# GATE EC 2002

 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 =$0^{+}$ is 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 $20^{\circ}$C, $V_{D}$ is found to be 700 mV. If the temperature rises to $40^{\circ}$C, $V_{D}$ 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}

There are 5 questions to complete.