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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

Solution:

v_{R}(t) = i(t) x 1 = -20 e^{-2t} = v_{c}(t)

= 80 e ^{-2t}

Now, i'(t) = i(t) + i_{c}(t)

= -20 e^{-2t} + 80 e^{-2t} = 60 e^{-2t}

So,

or,

v(t) = (60 - 30 - 20) e^{-2t} = 10 e^{-2t}

QUESTION: 2

The circuit shown in figure is critically damped.

The value of R is

Solution:

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

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

Solution:

Given,

Taking Laplace transform on both sides,

or,

or,

Using partial fraction expansion,

A = 1, B = 1,

C = - 3

So, V(t) = (t + cos*t* - 3 sin*t*)

QUESTION: 4

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

Solution:

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})

QUESTION: 5

Pole of a network is frequency at which

Solution:

QUESTION: 6

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

Solution:

Characteristic equation of series RLC circuit is

Here,

and

or,

For oscillatory response,

or,

QUESTION: 7

Which of the following conditions are necessary for the validity of initial value theorem

Solution:

QUESTION: 8

The poles and zeros of the transfer function for the circuit shown below are located a

Solution:

Applying KCL at the given node in s-domain, we have

or,

or,

Hence, there is no-zero and poles are at 4 s^{2} + s + 2 = 0

or,

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.

Solution:

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.

QUESTION: 10

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

Solution:

f(t) = e^{-t} sin 2t + e^{-2t} cos 5t

∴

∴ Find value of f(t) is

QUESTION: 11

At t = 0^{+} with zero initial condition, the voltage across 20 Ω resistor is

Solution:

At t = 0^{+}, capacitor will act as short circuit while inductor an open circuit

∴ V_{20Ω} = 10 volt

QUESTION: 12

Assuming zero-initial condition v_{c}(t) in the given circuit will be given by

Solution:

Applying node analysis,

or,

or,

Here

∴

or,

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

Solution:

At t = 0, inductor act as open circuit i(0^{+}) = 0 A

At t = capacitor act as open circuit i(∞) = 0 A

QUESTION: 14

The value of current through R at t = ∞ is

Solution:

At t = ∞, inductor will act as short circuit anc capacitor open circuit.

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?

Solution:

(characteristic equation)

Therefore

If R = 0, ξ = 0 (vice-versa) and for ξ < 1, response will be oscillatory.

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