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)s⁴+2s²+2
(ii) s⁷+2s⁶+2s⁵+s⁴+4s³+8s²+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)