Attempt any FOUR from the following
1 (a)
How many trees are possible for the given graph :
5 M
1 (b)
By mesh analysis determine the current through 2Ω resistor :
5 M
1 (c)
Find the condition of reciprocity for Z parameters
5 M
1 (d)
Find I, in the circuit if dependent voltage source is
(i) 2V2
(ii) 1.5V3
(i) 2V2
(ii) 1.5V3
5 M
2 (a)
Find the current through 5Ω resistor. :
10 M
2 (b)
Find the Network function \[
\frac{V_1}{I_1}, \frac{V_2}{V_1} \ and \ \frac{V_2}{I_1}
\]
10 M
3 (a)
The switch is changed from position 1 to position 2 at t=0, Steady state having reached before switching. Find values of
\[ i, \frac{di}{dt} \ and \ \frac{d^2i}{dt^2} \ and \ t=0^+ \]
\[ i, \frac{di}{dt} \ and \ \frac{d^2i}{dt^2} \ and \ t=0^+ \]
10 M
3 (b)
In the network, the switch is opened at t=0. Find i(t).
10 M
4 (a)
Write down the tieset matrix & obtain the network equilibrium equation in matrix form using KVL. Calculate loop currents:
10 M
4 (b)
Determine Y & Z parameters for the network
10 M
5 (a)
Synthesize the following function \[
Z\left(s
\right)= \frac{6\left(s+2
\right)\left(s+4
\right)}{s\left(s+3
\right)}\]
Use Foster -II Method.
Use Foster -II Method.
8 M
5 (b)
A driving point R-L admittance function is given by-
\[ y_{RL}\left(s \right)= \frac{s^2+6s+8}{s^2+4s+3} \]
Use cauer - I Method
\[ y_{RL}\left(s \right)= \frac{s^2+6s+8}{s^2+4s+3} \]
Use cauer - I Method
6 M
5 (c)
Synthesize the following YRL(s) using cauer II from
\[ Y_{RL}\left(s \right)= \frac{\left(s+1 \right)\left(s+4 \right)}{s\left(3s+4 \right)} \]
\[ Y_{RL}\left(s \right)= \frac{\left(s+1 \right)\left(s+4 \right)}{s\left(3s+4 \right)} \]
6 M
6 (a)
Find the current I in the network, using superposition theorem.
10 M
6 (b) (i)
Check the given polynomial for Hurwitz
\[ P\left(s \right)=s^5+8s^4+24s^3+28s^2+23s+6 \]
\[ P\left(s \right)=s^5+8s^4+24s^3+28s^2+23s+6 \]
5 M
6 (b) (ii)
Test whether \[
F\left(s
\right)= \frac{{5(s+1)}^2}{s^3+2s^2+2s+40}
\]
is positive real function.
5 M
7
(a) Find the current through 10Ω resistor (Thevenin's theorem).
![](data:image/png;base64,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)
(b) Determine the hybrid parameter of the network.
(b) Determine the hybrid parameter of the network.
20 M
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