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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 V_{s}

**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 V

_{1}and V

_{2}. (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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