GATE EC 2002 - PracticePaper

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Question 1

The dependent current source shown in Figure

A	delivers 80 W
B	absorbs 80 W
C	delivers 40 W
D	absorbs 40 W

Network Theory Basics of Network Analysis

Question 1 Explanation:

Applying KVL,

20-5 I-5\left(I+\frac{V_{1}}{5}\right)=0

20-10 I-20=0

\Rightarrow \quad I=0

\therefore

Only dependent source acts.

\frac{V_{1}}{5}=4 \mathrm{A}

Power delivered

=I^{2} R=16 \times 5=80 \mathrm{W}

Question 2

In figure, the switch was closed for a long time before opening at t = 0. the voltage

V_x

at t =

0^{+}

A	25 V
B	50 V
C	-50 V
D	0 V

Network Theory Transient Analysis

Question 2 Explanation:

When switch was closed circuit was in steady state,

i_{L}(O-) = 2.5 A

At,

t = 0^{+}

\begin{aligned} \Rightarrow & & V=I R \\ & &=2.5 \times 20=50 \mathrm{V} \end{aligned}

\therefore \quad V_{x}=-50 \mathrm{V}

(Polarity of

V_{x}

is given reverse of n)

Question 3

Convolution of x(t+5) with impulse function

\delta

(t-7) is equal to

A	x(t - 12)
B	x(t + 12)
C	x(t - 2)
D	x(t + 2)

Signals and Systems LTI Systems Continuous and Discrete

Question 3 Explanation:

\begin{aligned} x(t+5) * \delta(t-7) &=x(t+5-7) \\ &=x(t-2) \end{aligned}

Question 4

Which of the following cannot be the Fourier series expansion of a periodic signal?

A	x(t) = 2cos t + 3 cos 3t
B	x(t) = 2cos $\pi$ t + 7 cos t
C	x(t) = cos t + 0.5
D	x(t) = 2cos 1.5 $\pi$ t + sin 3.5 $\pi$ t

Signals and Systems Fourier Series

Question 4 Explanation:

\begin{aligned} x(t) &=2 \cos \pi t+7 \cos t \\ T_{1} &=\frac{2 \pi}{(0)}=2 \\ T_{2} &=\frac{2 \pi}{1}=2 \pi \\ \frac{T_{1}}{T_{2}} &=\frac{1}{\pi}=\text { irrational } \end{aligned}

\therefore x(t)

is not periodic and does not satisfy Dirichlet condition.

Question 5

In Figure shown below, a silicon is carrying a constant current of 1 mA. When the temperature of the diode is

20^{\circ}

V_{D}

is found to be 700 mV. If the temperature rises to

40^{\circ}

V_{D}

becomes approximately equal to

A	740 mV
B	660 mV
C	680 mV
D	700 mV

Electronic Devices PN-Junction Diodes and Special Diodes

Question 5 Explanation:

For either Si or Ge

\frac{d V}{d T} \simeq-2 \mathrm{mV} /^{\circ} \mathrm{C}

in order to maintain a constant value of I.

\begin{aligned} T_{2}-T_{1}&=40-20=20^{\circ} \mathrm{C} \\ -2 \times 20 \mathrm{mV}&=40 \mathrm{mV} \\ \text { Therefore, } \quad V_{D}&=700-40=660 \mathrm{mV} \end{aligned}

Question 6

In a negative feedback amplifier using voltage-series (i.e. voltage-sampling series mixing) feedback. (Ri and Ro denote the input and output resistance respectively)

A	Ri decreases and Ro decreases
B	Ri decreases and Ro increases
C	Ri increases and Ro decreases
D	Ri increases and Ro increases

Analog Circuits Feedback Amplifiers

Question 6 Explanation:

R_{i}

increases by factor of

1+A \beta

and

R_{0}

decreases by

1+A \beta

Question 7

A 741-type op-amp has a gain-bandwidth product of 1 MHz. A non-inverting amplifier using this op-amp and having a voltage gain of 20 dB will exhibit a 3-dB bandwidth of

A	50KHz
B	100KHz
C	1000/17KHz
D	1000/7.07KHz

Analog Circuits Operational Amplifiers

Question 7 Explanation:

\begin{aligned} 20 \log x &=20 \mathrm{dB} \\ x &=10 \\ \text{Gain} \times B W &=1 \times 10^{6} \\ B W &=\frac{1 \times 10^{6}}{\text { Gain }}=\frac{10^{6}}{10}=100 \mathrm{k}=10^{5} \end{aligned}

Question 8

Three identical RC-coupled transistor amplifiers are cascaded. If each of the amplifiers has a frequency response as shown in Figure, the overall frequency response is as given in