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QUESTION: 1

The ratio of the transfer function Io/Is is

Solution:

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

QUESTION: 2

The voltage across 200 μF capacitor is given by

The steady state voltage across capacitor is

Solution:

QUESTION: 3

The transformed voltage across the 60 μF capacitor is given by

The initial current through capacitor is

Solution:

⇒

QUESTION: 4

The current through an 4 H inductor is given by

The initial voltage across inductor is

Solution:

QUESTION: 5

The amplifier network shown in fig.is stable if

Solution:

⇒ s^{2} + (6 - 2K) s + 1 = 0

(6 - 2K) > 0 ⇒ K < 3

QUESTION: 6

The network shown in fig. is stable if

Solution:

Let v_{1} be the node voltage of middle node

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)

Solution:

QUESTION: 8

A circuit has input v_{in }(t) = cos 2t u(t) V and output i_{o }(t) = 2sin 2t u(t) A. The circuit had no internal stored energy at t = 0. The admittance transfer function is

Solution:

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

Solution:

QUESTION: 10

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

The response is

Solution:

The characteristic equation is s^{2} (s^{2} + 11s + 30) = 0 ⇒ s^{2} (s + 6)(s + 5) = 0

s = -6, -5, Being real and unequal, it is overdamped.

QUESTION: 11

The circuit is shown in fig.

The current ratio transfer function I_{o}/I_{S IS}

Solution:

QUESTION: 12

The circuit is shown in fig.

The response is

Solution:

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

QUESTION: 13

The circuit is shown in fig.

If input i_{s} is 2u(t) A, the output current i_{o} is

Solution:

QUESTION: 14

In the network of Fig. , all initial condition are zero. The damping exhibited by the network is

Solution:

The roots are imaginary so network is underdamped

QUESTION: 15

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

The response is

Solution:

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

Being real and repeated root, it is critically damped.

QUESTION: 16

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

Solution:

⇒

⇒

⇒

QUESTION: 17

Consider the following statements in the circuit shown in fig.

1. It is a first order circuit with steady state value of v_{C}= 10/3, i = 5/3A

2. It is a second order circuit with steady state of v_{C }= 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.

Solution:

It is a second order circuit. In steady state

It has one pole at s = -2

QUESTION: 18

The network function represent a

Solution:

The singularity near to origin is pole. So it may be RC impedance or RL admittance function.

QUESTION: 19

The network function represents an

Solution:

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

QUESTION: 20

The network function represents an

Solution:

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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