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Test: Network Theory


25 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Network Theory


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Attempt Test: Network Theory | 25 questions in 75 minutes | Mock test for GATE preparation | Free important questions MCQ to study GATE Electrical Engineering (EE) 2023 Mock Test Series for GATE Exam | Download free PDF with solutions
QUESTION: 1

Unit of inductance is ________.

Solution:

The unit of inductance is Henry. Weber is the unit of magnetic flux. Tesla is the unit of flux density. Farad is the unit of capacitance.

QUESTION: 2

Which of the following is not the energy stored in a capacitor?

Solution:

Energy stored in a capacitor, E = CV2/2
Using C = Q/V
E = CV2/2 = QV/2 = Q2/2C

QUESTION: 3

Two AC sources feed a common variable resistive load as shown in figure below.

The maximum power that can be transferred to a variable load RL is _______ W.

Solution:

 

QUESTION: 4

The switch of below circuit was open for long and at t = 0 it is closed. What is the final steady state voltage across the capacitor and the time constant of the circuit?
Solution:

Final value = 20/2 = 10 Volt
Time constant τ= 5 × 103 × 20 × 10-6
= 0.1 sec

QUESTION: 5

The y parameter of the network given in figure is:
Solution:


QUESTION: 6

The power consumed by a coil is 300 W when connected to 30 V dc source and 108 W. When connected to a 30 V A.C. source. The reactance of the coil is:
Solution:
  • In DC, inductive reactance X=0; since f=0;
  • Only, Resistance exist in coil for DC,
    R=(30*30/300)=3 ohm;
  • In AC, Z=R+jX;
  • But here in second part of question we given that real power in ac circuit is 108 watt. We can calculate current in the ac circuit:
    I=√(108/3)= √36=6 amp
  • This current flow through resistance of AC circuit so this is the current of AC circuit.
  • So,
    Z =V/I
    Z=30/6=5
    X=√{5^2–3^2} = 4ohm
QUESTION: 7

For a transmission line open circuit and short circuit impedances are 20 Ω and 5 Ω. Then characteristic impedance is:
Solution:
  • The characteristic impedance is the geometric mean of the short and open circuit impedance.
  • It is given by Zo2 = Zsc Zoc. On substituting Zoc = 20 and Zsc = 5, we get Zo2 = 20 X 5 = 100.
  • Thus Zo = 10 ohm.
QUESTION: 8

A human nerve cell has an open circuit voltage of 80 mV and it can deliver a current of 5 nA through a 6 MΩ load. What is the maximum power available from the cell?
Solution:

QUESTION: 9

The Thevenin impedance across the terminal AB of the given network is:
Solution:


QUESTION: 10

The circuit shown in the figure Rg is variable between 3 and 30 ohms RL being fixed.
Assertion (A): For Maximum power transfer across the terminals AB, Rg = 3?
Reason (R): When Maximum power transfer occurs RL = |Zg|
Solution:


  • PL is Maximum when IL is Maximum
  • IL is Maximum when Rg in Minimum = 3Ω 
  • Thus A is True
  • For Maximum power Transfer KL= |Zs|
  • But here Rg is variable, so it should be low so R is True but not the correct explanation of A. 
QUESTION: 11

A line to neutral voltage is 10∠150V for a balanced three phase star connected load with phase sequence ABC. The voltage of line B with respect to line C is given by:
Solution:

 = 10 ∠150 Volt
Phase sequence is ABC


Line Voltage


= 10[1∠ - 1200 x 1∠15 - 1∠1200 x 1∠15]

*Answer can only contain numeric values
QUESTION: 12

Determine Maximum power consumed in the load resistance RL _____ (in watts)

(Important - Enter only the numerical value in the answer)

Solution:

ω = 2πf = 2π x 50 = 100π
XL = ωL , Xc = 1/ωc
Thevenin equivalent across RL
 

PMax = ± 2RL = (0.026)2 x 132.07
PMax = 8.92 Watt 

QUESTION: 13

A series R-L-C circuit resonates at 4Hz it provides 0.707 lag P.F. at 8 Hz. The frequency at which it gives 0.707 lead P.F is?
Solution:

f0 = 4 Hz,
Upper cut off frequency
f2 = 8Hz
lower cutoff f1 = ?


(4)2 = f1 x 8
16 = f1 x 8
f1 = 2Hz 

QUESTION: 14

In series RLC circuit, the voltage across capacitor and inductor are ______ with each other.
Solution:

In series RLC circuit, the voltage across capacitor and inductor are 180⁰ out of phase with each other. The frequency at which the resonance occurs is called resonant frequency.

QUESTION: 15

A series R-L-C circuit has a resonance frequency of 1kHz and a quality factor Q = 100. If each of R, L and C is doubled from its original value then new Q of the circuit is:
Solution:


Quality factor:



if R, L, C double:
R' = 2R, L' = 2L, C' = 2C

QUESTION: 16

 A 25 Ω resistor has a voltage of 150 sin377 t. Find the corresponding power.
Solution:

QUESTION: 17

Consider the following function: 

1. 

2.

3.

4.

Which of the above function are LC driving point impedances?
Solution:

Only (1) and (2) are L-C driving point impedance.

QUESTION: 18

If an RC driving point impedance function Z(S) has an equal number of poles and zero’s at finite locations then:
Solution:

Let us Consider: 


QUESTION: 19

For the circuit shown below the pole’s of the driving point impedance function are at which one of the following location?
Solution:


A Pole at S = -1 and a zero at S = - 1/2.

QUESTION: 20

The voltage and current wave functions for an element are shown in the figures.

 

The circuit element and its value are:
Solution:

For L = 2H

So element is inductor and its value is 2H

QUESTION: 21

The steady state in the circuit shown in the given figure is reached with S open. S is closed at t = 0. The current I at t = 0+ is:
Solution:

KCL and node Vx



QUESTION: 22

The total impedance Z(Jω) of the circuit shown below is:
Solution:


QUESTION: 23

Identify which of the following is not a tree of the graph shown in figure.
Solution:

Tree

QUESTION: 24

Two lamps each of 230V and 60W rating are connected in series across a single phase 230V supply. The total power consumed by the two lamps would be:
Solution:

Resistance of each lamp


Hence Total resistance offered by 2 these lamps   
So total power consumed by two lamps 

QUESTION: 25

For the R-L circuit shown the current i(t) for unit step input voltage will rise to 0.63 is:
Solution:

The time at which the current rise to 63% of its final value is Time constant, 

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