MU Electronics Engineering (Semester 3)
Circuit Theory
May 2012
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

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

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 Va, Vb and Vc 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."
$F\left(s\right)=\frac{2s^3+2s^2+3s+2}{s^2+1}$
$Y_2\left(s\right)=\frac{s^3+5s}{s^4+2s^2+1}$
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
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
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 VR=VL
10 M
7 (b) Find I, di/dt d2i/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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