### Resonance (Series and Parallel) - Topicwise GATE Questions on Network Theory (from 2003)

2003
1. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q = 100. If each R, L and C is doubled from its original value, the new Q-factor of the circuit is
a) 25
b) 50
c) 100
d) 200

Solution : https://www.youtube.com/watch?v=DCfbRcxcOEM

2004
2. Consider the following statements S1 and S2
S1: at the resonant frequency, the impedance of a series RLC circuit is zero.
S2: In a parallel G-L-C 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

Solution : https://www.youtube.com/watch?v=s3hM-idhg2s

2005
3. The condition on R, L and C such that the step response y(t) in figure has no oscillations, is

Solution : https://www.youtube.com/watch?v=JfYzFU9Oc-0

4. In a series RLC circuit, R = 2 kΩ, L = 1 H, and C = 1/400 µF. The resonant frequency is
a) 2 x 104 Hz
b) (1/π) x 104 Hz
c) 104 Hz
d) 2π x 104 Hz

Solution : https://www.youtube.com/watch?v=B9Uk_uA0JbA

2007
5. Two series resonant filters are as shown in the figure. Let the 3-dB bandwidth of filter 1 is B1 and that of Filter 2 is B2. The value of B1/B2 is

a) 4
b) 1
c) 1/2
d) 1/4

Solution : https://www.youtube.com/watch?v=lMKem0ESd64

2010
6. For parallel RLC circuit, which one of the following statements is NOT correct?
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.

Solution : https://www.youtube.com/watch?v=wPSqMuj0YhY

2013
7. Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective resistances are R1 and R2. When connected in series, their effective Q factor at the same operating frequency is
a) q1 + q2
b) (1/q1) + (1/q2)
c) (q1R1 + q2R2) / (R1 + R2)
d) (q1R2 + q2R1) / (R1 + R2)
Solution : https://www.youtube.com/watch?v=v7q3ssCyLqw

2014
8. In the circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is ____________________

Solution : https://www.youtube.com/watch?v=MTY9pmGILi4

9. A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1H, 1F and 1Ω respectively, then the operating angular frequency (in rad/sec) is ____________________

Solution : https://www.youtube.com/watch?v=qJluHG5_mmk

10. 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 _____________

Solution : https://www.youtube.com/watch?v=doL-VE7tziY

2015
11. In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in volts) across the capacitor is ____________________

Solution : https://www.youtube.com/watch?v=YZq-lDiqadg

12. The voltage (Vc) across the capacitor (in volts) in the network shown is ______________

Solution : https://www.youtube.com/watch?v=BiEeuX6a218

13. An LC tank circuit consists of an ideal capacitor C connected in parallel with a coil of inductance L having an internal resistance R. The resonant frequency of the tank circuit is

Solution : https://www.youtube.com/watch?v=Y331K9dgrPs

14. In the circuit shown, the current I flowing through the 50 Ω resistor will be zero, if the value of the capacitor C (in µF) is __________________

Solution : https://www.youtube.com/watch?v=ZSJIgQWJiKU

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