linear electrical networks

1. Assignment – Cum – Tutorial Questions
A. Questions testing the remembering / understanding level of students
I) Objective Questions
1. Electric pressure is also called [ ]
a) Resistance b) Power c) voltage d) energy
2. The resistance of a conductor varies inversely as [ ]
a) Length b) area of cross section c) temperature d) resistivity
3. The circuit parameter in which energy is dissipated is [ ]
a) inductance b) Capacitance c) Resistance d) Mutual inductance
4. Identify the nonlinear circuit element [ ]
a) Resistor b) Capacitor c) air cored inductor d) semiconductor diode
5. The following constitutes a bilateral element [ ]
a) R b) FET c) Vacuum Tube d) metal rectifier.
6. Which of the following element does not allow the sudden change in voltage [ ]
a) Resistor b) Inductor c) Capacitor d) none of these.
7. Two or more number of current sources can be represent as single current source when they
are connected in [ ]
a) parallel b) series c) either series or parallel d) not possible
8. Short circuit is an element when the resistance approaches [ ]
a) zero b) infinity c) 1 Ω d) negative value
9. An ideal voltage source should have [ ]
a) large value of EMF b) small value of EMF
c) Zero source resistance d) Infinite source resistance
10. The resistivity of the conductor depends on [ ]
a) area of the conductor b) length of the conductor
c) type of material d) none of these
11. The resistance of a conductor of diameter d and length l is R Ω. If the diameter of the
conductor is halved and its length is doubled, the resistance will be [ ]
a) R Ω b) 2R Ω c) 4R Ω d) 8R
12. Which of the following element does not allow the sudden change in current [ ]
a) Resistor b) Inductor c) Capacitor d) none of these.
13. Two or more number of voltage sources can be represent as single voltage source when they
are connected in [ ]
a) parallel b) series c) either series or parallel d) not possible
14. Open circuit is an element when the resistance approaches [ ]
a) zero b) infinity c) 1 Ω d) negative value
15. An ideal current source should have [ ]
a) large value of EMF b) small value of EMF
c) Zero source resistance d) Infinite source resistance
II) Descriptive Questions
1. Explain the classification of network elements
2. Differentiate ideal and practical sources
3. Explain the V – I relations for R, L and C elements
4. Derive the expression for energy stored in an inductor
5. Derive the expression for energy stored in a capacitor
B. Questions testing the ability of students in applying the concepts
I) Multiple Choice Questions

2. 1. A coil of resistance 5 Ω and inductance 0.4H is connected to a 50V D.C supply. The energy
stored in the field is [ ]
a) 20 joules b) 10 joules c) 40 joules d) 30 joules
2. A unit step voltage is applied across an inductor. The current through the inductor will be
a) zero for all time b) a step function c) a ramp function d) a impulse function
3. The energy stored in a capacitor of 2µF and having a charge of 10*10-3coulombs is [ ]
a) 2.5J b) 25J c) 0.25J d) 5J
4. A ramp current flowing through an initially relaxed capacitor will result in a voltage across
it that [ ]
a) Varies inversely with time b) remains constant
c) varies directly with time d) varies as the square of time.
5. A voltage waveform v (t) = 12 t
2
is applied across 1H Inductor for t ≥ 0, with initial current
through it being zero. The current through the inductor for t≥0 is given by [ ]
a) 12t b) 24t c) 12 t
3
d) 4 t
3
6. It is desired to have a constant direct current i (t) through the ideal inductor L. The nature
of the voltage source v (t) must [ ]
a) Constant voltage b) Linearly increasing voltage
c) an ideal impulse d) Exponentially increasing voltage.
7. For the current and voltage waveforms, identify the element & its value. [ ]
a) L, 25
b) C, 25
c) L, 2
d) C, 2
II) Problems
1. A current wave form shown in the figure below is applied to a capacitor of value 2µF.
Find the voltage waveform across it.
2. A capacitor of 1F is supplied with voltage waveform shown in the figure below. Obtain
the current and energy waveforms in the capacitor.
3. A 0.5μF capacitor has voltage waveform V(t)
shown below. Plot
i(t) as a function of
time.

3. 4. A current of the waveform shown below, flows through a 25μF capacitor. Sketch the voltage
waveform and determine Vmax and qmax
5. A pure inductance of 3mH carries a current of waveform shown below. Sketch v(t) and p(t)
6. A series RL circuit with R = 5Ω and L = 0.004H contains a current with a waveform as
shown below. Sketch VR and VL

4. Assignment – Cum – Tutorial Questions
C. Questions testing the remembering / understanding level of students
III) Objective Questions
1. Kirchoff’s Laws fail in the case of [ ]
a) linear networks b) non linear networks
c) dual networks d) distributed networks.
2. Ohm’s law, KVL &KCL will fail at [ ]
a) Low frequency b) high frequency c) high power
d) none
3. In a network made up of linear resistors and ideal voltage sources, values of all resistors are
doubled. Then the voltage across each resistor is [ ]
a) doubled b) halved c) decreased four times d) not changed
4. Mesh analysis is a combination of [ ]
a) Ohm’s law and KCL b) Ohm’s law and KVL
c) KVL and KCL d) None of the above
5. Ohm’s law is applicable when the temperature is [ ]
a) Positive b) negative c) Variable d) Constant
6. Kirchhoff’s current law is based on law of conservation of [ ]
a) charge b) energy c) momentum d) mass
7. Nodal analysis can be applied for [ ]
a) Planar networks b) non-planar networks
c) both planar and non-planar networks d) neither planar nor non-planar networks
8. Mesh analysis is applicable for [ ]
a) Planar networks b) non-planar networks
c) both planar and non-planar networks d) neither planar nor non-planar networks
9. KCL works on the principle of which of the following [ ]
a) Law of conservation of charge b) Law of conservation of energy
c) Both d) None of the above
10. KVL works on the principle of which of the following [ ]
a) Law of conservation of charge b) Law of conservation of energy
c) Both d) None of the above
11. Super Mesh analysis is used in case of [ ]
a) Current source branch is common for two meshes
b) Ideal voltage source is connected between two non-reference nodes
c) Both d) Either a or b
12. Super Node analysis is used in case of [ ]
a) Current source branch is common for two meshes
b) Ideal voltage source is connected between two non-reference nodes
c) Ideal voltage source is connected between non-reference node and reference
d) All of the above
13. Three parallel resistive branches are connected across a DC supply. What will be the ratio
of the branch currents I1: I2: I3 if the branch resistances are in the ratio R1:R2:R3 : : 2:4:6
[ ]
a) 3:2:6 b) 2:4:6 c) 6:3:2 d) 6:2:4
IV)Descriptive Questions
1. State and explain Kirchhoff’s laws

5. 2. Derive the expressions for equivalent resistance when ‘n’ resistors are connected in series
and parallel
3. Derive the expressions for equivalent inductance when ‘n’ inductors are connected in
series and parallel
4. Derive the expressions for equivalent capacitance when ‘n’ capacitors are connected in
series and parallel
5. Explain the principle of source transformation with suitable example
D. Questions testing the ability of students in applying the concepts
III) Multiple Choice Questions
1. Three resistances having 10 ohms, 15 ohms, 30 ohms are connected in parallel. The total
resistance of the combination is [ ]
a) 5 ohms b) 10 ohms c) 15 ohms d) 55 ohms
2. Four wires of same material, the same cross sectional area and the same length when
connected in parallel gives a resistance of 0.25 ohms. If the same four wires are connected
in series, the effective resistance will be [ ]
a)1 ohm b) 2 ohm c) 3 ohm d) 4 ohm
3. A current of 16 amperes divides between two branches in parallel of resistances 8 ohms
and 12 ohms respectively. The current in each branch is [ ]
a)6.4A,6.9A b) 6.4A,9.6A c) 4.6A,6.9A d) 4.6A,9.6A
4. You have to replace 1500Ω resistor in a radio. You have no 1500Ω resistors but have
several 1000Ω resistors. Which way would you connect [ ]
a) Two in parallel b) two in parallel and one in series
c) three in parallel d) three in series
5. The total power dissipated in a series circuit is 10W.There are 4 equal resistors connected
in series. The power dissipated in each resistor is [ ]
a)10W b) 40W c) 2.5W d)5W
6. Find the equivalent resistance of the circuit in the figure [ ]
a) 3 ohms
b) 4 ohms
c) 5 ohms
d) 6 ohms
7. Find the value of R [ ]
a) 10 ohms b) 7 ohms c) 8.2 ohms d) 9 ohms
8. Find V in the circuit shown [ ]
a) 2V b) 3V c) 1V d) 4V
9. Find V in the circuit shown [ ]

6. a) 3V b) -3V c) -2V d) 2V
10. Find Vx in the circuit shown [ ]
a) 42.2 V b) 97.3 V c) 83.3V d) 103V
11. What value of R ensures that the current through 60Ω resistor of this circuit is 1A [ ]
a) 5Ω b) 10 Ω c) 15 Ω d) 20 Ω
12. What is the value of i1 [ ]
a) 0A b) -6A c) 6A d) 8A
13. Find the current through 5 Ω resistor [ ]
a) 1A b) 2A c) 3A d) 7A
14. In the circuit given below, the current I will be [ ]
a) 3A b) 4A c) 2A d) 6A

7. 15. If the 12Ω resistor draws a current of 1A as shown in figure, the value of resistance R is [ ]
a) 8Ω b) 6Ω c) 4Ω d) 2Ω
16. The value of voltage source in the network given below is [ ]
a) 10V b) 44V c) 37V d) 30V
IV)Problems
1. A resistance R is connected in series with a parallel circuit comprising two resistances of
12 and 8Ω respectively. The total power dissipated in the circuit is 70W when applied
voltage is 20V. Calculate R.
2. A resistance of 10Ω is connected in series with two resistances each of 15Ω arranged in
parallel. What resistance must be shunted across this parallel combination so that the total
current taken shall be 1.5A with 20V applied.
3. For the circuit shown below, use source transformation to find i.
4. Apply source transformation to find v0and vx in the circuit following circuits
5. Obtain the equivalent resistance Rab for the
circuits shown below and use it to find current i.

8. 6. Obtain the equivalent resistance at the terminals a-b for each of the circuits shown below
7. Calculate I0 in the circuit shown below
8. For the circuit shown below, find the node voltages.
9. Use mesh analysis to determine 𝑖1, 𝑖2 and 𝑖3 in the circuit shown below

9. 8. Find the equivalent capacitance between the terminals A and B in the circuit shown below
9. Determine the power delivered by dependent source
11. Determine the current i1 in the circuit shown below
12. Determine the
node
voltages
in the circuit shown below

10. 13. Evaluate the three unknown currents in the circuit given below
14. Find the voltage Vab in the circuit shown below using nodal analysis
15. Find the value of applied d.c. voltage for the network shown below
16. A bridge network ABCD is arranged as follows:
Resistance between terminals AB, BC, CD, DA and BD are 10 ohms, 30 ohms, 15 ohms,
20 ohms and 40 ohms respectively. A 4V battery is connected with negligible internal
resistance between terminals A and C. Determine the current through each element in the
network using network reduction techniques.
17. Find Req between the terminals x and y as shown in figure below. All the resistances are in
ohms.

11. 18. Determine the current through battery for the network shown. All resistance values are
in ohms.
Previous Gate / IES Questions:
1. In the circuit shown in figure, the value of current ‘i’ will be [ ]
[GATE 2008]
a) 0.31A b) 1.25A c) 1.75A d) 2.5A
2. Twelve 1Ω resistors are used to form a cube. The resistance between two diagonally
opposite corners of the cube is [ ]
a)
𝟓
𝟔
Ω b)
1
6
Ω c)
6
5
Ω d)
3
2
Ω [GATE-2003]
3. In the figure shown, the value of R is [ ]
[GATE 2005]
a) 2.5Ω b) 5.0Ω c) 7.5Ω d) 10.0Ω

12. 4. In figure, Ra, Rb and Rc are 20 Ω, 20 Ω and 10 Ω respectively. The resistances R1, R2 and R3
in Ω of an equivalent star-connection are [ ]
[GATE
2004]
a) 2.5, 5, 5 b) 5, 2.5, 5 c) 5, 5, 2.5 d) 2.5, 5, 2.5
5. In the figure, the value
of R is
[
]
[GATE 2003]
a) 10Ω
b) 18Ω
c) 24Ω
d) 12Ω
6. Find the voltage at node A, with respect to node O for the circuit shown [ ]
[IES 2009]
a) 40V b) 20V c) 50V d) 60V
7. For the circuit shown, I is [ ]
[IES 2010]
a) 0A b) 1A c) 2A d) 3A
8. The following mesh equations pertain to a network: [IES 2010]

13. 8I1 – 5I2 – I3 = 110
-5I1 + 10I2 + 0 = 0
-I1 + 0 + 7I3 = 115
i) Draw the network showing each element
ii) Calculate the current in 110V source
9. Find the current Ix which flows through 3Ω resistor in the circuit shown below [IES 2011]
10. If R1=R2=R4=R and R3=1.1R in the bridge circuit shown in figure, then the reading in the
ideal voltmeter connected between a and b is [ ]
GATE-2005
a) 0.238V b) 0.138V c) -0.238V d) 1V

14. Assignment-Cum-Tutorial Questions
A. Questions testing the remembering / understanding level of students
I) Objective Questions
1. Two waves of the same frequency have opposite phase when the phase angle between them is
a) 360° b) 180° c) 90° d) 0°
2. The r.m.s. value of alternating current is given by steady (D.C.) current which when flowing
through a given circuit for a given time produces
a) the more heat than produced by A.C. when flowing through the same circuit
b) the same heat as produced by A.C. when flowing through the same circuit
c) the less heat than produced by A.C. flowing through the same circuit
d) none of the above
3. A phasor is
a) a line which represents the magnitude and phase of an alternating quantity
b) a line representing the magnitude and direction of an alternating quantity
c) a coloured tag or band for distinction between different phases of a 3-phase supply
d) an instrument used for measuring phases of an unbalanced 3-phase load
4. The form factor is the ratio of
a) peak value to r.m.s. value b) r.m.s. value to average value
c) average value to r.m.s. value d) none of the above
5. The period of a sine wave is 20 milli seconds. Its frequency is
a) 20 Hz b) 30 Hz c) 40 Hz d) 50 Hz
6. A heater is rated as 230 V, 10 kW, A.C. The value 230 V refers to
a) average voltage b) r.m.s. voltage c) peak voltage d) none of the above
7. If two sinusoids of the same frequency but of different amplitudes and phase angles are
subtracted, the resultant is
a) a sinusoid of the same frequency b) a sinusoid of half the original frequency
c) a sinusoid of double the frequency d) not a sinusoid
8. If two sine waves of the same frequency have a phase difference of π radians, then
a) both will reach their minimum values at the same instant
b) both will reach their maximum values at the same instant
c) when one wave reaches its maximum value, the other will reach its minimum value
d) none of the above
II) Descriptive Questions
1. Define average value, RMS value, form factor, peak factor of an alternating quantity and
calculate the above values for a sinusoidal voltage wave form.
2. Calculate the form factor and peak factor of a triangular wave in which the voltage rises
uniformly from 0 to V volts in time T seconds and completes the cycle by falling instantly back
to zero.
3. a) Define the following (i) Phase (ii) Phase deference
4. Explainthesignificanceof‘j’operator.Whatarethedifferentformsof
expressing thesinusoidalquantityincomplexform?
B. Questions testing the Applying level of students
I) Multiple choice Questions
1. The peak value of a sine wave is 200 V. Its average value is
a) 127.4 V b) 141.4 V c) 282.8 V d)200V
2. For a sine wave with peak value Imax the r.m.s. value is
a) 0.5 Imax b) 0.707 c) 0.9 d) 1.414 Lmax
3. Form factor for a sine wave is

15. a) 1.414 b) 0.707 c) 1.11 d) 0.637
4. For a frequency of 200 Hz, the time period will be
a) 0.05 s b) 0.005 s c) 0.0005 s d) 0.5 s
5. If a sinusoidal wave has frequency of 50 Hz with 30 A r.m.s. current which of the following
equation represents this wave?
a) 42.42 sin 314t b) 60 sin 25 t c) 30 sin 50 t d) 84.84 sin 25 t
6. 𝑓(𝑡) = 2 + cos(𝜔𝑡 + 𝜋), the ratio of
𝑉
𝑟𝑚𝑠
𝑉
𝑎𝑣𝑒
⁄
a) 𝟑
𝟐√𝟐
⁄ b) √3
2
⁄ c) Π d) 𝜋 2
⁄
7. The rms value of the periodic waveform e(t) shown in
a) 𝐴√3 2
⁄ b) 𝑨√𝟐 𝟑
⁄ c)𝐴√1 3
⁄ d) 𝐴√2
8. Which of the waveforms are having unity peak factor?
a) fig a and b b) fig b and c c) fig a and c d) none
II) Problems
1. A sinusoidal voltage of 50 Hz has a maximum value of 200√2 volts. At what time measured
from a positive maximum value will the instantaneous voltage be equal to 141.4 volts?
2. Calculate the average and the effective values of the saw tooth waveform shown in Fig.
3. Find form factor for the waveform shown
4. Find RMS and average value of the waveform shown

16. 5. Find the average, RMS values, form and peak factor for the following waveform.
(3.75V, 4.0825V, 1.0887, 1.3333)
6. Determine average and RMS values for the following waveforms.

17. II) GATE /IES questions
1. The rms value of the periodic waveform given in figure is GATE 2004
2. The rms value of the resultant current in a wire which carries a dc current of 10 A and a sinusoidal
alternating current of peak value 20 A is GATE 2004
(a) 14.1 A (b) 17.3 A (c) 22.4 A (d) 30.0 A
3.

18. Assignment-Cum-Tutorial Questions
A. Questions testing the remembering / understanding level of students
I) Objective Questions
9. The power consumed in a circuit element will be least when the phase difference between the
current and voltage is
a) 180° b) 90° c) 60° d) 0°
10. Pure inductive circuit
a) consumes some power on average b) does not take power at all from a line
c) takes power from the line during some part of the cycle and then returns back to it
during other part of the cycle
d) none of the above
11. Pure inductive circuit takes power from the A.C. line when
a) applied voltage decreases but current increases
b) applied voltage increases but current decreases
c) both applied voltage and current increase
d) both applied voltage and current decrease
12. In a R-L-C circuit
a) power is consumed in resistance and is equal to I R
b) exchange of power takes place between inductor and supply line
c) exchange of power takes place between capacitor and supply line
d) exchange of power does not take place between resistance and the supply line
e) all above are correct
13. The safest value of current the human body can carry for more than 3 second is
a) 4 mA b) 9 mA c) 15 mA d) 25 mA
14. The power consumed in a circuit element will be least when the phase difference between the
current and voltage is
a) 180° b) 90° c) 60° d) 0°
15. Power factor of an electrical circuit is equal to
a) R/Z b) cosine of phase angle difference between current and voltage
c) kW/kVA d) ratio of useful current to total current Iw/I (e) all above
16. Pure inductive circuit
a) consumes some power on average b) does not take power at all from a line
c) takes power from the line during some part of the cycle and then returns back to it
during other part of the cycle
d) none of the above
17. In a pure resistive circuit
a) current lags behind the voltage by 90° b) current leads the voltage by 90°
c) current can lead or lag the voltage by 90° d) current is in phase with the voltage
18. In a pure inductive circuit
a) the current is in phase with the voltage b) the current lags behind the voltage by
90°
c) the current leads the voltage by 90° d) the current can lead or lag by 90°
19. In a circuit containing R, L and C, power loss can take place in
a) C only b) L only c) R only d) all above
20. Inductance of coil
a) is unaffected by the supply frequency
b) decreases with the increase in supply frequency
c) increases with the increase in supply frequency
d) becomes zero with the increase in supply frequency
21. The power factor at resonance in RLCparallel circuit is
a) zero b) 0.08 lagging c) 0.8 leading d) unity
22. Magnitude of current at resonance in RLCcircuit
a) depends upon the magnitude of R b) depends upon the magnitude of L
c) depends upon the magnitude of C d) depends upon the magnitude of R, LandC

19. 23. In RLCseries resonant circuit magnitude of resonance frequency can be changed by
changing the value of
a) R only b) L only c) C only d) L or C (e) R,L or C
24. In a series LCcircuit at the resonant frequency the
(a) current is maximum (b) current is minimum
(c) impedance is maximum (d) voltage across C is minimum
25. In a parallel RCcircuit, the current always______the applied voltage
(a) lags (b) leads (c) remains in phase with (d) none of the above
26. At very low frequencies a series RCcircuit behaves as almost purely
(a) resistive (b) inductive (c) capacitive (d) none of the above
27. At ______ frequencies the parallel RLcircuit behaves as purely resistive.
(a) low (b) very low (c) high (d) very high
28. The series and parallel resonance on L-C circuit differs in that
a) series resistance needs a low-resistance source for sharp rise in current
b) series resonance needs a high-resistance source for sharp increase in current
c) parallel resonance needs a low-resistance source for a sharp increase in impedance
d) parallel resonance needs a low-resistance source for a sharp rise in line current
29. The half – power frequency of, series RC circuit is
a) 1/ RC b) RC c) R/C d) C/R
II) Descriptive Questions
5. a) Define the following (i) impedance (ii) reactance
(iii) Phase angle difference (iv) power factor
b) A R-L series circuit having a resistance of 4Ω and 3 ohms inductive reactance is fed by
100V, 50Hz, 1- φ supply. Find the current, power drawn by the circuit and power factor.
6.
The voltage of a circuit is v=200sin(ωt+30°) and the current is i=50sin(ωt+60°)
Calculate i) the average power, reactive volt amperes and apparent power
ii) find the circuit elements , if ω=100π rad/sec.
7. a) Derive the expression for power in a single phase AC circuit containing R – L
elements in series.
b) A supply of 400V, 50Hz is applied to a series R-C circuit. Find the value of C if the power
absorbed by the resistor is 500W at 150V. What is the energy stored in a capacitor.
8. Explain resonance, bandwidth and Q factor in series RLC circuit.
9. Explain resonance, bandwidth and Q factor in parallel RLC circuit.
B. Questions testing the Applying level of students
I) Multiple choice Questions
9. The input of an A.C. circuit having power factor of 0.8 lagging is 40 kVA The power drawn by
the circuit is
a) 12 kW b) 22 kW c) 32 kW d) 64 kW
10. Given Z1 = 3 +j4 and Z2 is complex conjugate of Z1. The current I1 is 4/√2∠ − 430
rms and I2
is 4/√2∠ − 630
, then ammeter A1 reads

20. a) 5.55rms b) 4rms c) 8/√2 d) none
11. A unit step current is impressed across a parallel 3Ω, 2F circuit. Under steady state, the
capacitor voltage will be
a) 3V b) 2V c) 1V d) 0
12. In the given circuit, current in amp is
a) −𝟎. 𝟐 𝐜𝐨𝐬𝟏𝟎𝟎𝟎𝐭 b) 0.2cos1000t c) − 0.2sin1000t d) 0.2sin1000t
13. For the current in branch AB shown, the Voltage Vin volt is
a) 55 b) 110 c) 56 d) 90
14. Find iR(t) through the resistor, when the network shown is in steady state condition.
a) 5+2.23cos (2t-26.560) b) 5+2.23cos(2t+26.560
) c) 2.23cos(2t-26.560
) d) none
15. When a voltage Vo sin ωot is applied to the pure inductor, the ammeter shown reads Io. If the
voltage applied is – Vo sin ωot + 2Vo sin ωot - 3Vo sin ωot + 4Vo sin 4ωot.
a) 0 b) 10 Io c) √42 + 32 + 22 + 1 d) 2 Io
16. Voltage on R, L, C in a series circuit are shown below; value of voltage source is
a) 10V b)-27V c) 27V d) 5V
17. An alternating current source having voltage E= 110 sin (ωt + (Π/3)) is connected in an a.c.
circuit . If the current drawn from the circuit varies as I = 5 sin (ωt – (Π / 3)). Impedance of
the circuit will be
a) 22Ω b)16Ω c) 30.8Ω d) None of the above

21. 18. In the circuit Vs= Vmsin2t and Z2=1+j. What is the value of C so that the current I is in phase
with Vs.
a) ¼ b) 1/2√2 c) 2 d) 4
19. The voltage phasor of a circuit is 10∠150
V and the current phasor is 2∠−450
A. The active
and reactive powers in the circuit are
a) 10W and 17.32var b) 5W and 8.66 var c) 20W and 60 var
20. The current wave form as shown in fig is passed through resistor of 100Ω. What is the power
dissipation in resistor.
a) (10/𝜋)2
100 b) (2 ∗ 10/𝜋)2
100 c) (𝟏𝟎/√𝟐)𝟐
𝟏𝟎𝟎 d) (10/2)2
100
21. Find Zin at resonance?
a) 1.28 b) 12.8 c) 2 d) 128
22. A circuit with a resistor, inductor and capacitor in series is resonant at fo HZ. If all the
component values are now doubled, the new resonant frequency is
a)2fo b) fo c) fo / 4 d) fo /2
23. A coil (series RL ) has been designed for high Q performance at a rated voltage and a
specific frequency. If the frequency of operation is doubled, and the coil is operated at the
same rated voltage, then the Q factor and the active power P consumed by the coil will be
affected as follows
a)P is doubled, Q is halved b) P is halved, Q is doubled
c) P remain constant, Q is doubled d) P decreases 4 times, Q is doubled.
24. Match List-I (Quantities) with List-II (Units) and select the correct answer using the codes
given below the Lists:
List-I List-II
(Quantities) (Units)
A. R/ L 1. Second
B. 1 / LC 2. Ohm
C. CR 3. (Radian / second )2
D. √( L / C) 4. (second)-1
CODES:
A B C D A B C D
a) 4 3 1 2 b) 3 4 2 1
c) 4 3 2 1 d) 3 4 1 2

22. II) Problems
7. (a) An inductive coil draws a current of 2 A, when connected to a 230 V, 50 Hz supply. The
power taken by the coil is 100 watts. Calculate the resistance and inductance of the coil.
(b) A series circuit with a resistance R 10 and inductance 20 mH has a current of i=2sin500t.
Obtain the total voltage across the series circuit and angle by which the current lags the
voltage.
8. (a) A 20 Ω resistance and 30 mH inductance are connected in series and the circuit is fed from
a 230 V, 50 Hz AC supply. Find i) Reactance across the inductance, impedance, admittance,
current ii) Voltage across the resistance iii) Voltage across the inductance iv) Real, reactive and
active powers v) Power factor.
(b) A capacitor having a capacitance of 10 µF is connected in series with a non-inductive
resistance of 120 across 100 V, 50 Hz. Calculate the power, current and the phase difference
between current and voltage.
9. (a) A metal filament lamp rated 750 W, 110 V is to be connected in series with a capacitor
across a 220 V, 50 Hz supply. Calculate i) The capacitance required ii) The power factor.
(b) A circuit having a resistance of 12Ω, in inductance of 0.15 H and a capacitance of 100 μF in
series is connected across a 100 V, 50 Hz supply. Calculate the impedance, current,the phase
difference between the current and supply voltage.
10. A series RLC circuit has R=10ohm, L=0.5H and C=40µF. The applied voltage is 100V. Find
i) resonant frequency, ii) Quality factor of a coil, iii) Upper and lower half power
frequencies, iv) Band width, v) current at resonance, vi) current at half power points and vii)
voltage across inductance at resonance.
11. A supply of 400V, 50Hz is applied to a series R-C circuit. Find the value of C if the power
absorbed by the resistor is 500W at 150V. What is the energy stored in a capacitor.
12. The voltage of a circuit is v=200sin (ωt+30°) and the current is i=50sin(ωt+60°) Calculate
i) the average power, reactive voltamperes and apparent power ii) find the circuit
elements , if ω=100π rad/sec.
13. A R-L series circuit having a resistance of 4Ω and 3 ohms inductive reactance is fed by
100V, 50Hz, 1- φ supply. Find the current, power drawn by the circuit and power factor.
D) Previous Gate/IES Questions
1. In the circuit shown below, the supply voltage is 10 sin(1000t) volts. The peak value of the
steady state current through the 1 Ω resistor, in amperes, is ______. Gate 2016
2. The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the
admittance of the circuit becomes a pure conductance at all frequencies is _____________.
Gate 2016

23. 3. A resistance and a coil are connected in series and supplied from a single phase, 100 V, 50 Hz
ac source as shown in the figure below. The rms values of plausible voltages across the
resistance (VR) and coil (VC) respectively, in volts, are Gate 2016
a) 65, 35 b) 50, 50 c) 60, 90 d) 60, 80
4. The voltage (V) and current (A) across a load are as follows. Gate 2016
𝑣(𝑡) = 100 sin(𝜔𝑡),
𝑖(𝑡) = 10 sin(𝜔𝑡 − 60°) + 2 sin(3𝜔𝑡) + 5 sin(5𝜔𝑡)
The average power consumed by the load, in W, is___________. Gate 2016
5. For the network shown in the figure below, the frequency (in rad/s) at which the maximum
phase lag occurs is, ___________. Gate 2016
6. The circuit shown in the figure has two sources connected in series. The instantaneous voltage
of the AC source (in Volt) is given by (𝑡)=12sin𝑡 . If the circuit is in steady state, then the rms
value of the current (in Ampere) flowing in the circuit is ______ . Gate 2015
7. In the given network 𝑉1=100∠0° V, 𝑉2=100∠−120° V, V3=100∠+120° V. The phasor current 𝑖
(in Ampere) is Gate 2015
a) 173.2∠−60° b) 173.2∠ 120° c) 100.0∠−60° d) 100.0∠ 120°
8. The voltage across the capacitor, as shown in the figure, is expressed as Gate 2014
𝑉
𝑐(𝑡) = 𝐴1 sin(𝜔1𝑡 − 𝜃1) + 𝐴2 sin(𝜔2𝑡 − 𝜃2)

24. 9. The values of A1 and A2 respectively, are Gate 2014
a) 2.0 and 1.98 b) 2.0 and 4.20
c) 2.5 and 3.50 d) 5.0 and 6.40
10. The total power dissipated in the circuit, shown in the figure, is 1 kW. Gate 2014
The voltmeter, across the load, reads 200 V. The value of XL is _____.
11. The circuit shown below is driven by a sinusoidal input vi = Vpcos (t/RC). The steady state
output vois Gate 2011
a) (𝐕𝐩/𝟑)𝐜𝐨𝐬 (𝐭/𝐑𝐂) b) (Vp/3) sin(t/RC)
c) (Vp/2)cos (t/RC) d) (Vp/2) sin(t/RC)
12. In the circuit shown below, the current I is equal to GATE 2011
a) 1.4∠0°
A b) 2∠𝟎°
A c) 2.8∠0°
A d) 3.2∠0°
A
13. At resonance, the ratio |𝐼𝐿|/|𝐼𝑅|, i.e., the ratio of the magnitudes of the inductor current
phasor and the resistor current phasor, is _______ Gate 2016
14. The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the
admittance of the circuit becomes a pure conductance at all frequencies is _____________.
Gate 2016

25. 15. An inductor is connected in parallel with a capacitor as shown in the figure. Gate 2015
As the frequency of current iis increased, the impedance (Z) of the network varies as
16. In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in volts)across
the capacitor is ____________________ Gate 2015
17. The voltage (Vc) across the capacitor (in volts) in the network shown is________ Gate
2015
18. An LC tank circuit consists of an ideal capacitor C connected in parallel with a coil
ofinductance L having an internal resistance R. The resonant frequency of the tank circuit
is Gate 2015

26. a)
1
2𝜋√𝐿𝐶
b)
𝟏
𝟐𝝅√𝑳𝑪
√𝟏 − 𝑹𝟐 𝑪
𝑳
c)
1
2𝜋√𝐿𝐶
√1 −
𝐿
𝑅2𝐶
d)
1
2𝜋√𝐿𝐶
√1 − 𝑅2 𝐿
𝐶
19. In the circuit shown in the figure, the value of capacitor C (in mF) needed to havecritically
damped response i(t) is ____________________ Gate 2014
20. In the circuit shown in the figure, the angular frequency ω (in rad/sec), at which the Norton
equivalent impedance as seen from terminals b – b' is purely resistive, is___________Gate 2013
21. Two magnetically uncoupled inductive coils have Q factors 𝑞1 and 𝑞2 at the
chosenoperating frequency. Their respective resistances are R1 and R2. When connected in
series,their effective Q factor at the same operating frequency is Gate 2013
a) q1 + q2 b) (1/q1) + (1/q2)
c) (𝐪𝟏𝐑𝟏 + 𝐪𝟐𝐑𝟐) / (𝐑𝟏+ 𝐑𝟐) d) (q1R2 + q2R1) / (R1 + R2)
22. For parallel RLC circuit, which one of the following statements is NOT correct? Gate
2010
a) The bandwidth of the circuit decreases if R is increased
b) The bandwidth of the circuit remains same if L is increased
c) At resonance, input impedance is a real quantity
d) At resonance, the magnitude of input impedance attains its minimum value.
23. The condition on R, L and C such that the step response y(t) in figure has nooscillations, is
Gate 2005
a) 𝑅 ≥
1
2
√
𝐿
𝐶
b) 𝑅 ≥ √
𝐿
𝐶
c) 𝑹 ≥ 𝟐√
𝑳
𝑪
d) 𝑅 =
1
√𝐿𝐶
24. In a series RLC circuit, R = 2 kΩ, L = 1 H, and C = 1/400 μF. The resonant frequency is
Gate 2005
a) 2 x 104
Hz b) (1/π) x 104 Hz c) 104
Hz d) 2π x 104
Hz
25. Consider the following statements S1 and S2 Gate 2004
S1: at the resonant frequency, the impedance of a series RLC circuit is zero.
S2: In a parallel GLC circuit, increasing the conductance G results in increase in its Q
factor.
Which one of the following is correct?
a) S1 is FALSE and S2 is TRUE b) Both S1 and S2 are TRUE
c) S1 is TRUE and S2 is FALSE d) Both S1 and S2 are FALSE
26. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q = 100.
Ifeach R, L and C is doubled from its original value, the new Qfactorof the circuit is
Gate 2003
a) 25 b) 50 c) 100 d) 200