MU Electronics Engineering (Semester 3)
Circuit Theory
December 2012
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1 (a) How many trees are possible for the graph of the network?
5 M
1 (b) What are the conditions for a rational function f(s) with real co-efficients to be positive real function?
5 M
1 (c) Express hybrid parameter in terms of impedance parameters
5 M
1 (d) State the properties of Hurwitz polynomial
5 M

2 (a) Find voltage across 5Ω resistor using mesh analysis

10 M
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 M

3 (a) In the network shown what will be the RL to get maximum power delivered to it? What is the value of this power?
10 M
3 (b) Find Thevenin equivalent network
10 M

4 (a) In the network shown the switch closes at t=0. The capacitor is initially unchanged. Find Vc and ic
10 M
4 (b) Calculate the twig voltage using KCL equation for the network shown

10 M

5 (a) For the network shown, determine the current i(t) when switch is closed at t=0 with zero initial conditions
10 M
5 (b) Find impulse response of voltage across the capacitor in the network shown. Also detemine response Vc(t) for step input
10 M

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 M
6 (b) Two identical sections of the network shown are connected in cascade. Obtain the transmission parameter of overall connection

10 M

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 M
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 M

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