**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+10

^{o})+ 10√3 cos(2t+10

^{o}) 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 v

_{i}(t) = √2 sin10

^{3}t. The output voltage v

_{o}(t) is equal to

7. For the R-L circuit shown, the input voltage v

_{i}(t) = u(t). The current i(t) is

8. The circuit shown in figure has initial current i

_{L}(0

^{-}) = 1 A through the inductor and an initial voltage V

_{c}(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 V

_{o}at time t = 2 sec is

a) 3 V

b) -3 V

c) 4 V

d) -4 V

**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 V

_{i}(t) = 10 u(t) volts, then V

_{o}(t) is given by

**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

**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 B

_{1}and that of Filter 2 is B

_{2}. The value of B

_{1}/B

_{2}is

a) 4

b) 1

c) 1/2

d) 1/4

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

13. In the circuit shown, V

_{c}is 0 volts at t = 0 sec. For t > 0, the capacitor current i

_{c}(t), where t is in seconds, is given by

**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

**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 V

_{c}(t) is

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

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

**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) = V

_{o}/R, the steady state value of the current is given by

**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.

**2011**

19. The circuit shown below is driven by a sinusoidal input V

_{i}= V

_{p}cos(t/RC). The steady state output V

_{o}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 V

_{2}(s)/V

_{1}(s) of the circuit shown below is

**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 _________________

**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 ____________________

**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 ____________________

**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 ?

**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 V

_{S}, the resistance R, the capacitance C and the current i(t) is given below. Which one of the following represents the current i(t) ?

**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 V

_{3}(s)/V

_{1}(s) of the cascaded network is

**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 _____________

**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 ____________________

**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 V

_{c}(t) (in volts) at t = 1 sec is __________________

**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 R

_{L}is _______

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

32. In the circuit shown, the average value of the voltage V

_{ab}(in volts) in steady state condition is _________

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

33. The voltage (V

_{c}) across the capacitor (in volts) in the network shown is ______________

**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

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

35. In the circuit shown, the initial voltages across the capacitors C

_{1}and C

_{2}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 _______________

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

36. At High frequencies, the peak output voltage V

_{o}(in volts) is __________

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

37. In the circuit shown, assume that the diodes D

_{1}and D

_{2}are ideal. The average voltage V

_{ab}(in volts) across terminals a and b is _____________

**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 __________________

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