Derive expression for

1 (a) (i)
Star to delta transformation.

5 M

1 (a) (ii)
Data to star transformation.

5 M

1 (b)
For the Network shown in find the node voltage Vd and Ve Fig Q No. 1(b):

10 M

2 (a)
Define the following with examples:

i) Oriented graph

ii) Tree

iii) Fundamental cut set

iv) Fundamental tie set.

i) Oriented graph

ii) Tree

iii) Fundamental cut set

iv) Fundamental tie set.

8 M

2 (b)
For the network, shown fig write the tie set schedule, tie set matrix and obtain equilibrium equation in matrix formatting XVL. Calculate branch currents and branch voltage. Follows the same orientation and branch number use 4, 5 and 6 as tree branches.

12 M

3 (a)
State and prove Reciprocity theorem.

7 M

3 (b)
Find the output voltage Eo of the Network shown. Using Millman's theorem Fig Q No. 3(b).

6 M

3 (c)
Using superposition theorem, find the current IX the network shown in Fig Q No. 3(c).

7 M

4 (a)
State Norton's theorem. Shown that Thevenin's equivalent circuit is the dual of Norton's equivalent circuit.

6 M

4 (b)
Obtain the current I

_{x}by using Thevenin's theorem for the network shown in Fig Q No. 4(b):

8 M

4 (c)
State maximum power transfer theorem. Prove that Z

_{L}=Z_{0}* for Ac circuits.
6 M

5 (a)
Show that \[ f_0 = \sqrt{f_1 f_2} \] for series resistance circuit.

6 M

5 (b)
A voltage of 100 sin ωt applied an RLC series circuit at resonant frequency. The voltage across a capacitor was found to be 400V. The bandwidth is 75Hz. The impedance at resonance is 100Ω. Find the resonant frequency and constants of the circuit.

6 M

5 (c)
Derive an expression for the resonant frequency of a resonant frequency of a resonant circuit consisting of R

_{L}L in parallel with R_{c}C. Draw the frequency response curve of the above circuit.
8 M

6 (a)
In the circuit shown, switch K is changed from 1 to 2 at t=0, steady state having been attained in position 1, Find the value of \[ i, \dfrac {di}{dt} \ and \ \dfrac {d^2t} {dt^2} \ at \ t=0^+ \]

10 M

6 (b)
In the circuit shown, switch K is kept open for very long time, on closing K, after 10ms, V

_{C}=80V. Then the switch K is kep closed for a long time. When the switch is opened again, V_{C}=90 V after half second calculate value of R and C. Fig Q No. 6(b).

10 M

7 (a)
State and prove i) Initial value theorem ii) Final value theorem as applied to Laplace transform. What are the limitations of the initial value theorem.

10 M

7 (b)
In the circuit shown, in Fig Q. No 7(b), switch is initially closed. After steady the switch is opened. Determine the nodal voltage V

_{a}(t) and V_{b}(t) using Laplace transform method.

10 M

8 (a)
Define z-parameters. Express z-parameters in terms of y-paramters.

10 M

8 (b)
Find y parameters and z-parameters for the circuit theorem.

10 M

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