Any five :-

1 (a)
Following is a tree of graph (shown with firm lines) shown in linear graph of a network obtain fundamental cutset matrix

4 M

1 (b)
What are the conditions for a rational function F(s) with a real coefficients to be "positive real function ?"

4 M

1 (c)
Find the Z-parameter for the circuit shown

4 M

1 (d)
Draw the dual network of the following circuit and prove that it is a dual one

4 M

1 (e)
For the network shown find :-

(i) Power from voltage source

(ii) Voltage across A-B

(i) Power from voltage source

(ii) Voltage across A-B

4 M

1 (f)
The circuit operatingunder steady state condition when switch is at position 'a' of at t=0, the switch is moved to position 'b'. Determine current l(s) and i(t)

4 M

2 (a)
Find V

_{a}, V_{b}and V_{c}using Nodal Analysis
10 M

2 (b)
Find the Norton;s equivalent circuit across terminal a-b of given circuit and hence the power discipated in 10? resistor.

10 M

3 (a)
State giving appropriate reasons whether the following functions are "positive real functions."

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

\[Y_2\left(s\right)=\frac{s^3+5s}{s^4+2s^2+1}\]

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

\[Y_2\left(s\right)=\frac{s^3+5s}{s^4+2s^2+1}\]

10 M

3 (b)
Realise :-

\[Y\left(s\right)=\frac{s^4+6s^2+4}{2s^3+4s}\]

in Cauer II form.

\[Z\left(s\right)=\frac{4\left(s^2+1\right)(s^2+16)}{s(s^2+4)}\]

in Foster I form

\[Y\left(s\right)=\frac{s^4+6s^2+4}{2s^3+4s}\]

in Cauer II form.

\[Z\left(s\right)=\frac{4\left(s^2+1\right)(s^2+16)}{s(s^2+4)}\]

in Foster I form

10 M

4 (a)
For the network shown find branch current and branch voltages using loop current analysis. This is to be solved by graph theory.

10 M

4 (b)

Graph of a given network is to be drawn. Also find Aa, A, B and Q matrices for the same. How many trees are possible in the above graph?

10 M

5 (a)
Using Laplae transform find i(t) if the switch is closed at t=0. Assume initial condition to be zero.

10 M

5 (b)
A triangular voltage pulse of duration T and peak value unity is switched in to a series RL circuit which is initially relaxed. Determine i(t)

10 M

6 (a)
Two identical sections of this network are in parallel. Obtain Y-parameter for connected network

10 M

6 (b)
Define ABCD parameter and relate them to other parameter as indicated

(i) A and C in terms of Z

(ii) B in terms of Y

(iii) D in terms of H

(i) A and C in terms of Z

(ii) B in terms of Y

(iii) D in terms of H

10 M

7 (a)
A series R-L circuit with R=10Ωand L=1H is applied with constant 20V voltage at t=0. Find the time at which V

_{R}=V_{L}
10 M

7 (b)
Find I, di/dt d

^{2}i/dt at t=0^{+}in the following network when the switch is changed from position 1 to 2 at t=0. Steady state condition reached before switching
10 M

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