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This mock test of Network Theory for GATE helps you for every GATE entrance exam.
This contains 25 Multiple Choice Questions for GATE Network Theory (mcq) to study with solutions a complete question bank.
The solved questions answers in this Network Theory quiz give you a good mix of easy questions and tough questions. GATE
students definitely take this Network Theory exercise for a better result in the exam. You can find other Network Theory extra questions,
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QUESTION: 1

If a differential equation is said to be homogeneous, what would be the value of a forcing function?

Solution:

QUESTION: 2

For a series R-L-C resonant circuit, what is the total reactance at the lower half power frequency?

Solution:

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 R_{L} 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 × 10^{3} × 20 × 10^{-6}

= 0.1 sec

QUESTION: 5

The y parameter of the network given in figure.

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:

QUESTION: 8

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

Solution:

QUESTION: 9

The Thenenin impedance across the terminal AB of the given network is

Solution:

QUESTION: 10

The circuit shown in the figure R_{g }is variable between 3 and 30 ohms R_{L} being fixed

**Assertion (A):** For Maximum power transfer across the terminals AB, R_{g} = 3?

**Reason (R):** When Maximum power transfer occurs R_{L} = |Z_{g}|

Solution:

P_{L} is Maximum when I_{L} is Maximum

I_{L} is Maximum when R_{g} in Minimum = 3Ω

A is True

For Maximum power Transfer K_{L}= |Z_{s}|

But here R_{g} 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∠15^{0}V 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 ∠15^{0} Volt

Phase sequence is ABC

Line Voltage

= 10[1∠ - 120^{0} x 1∠15 - 1∠120^{0} x 1∠15]

*Answer can only contain numeric values

QUESTION: 12

Determine Maximum power consumed in the load resistance R_{L }_____ (in watts)

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

Solution:

ω = 2πf = 2π x 50 = 100π

X_{L} = ωL , X_{c} = 1/ω_{c}

Thevenin equivalent across R_{L}

P_{Max} = ± 2R_{L} = (0.026)^{2} x 132.07

P_{Max} = 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:

f_{0} = 4 Hz,

Upper cut off frequency

f_{2} = 8Hz

lower cutoff f_{1} = ?

(4)^{2} = f_{1} x 8

16 = f_{1} x 8

f_{1} = 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

*Answer can only contain numeric values

QUESTION: 16

The system is initially at rest for voltage signal of unit step i(t) = ?

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

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 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 ar t = 0^{+} is

Solution:

KCL and node V_{x}

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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