidth

Selectivity = fr/B.W

23. Show that in a series RLC circuit, f1f2 = fr2 where fr is the resonant frequency and f1, f2

are the half power frequencies.

Hence,

24. What are the classifications of tuned circuits and state the applications of it

1. Single tuned circuits

18

2. Double tuned circuitsDouble tuned circuits are used in radio receivers to produce uniform response to modulated signals over a specified bandwidth; double tuned circuits are very useful in communication system.

Part -B

1. Derive an expression for transient current, voltages and the energy stored in inductor of a RL transient circuit excited by a DC source.Ans:

i (t) = E/R- E/R e-Rt/L = E/R (1- E e-Rt/L ) eR = E(1 - e-Rt/L)eL = Ee-Rt/L ωL = ½ L(E/R )2 = ½ L Iss

2

2. Derive an expression for transient current of a RL .Decay transient excited by a DC source.Ans:

i(t) = E/R e-Rt/L

i(T)= 0.368 E/R = 36.8% of the initial value.

3. A series RL circuit with R = 100 ohms and L =20H has a DC voltage of 200v applied through a switch at t = 0. Find a) the equation for the current and voltage across the different elements, b) the current at t = 0.5 seconds, c) the current at 1 sec and d) the time at which eR =eL.Ans:

i(t) = 2 (1-e-5t ) b) i(t = 0.5) = 1.836 AeR = 200 (1-e-5t) c) i(t =1 ) = 1.987 A

eL = 200 e-5t d) t = 0.1386 sec.

4. Derive the expression for transient current, voltages and the energy stored in the capacitor of a series RC circuit, excited by a DC source.Ans: i(t) = E/R e(-t/RC)

eR = E e-t/RC

eC= E(1- e-t/RC) Wc= ½ CE2

5. Derive the transient current equation of a series RLC transient circuit excited by a DC source.Ans: Case1: Discriminant positive: (R/2L)2>1/LC

i(t) = e αt[K1eβt + K2e- βt], current is overdamped

Case 2: Discriminant zero: (R/2L)2=1/LC

19

i(t) = e αt[K1 t+K2], current is critically damped

Case 3: Discriminant negative: (R/2L)2<1/LC i(t) = e αt[K1ejβt+K2e-j βt], current is under damped

6. A series RLC circuit with R=300ohms, L=1H and C=100µF has a constant voltage of 50V applied to it at t=0.Find the maximum current value .Assume zero initial conditions.Ans: imax=0.1377 A

7. Derive the expression for transient current of the series RL circuit excited by an AC voltage source.Ans: i = Em/(R2+ω2L2) [ e-Rt/L sin(φ-θ) + sin (ω t+φ-θ)] 8. A non-inductive resistance in series with an ideal condenser is connected to a 125V, 50 Hz supply. The current in the circuit is 2.2A and the power loss in resistor is 96.8W. Calculate the resistance and capacitance and draw a vector diagram for the circuit.coil of resistance 10 ohms and inductance 0.1H is connected in series with a 150 micro farad capacitor across a 200V, 50Hz supply. Calculate (i) the inductive reactance, (ii) the capacitive reactance, (iii) the impedance, (iv) the current, (v) the power factor, (vi) the voltage across the coil and the capacitor respectively

9. Calculate (a) impedance of the entire circuit, (b) the total current, (c) the current in each parallel branch, (d) the total power supplied, (e) the power factor.

10. In series R-L-C circuit f = 500Hz, L =10mH, C = 5F with applied voltage of 200V. Phase difference between current & voltage is 50. Find R and the voltage across L & C. Also draw the phase diagram.

Ans: R = 27.05, VL & Vc = 337.2 V

11. What is time constant? Explain time constant in case of series R-L and series R-C circuit.

12. A RLC series circuit with a resistance of 10Ω impedance of 0.2 H and a capacitance of 40 μF is supplied with a 100V supply at variable frequency. Find the following w.r.t the series resonant circuit:-i) the frequency at resonance ii) the current iii) power iv) power factor v) voltage across R,L,C at that time vi) quality factor of the circuit vii) half power points viii) phasor diagram.

20

Ans: i) 56.2697 Hz ii) 10A, iii) 1000W, iv) unit, v) VR=100V vi) Q=7.071, vii) f1=52.29Hz & f2= 60.25Hz.

13. A series RLC circuit consists of a resistance of 1kΩ and an inductance of 100mH in series with capacitance of 10pF. If 100V is applied as input across the combination, Determine,i) The resonant frequency ii) Maximum current in the circuit.iii) Q-factor of the circuit iv) The half-power frequencies.Ans: 159.15Hz, 0.1A, 100, 158.35 kHz & 159.95 kHz

14. Prove that for series resonant circuit, the resonant frequency is the geometric mean of two half power frequencies

15. Derive the expression of resonant frequency and bandwidth of a series resonant circuit.

16. Derive the expression for transfer function and maximum voltage amplification of a single tuned circuit.

17. Derive the expression for transfer function and maximum voltage amplification of a double tuned circuit.

21