1 (a)
Determine K for the given network.

4 M

1 (b)
The reduced incidence matrix of an oriented graph is -

\[ A=\begin{bmatrix} 0 &-1 &1 &0 &0 \\ 0&0 &-1 &-1 &-1 \\ -1&0 &0 &0 &1 \end{bmatrix} \] Draw oriented graph and how many trees are possible for this graph.

\[ A=\begin{bmatrix} 0 &-1 &1 &0 &0 \\ 0&0 &-1 &-1 &-1 \\ -1&0 &0 &0 &1 \end{bmatrix} \] Draw oriented graph and how many trees are possible for this graph.

4 M

1 (c)
For the circuit shown, V

_{c}is 0 at t= 0 sec. Find I_{cc}tj for t > 0
4 M

1 (d)
For the circuit shown below, find current I:

4 M

1 (e)
Derive the expression for transmission parameters in terms of Z parameters.

4 M

2 (a)
Linear graph of a network is shown below. For the given tree (shown with firm lines) obtain -

(i) Fundamental cutset matrix

(ii) Fundamental tieset matrix

(i) Fundamental cutset matrix

(ii) Fundamental tieset matrix

10 M

2 (b)
A series R-L circuit has a constant voltage 25V applied at t = 0. At what time does V

_{R}= V_{L}
10 M

3 (a)
Find the voltage across 6Ω resistor using mesh analysis.

10 M

3 (b)
In the given circuit, switch is charged from position 1 to position 2 at t= 0, steady state has been reached before switching. Find the values of

\[ i, \dfrac{di}{dt} \ and \ \dfrac{d^2i}{dt^2} at t=0^+ \]

\[ i, \dfrac{di}{dt} \ and \ \dfrac{d^2i}{dt^2} at t=0^+ \]

10 M

4 (a)
Find the current through 50Ω resistor using Thevenin's theorem.

10 M

4 (b)
Find the h-parameter for the network shown below.

10 M

5 (a)
Determine whether following functions are positive real. \[ (i)\ \dfrac {s(s+3)(s+5)}{(s+1)(s+4)} \\
(ii)\ \dfrac {2s^2+2s+4}{(s+1)(s^2+2)}
\]

10 M

5 (b)
Check whether following polynomials are Hurwitz or not

\[ (i) s^3+4s^2+5s+2 \\ (ii) s^4+s^3+2s^2+3s+2 \]

\[ (i) s^3+4s^2+5s+2 \\ (ii) s^4+s^3+2s^2+3s+2 \]

4 M

5 (c)
For the network shown below, find \[ \dfrac {V_C}{Y} \]

6 M

6 (a)
Realise the following function in Cauer-I and Cauer-II from

\[ Z(s)=\dfrac {(s+1)(s+3)}{(s+2)(s+6)} \]

\[ Z(s)=\dfrac {(s+1)(s+3)}{(s+2)(s+6)} \]

10 M

6 (b)
Find Z parameter for the network shown below.

10 M

7 (a)
Find V

_{2}/V_{1}and I_{2}/I_{1}for the network shown below
10 M

7 (b)
For the network shown below reaches steady with switch K opened. At t=0, the switch is closed, find i(t) for t> 0.

10 M

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