Circuit Theory - Dec 2011

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. 1 (a) State the properties of Hurwitz polynomial(5 marks) 1 (b) Find the voltage at mode 2 for the figure shown below
(5 marks) 1 (c) State the condition for receiprocity of h-parameter and prove it(5 marks) 1 (d) Draw the dual of the network shown in figure below :(5 marks) 2 (a) Find the voltage across the 5Ωresistor for the circuit shown below :-
(10 marks) 2 (b) Find the current through the 30Ω resistor for the circuit shown below :-
(10 marks) 3 (a) The graph of network is shown in figure below, write the -
(i) Incidence matrix
(ii) F-cutset matrix
(iii) Tie set matrix(10 marks) 3 (b) In the network shown in figure below the switch is closed at t=0, the steady-state being reached before t=0. determine current through inductor of 3H
(10 marks) 4 (a) Find the values of I, di/dt and d²i/dt at t=0⁺ for the network shown in figure below, when switch is changed from the position 1 to be the position 2 at t=0. steady condition having reached before switching
(10 marks) 4 (b) Determine Y parameter for the network, shown in figure below :-
(10 marks) 5 (a) Test whether following polynomial are Hurwitz :-
(i) P(s)=s⁴ s³ 5s² 3s 4
(ii) P(s)=s⁴ s³ 2s² 3s 2(10 marks) 5 (b) Test wheather the following functions are positive real function :-
$$F\left(s\right)=\frac{2s^3+2s^2+3s+2}{s^2+1}$$
$$F\left(s\right)=\frac{s^2+1}{s^3+4s}$$
(10 marks) 6 (a) Obtain the Cauer forms of the following RC impedance function :-
$$Z\left(s\right)=\frac{\left(s+2\right)\left(s+6\right)}{2\left(s+1\right)\left(s+3\right)}$$(10 marks) 6 (b) For the network shown in figure below find. Z and Y parameter
(10 marks) 7 (a) In the network shown in figure below the switch is changed from the position '1' to position '2' at t=0. steady condition having reached before switching.
find the values of I, di/dt and d²i/dt at t=0⁺
(10 marks) 7 (b) For the network shown in figure below find the response V₀(t)
(10 marks)