Test: Circuit Analysis in the S-Domain

# Test: Circuit Analysis in the S-Domain

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## 20 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Circuit Analysis in the S-Domain

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Test: Circuit Analysis in the S-Domain - Question 1

### The ratio of the transfer function Io/Is is Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 1

Io/Is = (s + 4)/ (s + 4 + 3/s) = s(s + 4)/(s + 1)(s + 3).

Test: Circuit Analysis in the S-Domain - Question 2

### The voltage across 200 μF capacitor is given by The steady state voltage across capacitor is

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 2  Test: Circuit Analysis in the S-Domain - Question 3

### The transformed voltage across the 60 μF capacitor is given by The initial current through capacitor is

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 3   ⇒     Test: Circuit Analysis in the S-Domain - Question 4

The current through an 4 H inductor is given by The initial voltage across inductor is

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 4     Test: Circuit Analysis in the S-Domain - Question 5

The amplifier network shown in fig.is stable if Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 5   ⇒ s2 + (6 - 2K) s + 1 = 0
(6 - 2K) > 0  ⇒ K < 3

Test: Circuit Analysis in the S-Domain - Question 6

The network shown in fig. is stable if Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 6

Let v1 be the node voltage of middle node        Test: Circuit Analysis in the S-Domain - Question 7

A circuit has a transfer function with a pole s = -4 and a zero which may be adjusted in position as s= -a The response of this system to a step input has a term of form Ke -4t. The K will be (H= scale factor)

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 7    Test: Circuit Analysis in the S-Domain - Question 8

A circuit has input vin (t) = cos 2t u(t) V and output io (t) = 2sin 2t u(t) A. The circuit had no internal stored energy at t = 0. The admittance transfer function is

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 8  Test: Circuit Analysis in the S-Domain - Question 9

A two terminal network consists of a coil having an inductance L and resistance R shunted by a capacitor C. The poles of the driving point impedance function Z of this network are at and zero at -1. If Z(0) =1the value of R, L, C are

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 9  Test: Circuit Analysis in the S-Domain - Question 10

The current response of a network to a unit step input is The response is

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 10

The characteristic equation is  s2 (s2 + 11s + 30) = 0 ⇒ s2 (s + 6)(s + 5) = 0
s = -6, -5, Being real and unequal, it is overdamped.

Test: Circuit Analysis in the S-Domain - Question 11

The circuit is shown in fig. The current ratio transfer function Io/IS  IS

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 11  Test: Circuit Analysis in the S-Domain - Question 12

The circuit is shown in fig. The response is

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 12

The characteristic equation is (s+1 (s+3) = 0. Being real and unequal root, it is overdamped response.

Test: Circuit Analysis in the S-Domain - Question 13

The circuit is shown in fig. If input is is 2u(t) A, the output current io is

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 13    Test: Circuit Analysis in the S-Domain - Question 14

In the network of Fig. , all initial condition are zero. The damping exhibited by the network is Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 14  The roots are imaginary so network is underdamped

Test: Circuit Analysis in the S-Domain - Question 15

The voltage response of a network to a unit step input is The response is

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 15

The characteristic equation is s(s2 + 8s + 16) = 0 , (s + 4)2 = 0, s = -4, -4

Being real and repeated root, it is critically damped.

Test: Circuit Analysis in the S-Domain - Question 16

The response of an initially relaxed circuit to a signal vs is e-2t u(t). If the signal is changed to , the response would be

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 16 ⇒  ⇒    ⇒ Test: Circuit Analysis in the S-Domain - Question 17

Consider the following statements in the circuit shown in fig. 1. It is a first order circuit with steady state value of vC= 10/3, i = 5/3A

2. It is a second order circuit with steady state of v= 2 V , i = 2 A

3. The network function V(s)/I(s)has one pole.

4. The network function V(s)/I(s) has two poles.

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 17

It is a second order circuit. In steady state      It has one pole at s = -2

Test: Circuit Analysis in the S-Domain - Question 18

The network function represent a

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 18  The singularity near to origin is pole. So it may be RC impedance or RL admittance function.

Test: Circuit Analysis in the S-Domain - Question 19

The network function represents an

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 19

Poles and zero does not interlace on negative real axis so it is not a immittance function

Test: Circuit Analysis in the S-Domain - Question 20

The network function represents an

Detailed Solution for Test: Circuit Analysis in the S-Domain - Question 20

The singularity nearest to origin is a zero. So it may be RL impedance or RC admittance function. Because of (D) option it is required to check that it is a valid RC admittance function. The poles and zeros interlace along the negative real axis. The residues are real and positive.

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