1
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
$$\frac{{\mathrm R}_2}{{\mathrm R}_1\;+\;{\mathrm R}_2}\mathrm e^\frac1{{\mathrm R}_1{\mathrm C}_1}\mathrm u\left(\mathrm t\right)$$
2
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
3
GATE ECE 1989
+2
-0.6

A 10 Ω resistor, a 1 H inductor and 1 $$\mathrm{μF}$$ capacitor are connected in parallel.The combination is driven by a unit step current.Under the steady state condition, the source current flows through

A
the resistor
B
the inductor
C
the capacitor only
D
all the three elements
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