1
GATE ECE 2003
+2
-0.6

The circuit is given in figure.Assume that the switch S is in position 1 for a long time and thrown to position 2 at t = 0.

I1(s) and I2(s) are the Laplace transforms of i1(t) and i2(t) respectively. The equations for the loop currents I1(s) and I2(s) for the circuit shown in figure, after the switch is brought from position 1 to position 2 at t = 0, are

A
B
C
D
2
GATE ECE 1996
+2
-0.6

The voltage VC1, VC2 and VC3 across the capacitors in the circuit in Fig., under steady state, are respectively

A
80 V, 32 V, 48 V
B
80 V, 48 V, 32 V
C
20 V, 8V, 12 V
D
20 V, 12 V, 8 V
3
GATE ECE 1992
+2
-0.6

For the compensated attenuator of figure, the impulse response under the condition $$R_1C_1\;=\;R_2C_2$$ is:

A
$$\frac{{\mathrm R}_2}{{\mathrm R}_1\;+\;{\mathrm R}_2}\left[1\;-\;\mathrm e^\frac1{{\mathrm R}_1{\mathrm C}_1}\right]\mathrm u\left(\mathrm t\right)$$
B
$$\frac{{\mathrm R}_2}{{\mathrm R}_1\;+\;{\mathrm R}_2}\mathrm\delta\left(\mathrm t\right)$$
C
$$\frac{{\mathrm R}_2}{{\mathrm R}_1\;+\;{\mathrm R}_2}\mathrm u\left(\mathrm t\right)$$
D
$$\frac{{\mathrm R}_2}{{\mathrm R}_1\;+\;{\mathrm R}_2}\mathrm e^\frac1{{\mathrm R}_1{\mathrm C}_1}\mathrm u\left(\mathrm t\right)$$
4
GATE ECE 1990
+2
-0.6

If the Laplace transform of the voltage across a capacitor of value of $$\frac12\;\mathrm F$$ is $$V_C\;\left(s\right)\;=\;\frac{s\;+\;1}{s^3\;+\;s^2\;+\;s\;+\;1}$$ , the value of the current through the capacitor at t = 0+ is

A
0 A
B
2 A
C
$$\frac12\;\mathrm A$$
D
1 A
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