Circuit Theory - May 2012

Electronics Engineering (Semester 3)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.

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 marks) 1 (b) What are the conditions for a rational function F(s) with a real coefficients to be "positive real function ?"(4 marks) 1 (c) Find the Z-parameter for the circuit shown (4 marks) 1 (d) Draw the dual network of the following circuit and prove that it is a dual one(4 marks) 1 (e) For the network shown find :-
(i) Power from voltage source
(ii) Voltage across A-B (4 marks) 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 marks) 2 (a) Find V_a, V_b and V_c using Nodal Analysis
(10 marks) 2 (b) Find the Norton;s equivalent circuit across terminal a-b of given circuit and hence the power discipated in 10? resistor.
(10 marks) 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 marks) 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 marks) 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 marks) 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 marks) 5 (a) Using Laplae transform find i(t) if the switch is closed at t=0. Assume initial condition to be zero.
(10 marks) 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 marks) 6 (a) Two identical sections of this network are in parallel. Obtain Y-parameter for connected network
(10 marks) 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 marks) 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 V_R=V_L(10 marks) 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 marks)