1
GATE ECE 2008
+2
-0.6
The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t). For t > 0, the output voltage Vc(t) is
A
$$\frac2{\sqrt3}\left(e^{-\frac{\displaystyle1}{\displaystyle2}t}-e^{-\frac{\displaystyle\sqrt3}{\displaystyle2}t}\right)$$
B
$$\frac2{\sqrt3}te^{-\frac12t}$$
C
$$\frac2{\sqrt3}e^{-\frac12t}\cos\left(\frac{\sqrt3}2t\right)$$
D
$$\frac2{\sqrt3}e^{-\frac12t}\sin\left(\frac{\sqrt3}2t\right)$$
2
GATE ECE 2008
+2
-0.6
The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t). For t > 0, the voltage across the resistor is
A
$$\frac1{\sqrt3}\left(e^{-\frac{\displaystyle\sqrt3}{\displaystyle2}t}-\;e^{-\frac12t}\right)$$
B
$$e^{-\frac12t}\left[\cos\left(\frac{\sqrt3}2t\right)\;-\;\frac1{\sqrt3}\sin\left(\frac{\sqrt3}2t\right)\right]$$
C
$$\frac2{\sqrt3}e^{-\frac{\displaystyle1}{\displaystyle2}t}\sin\left(\frac{\sqrt{3t}}2\right)$$
D
$$\frac2{\sqrt3}e^{-\frac{\displaystyle1}{\displaystyle2}t}\cos\left(\frac{\sqrt{3t}}2\right)$$
3
GATE ECE 2008
+2
-0.6

The circuit shown in the figure is used to charge the capacitor C alternately from two current sources as indicated. The switches S1 and S2 are mechanically coupled and connected as follows

Assume that the capacitor has zero initial charge. Given that u(t) is a unit step function, the voltage Vc(t) across the capacitor is given by

A
B
C
D
4
GATE ECE 2007
+2
-0.6
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
A
0.50 exp(-25t) mA
B
0.25 exp(-25t) mA
C
0.50 exp(-12.5t) mA
D
0.25 exp (-6.25t) mA
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