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Circuit Theory & Control - MCQs from AMIE exams (Winter 2019)

Answer the following (10 x 2)

1. The number of branches in a graph is 8. The number of sub-graphs in the network is
(a) 256
(b) 254
(c) 128
(d) 126

2. The dual of a parallel R-C circuit is a
(a) Parallel RC circuit
(b) Series RC circuit
(c) Series RL circuit
(d) Parallel RL circuit

3. The bandwidth of a series resonant circuit with R=10 KΩ, L= 20 mH, C = 5 µF is
(a) 80 kHz
(b) 800 kHz
(c) 100 Hz
(d) 1 GHz

4. The value of h22 of the circuit shown in the figure.

(a) 0.3
(b) 20
(c) 3.33
(d) 0.05

5. The maximum value of mutual inductance of two inductively coupled coils leaving equal self-inductance of 6 mH is
(a) 6 mH
(b) 36 mH
(c) 12 mH
(d) 3 mH

6. A system has transfer function G(s) = 1/(s + 12). Its settling time and rise time respectively are
(a) 0.33, 0.183
(b) 0.183, 0.33
(c) 0.077, 0.33
(d) 0.33, 0.077

7. A unity feedback system has the following forward transfer function:
G(s) = \frac{{10(s + 20)(s + 30)}}{{s(s + 25)(s + 35)}}
The steady-state error when the input is 15tu(t) is
(a) 0
(b) 0.4
(c) Infinity
(d) 2.1875

8. For a unity feedback system with die forward transfer function  
G(s) = \frac{K}{{s(s + 1)(s + 2)}}
the range of k for which the system is stable.
(a) 0 < K < 3
(d) K > 6
(c) 0 < K < 6
(d) K < 1 and k > 2

9. The output is said to be zero state response because ______conditions are made equal to zero.
(a) Initial
(b) Final
(c) Steady-state
(d) Impulse response

10. Use mason’s gain formula to calculate the transfer function of the given figure:


(a) G1/1+G2H
(b) G1+G2/1+G1H
(c) G2/1+G1H
(d) None of the mentioned

Answers

1. (a) 28 = 256 (without edges)

2. (c)

3. (a) 

Resonant frequency
{f_r} = \frac{1}{{2\pi \sqrt {LC} }} = \frac{1}{{2x3.14\sqrt {20x{{10}^{ - 3}}x5x{{10}^{ - 6}}} }} = 0.50kHz
Quality factor
Q = \frac{1}{R}\sqrt {\frac{L}{C}} = \frac{1}{{10x{{10}^3}}}\sqrt {\frac{{20x{{10}^{ - 3}}}}{{5x{{10}^{ - 6}}}}} = 0.632x{10^{ - 2}}
Bandwidth
BW = \frac{{{f_r}}}{Q} = \frac{{0.50}}{{0.632x{{10}^{ - 2}}}} = 80kHz

4. (d) 
See the following figure


Here 
{h_{12}} = {\left. {\frac{{{V_1}}}{{{V_2}}}} \right|_{{I_1} = 0}} = \frac{{{R_B}}}{{{R_B} + {R_C}}} and
{h_{22}} = {\left. {\frac{{{I_2}}}{{{V_2}}}} \right|_{{I_1} = 0}} = \frac{1}{{{R_B} + {R_C}}}

Hence 
{h_{22}} = \frac{1}{{{R_B} + {R_C}}} = \frac{1}{{20 + 0}} = 0.05

5. (a) Mmax = √L1L2 = √6 x 6 = 6 mH

6. (b) 

tr = ln 9/a = 2.2/12 = 0.18
ts = 3.91/a = 3.91/12 = 0.33

7. (d) 

{e_{ramp}}(\infty ) = \frac{{15}}{{(10x20x30)/(25x35)}} = 2.1875

8. (c)
Characteristic equation: s3 + 3s2 + 2s + k = 0
By applying the Routh tabulation method,

For the system to become stable, the sign changes in the first column of the Routh table must be zero.
6 - K > 0 and K > 0
0 < K < 6

9. (a)

10. (b) Use mason’s gain formula to solve the signal flow graph and by using mason’s gain formula transfer function from the signal flow graph can be calculated which relates the forward path gain to the various paths and loops.

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