Attempt any four:

1 (a)
Find V

_{s}

5 M

1 (b)
Switch is closed at t=0. Assuming all initial conditions as zero, find i and di/dt at t=0* for the following network.

5 M

1 (c)
Determine Z(s) in the network. Find poles and zeros of Z(s) and plot them on s-plane.

5 M

1 (d)
Test whether the following polynomials are Hurwitz.

i) P(s)=s4+s3+3s2+2s+12

ii) P(s) = s4+7s3+6s2+21s+8.

i) P(s)=s4+s3+3s2+2s+12

ii) P(s) = s4+7s3+6s2+21s+8.

5 M

1 (e)
Using the relation Y=Z-1, show that \( |z| = \dfrac {1}{2} \left ( \dfrac {z_{22}}{y_{11}}+ \dfrac {z_{11}}{y_{22}} \right ) \)

5 M

2 (a)
For the network shown below, switch is opened at t=0. If steady state is attained before switching, find the current through inductor.

10 M

2 (b)
Find voltage across 5 Ω resistor using mesh anlysis.

10 M

3 (a)
For the following graph of the network, write.

i) Incidence Matrix, ii) Tieset Matrix and iii) Cutset Matrix

i) Incidence Matrix, ii) Tieset Matrix and iii) Cutset Matrix

10 M

3 (b)
Using Superposition theorem, determine the voltages V

_{1}and V_{2}.

10 M

4 (a)
In the following network switch is changed from position 1 to 2 at t=0. Before switching, steady state condition has been attained.

Find: \( i, \dfrac {di}{dt} \ \text{and }\dfrac {d^2i}{dt^2} \ \text{at t}=0^+ \)

Find: \( i, \dfrac {di}{dt} \ \text{and }\dfrac {d^2i}{dt^2} \ \text{at t}=0^+ \)

10 M

4 (b)
Find Z parameters for the network

10 M

5 (a)
Test whether the following functions are positive real. \[ i) \ \ F(x) = \dfrac {s^2 + 6x +5}{x^2 + 9s+14} \\
ii) \ \ f(s) = \dfrac {s^2+i}{s^3 + 4s} \]

10 M

5 (b)
Realize Foster I and Foster II forms of the following impedance function. \[ Z(s) = \dfrac {(s^2 +1)(s^2+3)}{s(s^2+2)} \]

10 M

6 (a)
Find the network functions \( \dfrac {V_1}{I_1} ; \dfrac {V_2}{V_1} \text{and } \dfrac {V_2}{I_1} \)

10 M

6 (b)
Find Cauer I and II forms of RL impedance function: \[ Z(s) = \dfrac {2 (s+1)(s+3)}{(s+2)(s+6)} \]

10 M

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