1
GATE ECE 2010
+2
-0.6
In the circuit shown, the switch S is open for a long time and is closed at t=0. The current i(t) for t ≥ 0+ is
A
i(t) = 0.5 - 0.125e-1000t A
B
i(t) = 1.5 - 0.125e-1000t A
C
i(t) = 0.5 - 0.5e-1000t A
D
i(t) = 0.375e-1000t A
2
GATE ECE 2009
+2
-0.6
The time domain behavior of an RL circuit is represented by $$\mathrm L\frac{\mathrm{di}\left(\mathrm t\right)}{\mathrm{dt}}+\mathrm{Ri}\;=\;{\mathrm V}_0\left(1\;+\;\mathrm{Be}^{-\mathrm{Rt}/\mathrm L}\;\sin\;\mathrm t\right)\mathrm u\left(\mathrm t\right)$$\$ For an initial current of i(0) = $$\frac{{\mathrm V}_0}{\mathrm R}$$, the steady state value of the current is given by
A
$$\mathrm i\left(\mathrm t\right)\rightarrow\frac{{\mathrm V}_0}{\mathrm R}$$
B
$$\mathrm i\left(\mathrm t\right)\rightarrow\frac{2{\mathrm V}_0}{\mathrm R}$$
C
$$\mathrm i\left(\mathrm t\right)\rightarrow\frac{{\mathrm V}_0}{\mathrm R}\left(1+\mathrm B\right)$$
D
$$\mathrm i\left(\mathrm t\right)\rightarrow\frac{2{\mathrm V}_0}{\mathrm R}\left(1+\mathrm B\right)$$
3
GATE ECE 2009
+2
-0.6
The switch in the circuit shown was on position ‘a’ for a long time and is moved to position ‘b’ at time t = 0. The current i(t) for t > 0 is given by
A
0.2e-125t u(t) mA
B
20e-1250t u(t) mA
C
0.2e-1250t u(t) mA
D
20e-1000t u(t) mA
4
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
$$\frac2{\sqrt3}e^{-\frac12t}\sin\left(\frac{\sqrt3}2t\right)$$
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