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
2. The differential equation for the current i(t) in the circuit shown is
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
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
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
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
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
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
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
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 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
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
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 Vc(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) = Vo/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.
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
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
Solution : https://www.youtube.com/watch?v=hQdNpuDt3zU
2013
21. The transfer function V2(s)/V1(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 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) ?
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
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 Vc(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 RL is _______
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 _________
Solution : https://www.youtube.com/watch?v=ysVaNyiOZtw
33. The voltage (Vc) 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 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 _______________
Solution : https://www.youtube.com/watch?v=wj9gkVjceEk
36. At High frequencies, the peak output voltage Vo (in volts) is __________
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 _____________
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
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
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.
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.
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 __________________
