GATE EC 2004 - PracticePaper

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Question 1

Consider the network graph shown in the figure. Which one of the following is NOT a 'tree' of this graph ?

A	a
B	b
C	c
D	d

Network Theory Graph Theory and State Equations

Question 1 Explanation:

It is forming a closed loop. So it can't be a tree.

Question 2

The equivalent inductance measured between the terminals 1 and 2 for the circuit shown in the figure is

A	$L_{1}+L_{2}+M$
B	$L_{1}+L_{2}-M$
C	$L_{1}+L_{2}+2M$
D	$L_{1}+L_{2}-2M$

Network Theory Basics of Network Analysis

Question 2 Explanation:

If current enters the dotte terminals of coil 1 then a voltage is developed across coil 2 whose higher potential is at dotted terminals.

\begin{aligned} V &=\frac{-M d I}{d t}+\frac{L_{1} d I}{d t}-\frac{M d I}{d t}+L_{2} \frac{d I}{d t} \\ &=\left(L_{1}+L_{2}-2 M\right) \frac{d I}{d t}\\ V&=L_{e q} \frac{d I}{d t} \end{aligned}

Question 3

The circuit shown in the figure, with

R=\frac{1}{3}\Omega ,L=\frac{1}{4}H

and C = 3 F has input voltage v(t) = sin2t. The resulting current i(t) is

A	5 sin(2t + 53.1 $^{\circ}$ )
B	5 sin(2t - 53.1 $^{\circ}$ )
C	25 sin(2t + 53.1 $^{\circ}$ )
D	25 sin(2t - 53.1 $^{\circ}$ )

Network Theory Sinusoidal Steady State Analysis

Question 3 Explanation:

\begin{aligned} i(t)=& V(t), Y \\ Y=& V(t)\left[\frac{1}{R_{1}}+\frac{1}{j \omega L}+j \omega C\right] \\ =& \sin 2 t\left[3+\frac{4}{2 j}+j \times 2 \times 3\right] \\ =& \sin 2 t[3-2 j+6 j]=\sin 2 t[3+4 j] \\ =& 5 \sin 2 t \angle \tan ^{-1} \frac{4}{3}=5 \sin \left(2 t+53.1^{\circ}\right) \end{aligned}

Question 4

For the circuit shown in the figure, the time constant RC = 1 ms. The input voltage is

v_{i}(t)=\sqrt{2}sin10^{3}t

. The output voltage

v_{o}(t)

is equal to

A	$sin(10^{3}t-45^{\circ})$
B	$sin(10^{3}t+45^{\circ})$
C	$sin(10^{3}t-53^{\circ})$
D	$sin(10^{3}t+53^{\circ})$

Network Theory Sinusoidal Steady State Analysis

Question 4 Explanation:

\begin{aligned} v_{0}(t)&=\frac{\frac{1}{j \omega C}}{R+\frac{1}{j \omega C}}\; v_{i}(t)=\frac{1}{1+j \omega C R} \sqrt{2} \sin 10^{3} t \\ &=\frac{1}{1+j \times 10^{3} \times 10^{-3}} \sqrt{2} \sin 10^{3} t \\ v_{0}(t) &=\sin \left(10^{3} t-45^{\circ}\right) \end{aligned}

Question 5

For the R - L circuit shown in the figure, the input voltage

v_{i}

(t) = u(t). The current i(t) is

A	a
B	b
C	c
D	d

Network Theory Transient Analysis

Question 5 Explanation:

\begin{aligned} I(s)&=\frac{V(s)}{s+2}=\frac{1}{s(s+2)} \\ I(s)&=\frac{1}{s(s+2)}=\frac{1}{2}\left[\frac{1}{s}-\frac{1}{s+2}\right] \\ i(t)&=\frac{1}{2}\left(1-e^{-2 t}\right) \\ \text { At } \quad t&=0, i(t)=0 \\ t&=\infty, i(t)=0.5 \\ t&=\frac{1}{2}, i(t)=0.31 \end{aligned}

Graph (c) satisfies all conditions .

Question 6

The impurity commonly used for realizing the base region of a silicon n - p - n transistor is

A	Gallium
B	Indium
C	Boron
D	Phosphorus

Electronic Devices Basic Semiconductor Physics

Question 7

If for a silicon npn transistor, the base-to-emitter voltage (

V_{BE}

) is 0.7 V and the collector-to-base voltage (

V_{CB}

) is 0.2 V, then the transistor is operating in the

A	normal active mode
B	saturation mode
C	inverse active mode
D	cutoff mode

Electronic Devices BJT and FET Basics

Question 8

Consider the following statements S1 and S2.
S1 : The

\beta

of a bipolar transistor reduces if the base width is increased.
S2 : The

\beta

of a bipolar transistor increases if the dopoing concentration in the base is increased.
Which remarks of the following is correct ?

A	S1 is FALSE and S2 is TRUE
B	Both S1 and S2 are TRUE
C	Both S1 and S2 are FALSE
D	S1 is TRUE and S2 is FALSE

Electronic Devices BJT and FET Basics

Question 8 Explanation:

\beta=\frac{I_{C}}{I_{B}}=\frac{\alpha}{1-\alpha}

When base width increases, recombination in base region increases and

\alpha

decreases and hence

\beta

decreases.
If doping in base region increases , then recombination in base increases and

\alpha

decreases, thereby decreasing

\beta.

Question 9

An ideal op-amp is an ideal

A	voltage controlled current source
B	voltage controlled voltage source
C	current controlled current source
D	current controlled voltage source

Analog Circuits Operational Amplifiers

Question 10

Voltage series feedback (also called series-shunt feedback) results in

A	increase in both input and output impedances
B	decrease in both input and output impedances
C	increase in input impedance and decrease in output impedance
D	decrease in input impedance and increase in output impedance

Analog Circuits Feedback Amplifiers

There are 10 questions to complete.