*Choose the appropriate answer (10 x 2)*

1. The driving point impedance of a network can be calculated from

(a) V(s)/I(s)

(b) I(s)/V(s)

(c) V(s)I(s)

(d) None of these

(The terms have their usual meaning)

2. A resistance of 10Ω in parallel with a reactance of (j10)Ω. shall have a phase angle

(a) 45

^{0}(b) 30

^{0}(c) 60

^{0}(d) None of these

3. A function f(t) is an even function if for all values of (f)

(a) f(t) = f(-t)

(b) f(t) = -f(-t)

(c) f(t) = f(t + T)

(d) f(t) = -f(t + T/2)

4. Which of the following gives the correct number of basic loops?

(a) Equal to the number of branches

(b) Equal to the number of links

(c) Equal to the number of elements

(d) Equal to the number of nodes

5. When a pure LC parallel circuit is in resonance, the circuit condition can be represented by

(a) A short circuit

(b) Normal parallel circuit

(c) An open circuit

(d) None of these

6. Function Ks/[(s + 2) (s + 3)] has

(a) 2 zeros and 1 pole

(b) 2 zeros and 2 poles

(c) 1 zero and 1 pole

(d) 1 zero and 2 poles

7. A transfer function is the Laplace transform of the output of a system whose input is

(a) Unity

(6) Ramp

(c) Zero

(d) Impulse

8. To reduce steady-state error

(a) Decrease natural frequency

(b) Decrease damping

(c) Increase damped frequency

(d) Increase gain constant of the system

9. A negative feedback control system is characterized by

(a) reduced bandwidth

(b) reduced distortion

(c) increased non-linearity

(d) none of these

10. Free response of a control system is the one characterized by

(a) input approaching infinity with time

(b) input being a finite value

(c) zero input

(d) all initial conditions being zero

### Answer

1. (a)

2. (a) Φ = tan

^{-1}(X_{L}/R)3. (a)

A function f(t) is said to be even if, f (t) = f (-t)

A function f(t) is said to be odd if, f (-t) = -f (t)

4. (b) The number of fundamental loops for any given graph = b – (n – 1) = number of Links

5. (c)

In LC parallel resonant circuit, at the resonant frequency, we have

X

_{C}= X_{L}∴ Z = ∞

In a parallel LC circuit, the impedance is at its maximum value (minimum current).

6. (d)

Let's say we have a transfer function defined as a ratio of two polynomials:

H(s) = N(s)/D(s)

Where N(s) and D(s) are simple polynomials.

Zeros are the roots of N(s) (the numerator of the transfer function) obtained by setting N(s) = 0 and solving for s.

Poles are the roots of D(s) (the denominator of the transfer function), obtained by setting D(s) = 0 and solving for s.

7. (d) The transfer function is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input by assuming initial conditions are zero.

TF = L

_{output}/L_{input}So, TF = C(s)/R(s)

So that transfer function of the system is used to calculate the output for a given input.

if the input is an impulse signal then the output is 1, and hence transfer function will be equal to the output of the system.

8. (d) The steady-state error is inversely proportional to the gain. Therefore, it can be reduced by increasing the system gain.

9. (b) Distortion refers to the error in the open-loop system and it has many oscillations in the output and is reduced in case of negative feedback. The gain of the amplifier at an operating point is also reduced accordingly.

10. (c) The free-response of a system is the solution of the describing differential equation of the system when the input is zero.

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