## Circuit Theory - Dec 2012

### Electronics Engineering (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.
**1 (a)** How many trees are possible for the graph of the network?
(5 marks)
**1 (b)** What are the conditions for a rational function f(s) with real co-efficients to be positive real function?(5 marks)
**1 (c) ** Express hybrid parameter in terms of impedance parameters(5 marks)
**1 (d)** State the properties of Hurwitz polynomial(5 marks)
**2 (a)** Find voltage across 5Ω resistor using mesh analysis
(10 marks)
**2 (b)** For the network shown write down the tieset matrix and obtain network equillibrium equation in matrix form using KVL. Calculate loop currents 2?(10 marks)
**3 (a)** In the network shown what will be the R_{L} to get maximum power delivered to it? What is the value of this power?

(10 marks)
**3 (b)** Find Thevenin equivalent network

(10 marks)
**4 (a)** In the network shown the switch closes at t=0. The capacitor is initially unchanged. Find V_{c} and i_{c}

(10 marks)
**4 (b)** Calculate the twig voltage using KCL equation for the network shown
(10 marks)
**5 (a)** For the network shown, determine the current i(t) when switch is closed at t=0 with zero initial conditions

(10 marks)
**5 (b)** Find impulse response of voltage across the capacitor in the network shown. Also detemine response V_{c}(t) for step input

(10 marks)
**6 (a)** Test whether the following polynomial are hurwitz. Use continued fraction Expansion.

(i)s^{4}+2s^{2}+2

(ii) s^{7}+2s^{6}+2s^{5}+s^{4}+4s^{3}+8s^{2}+8s+4

(10 marks)
**6 (b)** Two identical sections of the network shown are connected in cascade. Obtain the transmission parameter of overall connection
(10 marks)
**7 (a)** Find the first and second couer form of the given function :-

$$z\left(s\right)=\frac{\left(s+1\right)\left(s+3\right)}{s\left(s+2\right)}$$ (10 marks)
**7 (b)** Test whether the following functions are positive real function :-

$$f\left(s\right)=\frac{s^2+6s+5}{s^2+9s+14}$$

$$f\left(s\right)=\frac{s^3+6s^2+7s+3}{s^2+2s+1}$$(10 marks)