Test: Second Order RLC Circuits- 2

# Test: Second Order RLC Circuits- 2

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## 15 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Second Order RLC Circuits- 2

Test: Second Order RLC Circuits- 2 for Electrical Engineering (EE) 2023 is part of GATE Electrical Engineering (EE) 2023 Mock Test Series preparation. The Test: Second Order RLC Circuits- 2 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Second Order RLC Circuits- 2 MCQs are made for Electrical Engineering (EE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Second Order RLC Circuits- 2 below.
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Test: Second Order RLC Circuits- 2 - Question 1

### If the value of current i(t) for the circuit shown below is i(t) -20 e-2t, then the voltage source v(t) will be given by Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 1 vR(t) = i(t) x 1 = -20 e-2t = vc(t) = 80 e -2t
Now, i'(t) = i(t) + ic(t)
= -20 e-2t + 80 e-2t = 60 e-2t
So, or,
v(t) = (60 - 30 - 20) e-2t = 10 e-2t

Test: Second Order RLC Circuits- 2 - Question 2

### The circuit shown in figure is critically damped. The value of R is

Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 2 For an RLC series circuit to be critically damped or, or, 120 R = 40 ( R + 120)
or, 3 R = R + 120 or R = 60 Ω

Test: Second Order RLC Circuits- 2 - Question 3

### The voltage across a passive element in an electric circuit is given by It is given that V(0+) The value of v(t) is

Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 3

Given, Taking Laplace transform on both sides,   or, or, Using partial fraction expansion,
A = 1, B = 1,
C = - 3 So, V(t) = (t + cost - 3 sint)

Test: Second Order RLC Circuits- 2 - Question 4

A voltage is given by V(s) = 1/S(S + a). If V(∞) = 2 volts, then V(1) is

Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 4

Given, = 1/a = 2
or, a = 0.5
Thus,  or v(t) = 2(1 - e - 0.5t)
Hence, v(1) = 2(1 - e-0.5)

Test: Second Order RLC Circuits- 2 - Question 5

Pole of a network is frequency at which

Test: Second Order RLC Circuits- 2 - Question 6

Transient current in an R-L-C circuit oscillatory when

Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 6

Characteristic equation of series RLC circuit is Here, and or, For oscillatory response, or, Test: Second Order RLC Circuits- 2 - Question 7

Which of the following conditions are necessary for the validity of initial value theorem Test: Second Order RLC Circuits- 2 - Question 8

The poles and zeros of the transfer function for the circuit shown below are located a Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 8

Applying KCL at the given node in s-domain, we have or, or, Hence, there is no-zero and poles are at 4 s2 + s + 2 = 0
or, Test: Second Order RLC Circuits- 2 - Question 9

Assertion (A): Laplace transformation finds its application in solving the transient behaviour of the electric circuits.
Reason (R): The transient response of an electrical circuit can best be described by a linear differential equation.

Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 9

Because the transient response of an electrical circuit can best be described by a differential equation hence, Laplace transformation finds its application in solving the transient behaviour of the electric circuits.

Test: Second Order RLC Circuits- 2 - Question 10

The final value of f(t) = e-t (sin 2t + cos 5t) is

Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 10

f(t) = e-t sin 2t + e-2t cos 5t
∴  ∴ Find value of f(t) is  Test: Second Order RLC Circuits- 2 - Question 11

At t = 0+ with zero initial condition, the voltage across 20 Ω resistor is Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 11

At t = 0+, capacitor will act as short circuit while inductor an open circuit ∴ V20Ω = 10 volt

Test: Second Order RLC Circuits- 2 - Question 12

Assuming zero-initial condition vc(t) in the given circuit will be given by Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 12

Applying node analysis, or, or, Here  ∴ or, Test: Second Order RLC Circuits- 2 - Question 13

The initial and final value of current through the resistor Rina series RLC circuit with unit step input and zero initial condition are respectively

Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 13 At t = 0, inductor act as open circuit i(0+) = 0 A
At t = capacitor act as open circuit i(∞) = 0 A

Test: Second Order RLC Circuits- 2 - Question 14

The value of current through R at t = ∞ is Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 14

At t = ∞, inductor will act as short circuit anc capacitor open circuit. Test: Second Order RLC Circuits- 2 - Question 15

Consider the following statements for a series RLC circuit excited with a voltage v(t)
1. For ξ, = 0, there is no-loss in the circuit.
2. The damping ratio of the circuit is independent of resistance R of the circuit.
3. The response of the circuit is oscillator if ξ value is more than unity.

Q. Which of the above statements is/are true?

Detailed Solution for Test: Second Order RLC Circuits- 2 - Question 15 (characteristic equation)
Therefore If R = 0, ξ = 0 (vice-versa) and for ξ < 1, response will be oscillatory.

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