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Electrical Network Analysis and Synthesis : Question Paper Dec 2015 - Instrumentation Engg. (Semester 3) | Mumbai University (MU)

## Electrical Network Analysis and Synthesis - Dec 2015

### Instrumentation Engg. (Semester 3)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.

### Attempt any four:

1 (a) Find Vs (5 marks) 1 (b) Switch is closed at t=0. Assuming all initial conditions as zero, find i and di/dt at t=0* for the following network. (5 marks)
1 (c) Determine Z(s) in the network. Find poles and zeros of Z(s) and plot them on s-plane. (5 marks)
1 (d) Test whether the following polynomials are Hurwitz.
i) P(s)=s4+s3+3s2+2s+12
ii) P(s) = s4+7s3+6s2+21s+8.
(5 marks)
1 (e) Using the relation Y=Z-1, show that $|z| = \dfrac {1}{2} \left ( \dfrac {z_{22}}{y_{11}}+ \dfrac {z_{11}}{y_{22}} \right )$(5 marks) 2 (a) For the network shown below, switch is opened at t=0. If steady state is attained before switching, find the current through inductor. (10 marks)
2 (b) Find voltage across 5 Ω resistor using mesh anlysis. (10 marks)
3 (a) For the following graph of the network, write.
i) Incidence Matrix,   ii) Tieset Matrix and   iii) Cutset Matrix (10 marks)
3 (b) Using Superposition theorem, determine the voltages V1 and V2. (10 marks)
4 (a) In the following network switch is changed from position 1 to 2 at t=0. Before switching, steady state condition has been attained.
Find: $i, \dfrac {di}{dt} \ \text{and }\dfrac {d^2i}{dt^2} \ \text{at t}=0^+$ (10 marks)
4 (b) Find Z parameters for the network (10 marks)
5 (a) Test whether the following functions are positive real. $$i) \ \ F(x) = \dfrac {s^2 + 6x +5}{x^2 + 9s+14} \\ ii) \ \ f(s) = \dfrac {s^2+i}{s^3 + 4s}$$(10 marks) 5 (b) Realize Foster I and Foster II forms of the following impedance function. $$Z(s) = \dfrac {(s^2 +1)(s^2+3)}{s(s^2+2)}$$(10 marks) 6 (a) Find the network functions $\dfrac {V_1}{I_1} ; \dfrac {V_2}{V_1} \text{and } \dfrac {V_2}{I_1}$ (10 marks)
6 (b) Find Cauer I and II forms of RL impedance function: $$Z(s) = \dfrac {2 (s+1)(s+3)}{(s+2)(s+6)}$$(10 marks)

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