Sunday, May 1, 2016

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

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

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

Answer:C
Solution : https://www.youtube.com/watch?v=o3XhO6h9PhQ

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

Answer:C
Solution : https://www.youtube.com/watch?v=n5soJALqqaw


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

Answer:A
Solution : https://www.youtube.com/watch?v=pwwj_ZnIDqU


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

Answer:A
Solution : https://www.youtube.com/watch?v=SEANHyPcKRk


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

Answer:C
Solution : https://www.youtube.com/watch?v=OFlCLWEvc2U


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

Answer:B
Solution : https://www.youtube.com/watch?v=Xa5N6PQTPLs


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

Answer:B
Solution : https://www.youtube.com/watch?v=lCb51w-rL_g

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

Answer:B
Solution : https://www.youtube.com/watch?v=oA-NdSmNq1c


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

Answer:C
Solution : https://www.youtube.com/watch?v=0f9FRURijpw


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

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


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

Answer:A
Solution : https://www.youtube.com/watch?v=U9lh2d-zwTg


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

Answer:D
Solution : https://www.youtube.com/watch?v=CI2Na_stYRg


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

Answer:D
Solution : https://www.youtube.com/watch?v=DB4jmdoaFIk


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

Answer:B
Solution : https://www.youtube.com/watch?v=nn6PggFjKgA

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

Answer:A
Solution : https://www.youtube.com/watch?v=VBFOXuUEuKE


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.

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

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

Answer:A
Solution : https://www.youtube.com/watch?v=51KGart3zsQ


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

Answer:A
Solution : https://www.youtube.com/watch?v=hQdNpuDt3zU

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

Answer:D
Solution : https://www.youtube.com/watch?v=iVJ4qUlg8BE

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 _________________
Answer:0.41
Solution : https://www.youtube.com/watch?v=7v7xe71hIos

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

Answer:10
Solution : https://www.youtube.com/watch?v=MTY9pmGILi4


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 ____________________
Answer:0.46
Solution : https://www.youtube.com/watch?v=qJluHG5_mmk

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 ?

Answer:A
Solution : https://www.youtube.com/watch?v=KRDH7b0xQNc

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) ?

Answer:A
Solution : https://www.youtube.com/watch?v=kqPA3ph-4Lw


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
Answer:B
Solution : https://www.youtube.com/watch?v=kzKMHQ1Fbd4

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 _____________

Answer:2
Solution : https://www.youtube.com/watch?v=doL-VE7tziY

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

Answer:25
Solution : https://www.youtube.com/watch?v=YZq-lDiqadg

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 __________________

Answer:2.528
Solution : https://www.youtube.com/watch?v=_hcH81bC-cg

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

Answer:1.649
Solution : https://www.youtube.com/watch?v=Hr4AS712hRM

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

Answer:5
Solution : https://www.youtube.com/watch?v=ysVaNyiOZtw

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

Answer:100
Solution : https://www.youtube.com/watch?v=BiEeuX6a218

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

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

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 _______________

Answer:3
Solution : https://www.youtube.com/watch?v=wj9gkVjceEk

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

Answer:0.5
Solution : https://www.youtube.com/watch?v=_O4UfZGA87c

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 _____________

Answer:5
Solution : https://www.youtube.com/watch?v=nK21y4c_m0Q

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 __________________

Answer:20
Solution : https://www.youtube.com/watch?v=ZSJIgQWJiKU

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