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 R

_{L}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 V

_{c}and i_{c}
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 V

_{c}(t) for step input
10 M

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

(i)s

(ii) s

(i)s

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

^{7}+2s^{6}+2s^{5}+s^{4}+4s^{3}+8s^{2}+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 :-

\[z\left(s\right)=\frac{\left(s+1\right)\left(s+3\right)}{s\left(s+2\right)}\]

\[z\left(s\right)=\frac{\left(s+1\right)\left(s+3\right)}{s\left(s+2\right)}\]

10 M

7 (b)
Test whether the following functions are positive real function :-

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

\[f\left(s\right)=\frac{s^3+6s^2+7s+3}{s^2+2s+1}\]

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

\[f\left(s\right)=\frac{s^3+6s^2+7s+3}{s^2+2s+1}\]

10 M

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