1
GATE ECE 2017 Set 1
Numerical
+2
-0
In the circuit shown the voltage $${V_{IN}}\,\left( t \right)$$ is described by: $${V_{IN}}\,\left( t \right) = \left\{ {\matrix{ {0,} & {for\,\,\,t < 0} \cr {15Volts,} & {for\,\,\,t \ge 0} \cr } } \right.$$\$

where $$'t'$$ is in seconds. The time (in seconds) at which the current $${\rm I}$$ in the circuit will reach the value $$2$$ Ampere is ______ .

2
GATE ECE 2017 Set 1
Numerical
+2
-0
The figure shows an RLC circuit excited by the sinusoidal voltage $$100cos(3t)$$ Volts, where $$t$$ is in seconds. The ratio $${{amplitude\,\,of\,\,{V_2}} \over {amplitude\,\,of\,\,{V_1}}}\,\,$$ is ________ .
3
GATE ECE 2016 Set 1
Numerical
+2
-0

An AC voltage source V = 10 sin(t) volts is applied to the following network. Assume that R1 = 3 kΩ, R2 = 6 kΩ and R3 = 9 kΩ and that the diode is ideal.

RMS current Irms (in mA) through the diode is _________.

4
GATE ECE 2016 Set 1
+2
-0.6
A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of the form
$$\sum\limits_{k = 1}^3 {{a_k}\,\,\cos \,\left( {k{\omega _0}t} \right),\,\,\,}$$ where $${a_k} \ne 0,\,\,{\omega _0} \ne 0$$.

The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?

A
$$\sum\limits_{k = 1}^3 {{b_k}{\mkern 1mu} {\mkern 1mu} \cos \left( {k{\omega _0}t + {\phi _k}} \right),{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} }$$ where $${b_k} \ne {a_k},\,\,\forall k$$
B
$$\sum\limits_{k = 1}^3 {{b_k}\,\,\cos \left( {k{\omega _0}t + {\phi _k}} \right)\,\,\,}$$ , where $${b_k} \ne 0,\,\,\forall k$$
C
$$\sum\limits_{k = 1}^3 {{a_k}\,\,\cos \left( {k{\omega _0}t + {\phi _k}} \right)\,\,\,}$$
D
$$\sum\limits_{k = 1}^3 {{a_k}\,\,\cos \left( {k{\omega _0}t + {\phi _k}} \right)\,\,\,}$$
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