GATE EC 2003

Question 1
The minimum number of equations required to analyze the circuit shown in the figure is
A
3
B
4
C
6
D
7
Network Theory   Basics of Network Analysis
Question 1 Explanation: 
As voltage at 1 node is known
\therefore using nodal analysis only 3 equations required.
Question 2
A source of angular frequency 1 rad/sec has a source impedance consisting of 1 \Omega resistance in series with 1 H inductance. The load that will obtain the maximum power transfer is
A
1 \Omega resistance
B
1 \Omega resistance in parallel with 1 H inductance
C
1 \Omega resistance in series with 1 F capacitor
D
1 \Omega resistance in parallel with 1 F capacitor
Network Theory   Network Theorems
Question 2 Explanation: 
\begin{aligned} Z_{L}&=R_{S}-j X_{s} \\ \therefore \quad Z_{L}&=1-1 j \end{aligned}
Question 3
A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q=100. If each of R, L and C is doubled from its original value, the new Q of the circuit is
A
25
B
50
C
100
D
200
Network Theory   Sinusoidal Steady State Analysis
Question 3 Explanation: 
\begin{aligned} Q=& \frac{f_{o}}{B W} \\ f_{0} &=\frac{1}{2 \pi \sqrt{L C}} \\ B W &=\frac{R}{L} \\ \text { (Characteristic equation } &\left.=s^{2}+\frac{R s}{L}+\frac{1}{L C}\right)\\ \text{or}\qquad&=\frac{1}{R} \sqrt{\frac{L}{C}} \\ \text{When R, L, C are doubled,}\\ Q&=\frac{1}{2} Q=50 \end{aligned}
Question 4
The Laplace transform of i(t) is given by
I(s)=\frac{2}{s\left ( 1+s \right )}
At t\rightarrow \infty
The value of i(t) tends to
A
0
B
1
C
2
D
\infty
Signals and Systems   Laplace Transform
Question 4 Explanation: 
\begin{aligned} \lim _{t \rightarrow \infty} i(t) &=\lim _{s \rightarrow 0} s I(s) \\ &=\operatorname{lims}_{s \rightarrow 0} \frac{2}{s(1+s)}=2 \end{aligned}
Question 5
The differential equation for the current i(t) in the circuit of the figure is
A
2\frac{d^{2}i}{dt^{2}}+2\frac{di}{dt}+i(t)=\sin t
B
\frac{d^{2}i}{dt^{2}}+2\frac{di}{dt}+2i(t)=\cos t
C
2\frac{d^{2}i}{dt^{2}}+2\frac{di}{dt}+i(t)=\cos t
D
\frac{d^{2}i}{dt^{2}}+2\frac{di}{dt}+2i(t)=\sin t
Network Theory   Graph Theory and State Equations
Question 5 Explanation: 
Applying KVL,
\sin t=i(t) \times 2+L \frac{d i(t)}{d t}+\frac{1}{c} \int i(t) d t
\sin t=2 i(t)+2 \frac{d i(t)}{d t}+\int i(t) d t
Differentiating with respect to t
\cos (t)=\frac{2 d i(t)}{d t}+\frac{2 d^{2} i(t)}{d t^{2}}+i(t)
Question 6
n-type silicon is obtained by doping silicon with
A
Germanium
B
Aluminium
C
Boron
D
Phosphorus
Electronic Devices   Basic Semiconductor Physics
Question 7
The Bandgap of silicon at 300 K is
A
1.36 eV
B
1.10 eV
C
0.80 eV
D
0.67 eV
Electronic Devices   Basic Semiconductor Physics
Question 8
The intrinsic carrier concentration of silicon sample at 300 K is 1.5\times 10^{16}/m^{3}. If after doping, the number of majority carriers is 5\times 10^{20}/m^{3}, the minority carrier density is
A
4.50\times 10^{11}/m^{3}
B
3.333\times 10^{4}/m^{3}
C
5.00\times 10^{20}/m^{3}
D
3.00\times 10^{-5}/m^{3}
Electronic Devices   Basic Semiconductor Physics
Question 8 Explanation: 
\begin{aligned} n_{i}^{2} &=n p \\ n_{i} &=\text { intrinsic concentration } \\ p &=\frac{n_{1}^{2}}{n}=\frac{1.5 \times 10^{16} \times 1.5 \times 10^{16}}{5 \times 10^{20}} \\ &=45 \times 10^{10}=4.5 \times 10^{11} / \mathrm{cm}^{3} \end{aligned}
Question 9
Choose proper substitutes for X and Y to make the following statement correct Tunnel diode and Avalanche photo diode are operated in X bias ad Y bias respectively
A
X: reverse, Y: reverse
B
X: reverse, Y: forward
C
X: forward, Y: reverse
D
X: forward, Y: forward
Electronic Devices   PN-Junction Diodes and Special Diodes
Question 10
For an n - channel enhancement type MOSFET, if the source is connected at a higher potential than that of the bulk (i.e. V_{SB} \gt 0), the threshold voltage V_{T} of the MOSFET will
A
remain unchanged
B
decrease
C
change polarity
D
increase
Electronic Devices   BJT and FET Basics
Question 10 Explanation: 
V_{T}=V_{T_{0}}+\gamma \sqrt{\left|-2 \phi_{F}+V_{S B}\right|}-\sqrt{\left|2 \phi_{F}\right|}
\gamma= substrate bias coefficient
V_{S B}= substrate bias voltage
There are 10 questions to complete.
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