### AC analysis of RC, RL and RLC circuits - 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

2. The differential equation for the current i(t) in the circuit shown is

3. The current flowing through the resistance R in the circuit shown has the form Pcos4t, where p is
a) (0.18 + j0.72)
b) (0.46 + j1.90)
c) - (0.18 + j1.90)
d) - (0.192 + j0.144)

Answer: Data is insufficient as inductor values are not given in the figure.

4. An input voltage v(t) = 10√2 cos(t+10o)+ 10√3 cos(2t+10o) volts is applied to a series combination of resistance R = 1Ω and an inductance L = 1H. The resulting steady state current i(t) in amperes is

2004
5. The circuit shown in figure, has R = 1/3 Ω, L = 1/4 H, C = 3 F has input voltage v(t) = sin2t. The resulting current i(t) is

6. For the circuit shown, the time constant RC = 1 ms. The input voltage is vi(t) = √2 sin103t. The output voltage vo(t) is equal to

7. For the R-L circuit shown, the input voltage vi(t) = u(t). The current i(t) is

8. The circuit shown in figure has initial current iL(0-) = 1 A through the inductor and an initial voltage Vc(0-) = - 1 volt across the capacitor. For input v(t) = u(t), the Laplace transform of the current i(t) for t ≥ 0 is

2005
9. A square pulse of 3 volts amplitude is applied to RC circuit shown in figure. The capacitor is initially uncharged. The output voltage Vo at time t = 2 sec is

a) 3 V
b) -3 V
c) 4 V
d) -4 V

2006
10. In the figure shown below, assume that all the capacitors are initially uncharged. If Vi(t) = 10 u(t) volts, then Vo(t) is given by

2007
11. The RC circuit shown in the figure is a

a) Low Pass Filter
b) High Pass Filter
c) Band Pass Filter
d) Band Reject Filter

12. 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

13. In the circuit shown, Vc is 0 volts at t = 0 sec. For t > 0, the capacitor current ic(t), where t is in seconds, is given by

2008
14. The driving point impedance of the following network is given as shown. The component values are

Common Data Questions: 15 & 16
The following series RLC circuit with zero initial conditions is excited by a unit impulse function δ(t).

15. For t > 0, the output voltage Vc(t) is

16. For t > 0, the voltage across the resistor is

2009
17. The time domain behaviour of an RL circuit is represented as shown below. For an initial current of i(0) = Vo/R, the steady state value of the current is given by

2010

18. 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.

2011
19. The circuit shown below is driven by a sinusoidal input Vi = Vpcos(t/RC). The steady state output Vo is

20. In the circuit shown below, the initial charge on the capacitor is 2.5 mC, with the voltage polarity as indicated. The switch is closed at time t = 0. The current i(t) at a time t after the switch is closed is

2013
21. The transfer function V2(s)/V1(s) of the circuit shown below is

2014
22. A periodic variable x is shown in the figure as a function of time.

The root-mean-square (rms) value of x is _________________

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

24. 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 ____________________

25. In the figure shown, the capacitor is initially uncharged.
Which one of the following expressions describes the current I(t) in mA for t > 0 ?

26. A series RC circuit is connected to a DC voltage source at time t = 0. The relation between the source voltage VS, the resistance R, the capacitance C and the current i(t) is given below. Which one of the following represents the current i(t) ?

27. Consider the building block called 'Network N' shown in the figure. Let C = 100 µF and R = 10 kΩ.
Two such blocks are connected in cascade, as shown in the figure,

find the transfer function V3(s)/V1(s) of the cascaded network is

28. 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 _____________

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

30. In the circuit shown, switch SW is closed at t =0. Assuming zero initial conditions, the value of Vc(t) (in volts) at t = 1 sec is __________________

31. In the given circuit, the maximum power (in Watts) that can be transferred to the load RL is _______

32. In the circuit shown, the average value of the voltage Vab (in volts) in steady state condition is _________

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

34. 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

35. In the circuit shown, the initial voltages across the capacitors C1 and C2 are 1 volt and 3 volts respectively. The switch is closed at time t = 0. The total energy dissipated (in Joules) in the resistor R until steady state is reached, is _______________

36. At High frequencies, the peak output voltage Vo (in volts) is __________

37. In the circuit shown, assume that the diodes D1 and D2 are ideal. The average voltage Vab (in volts) across terminals a and b is _____________

38. 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 __________________

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