## Circuit Theory - May 2013

### 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)** Explain Y-parameter in terms of Z-parameters(5 marks)
**1 (b)** Draw the dual of the network shown in figure (a)(5 marks)
**1 (c) ** Find the poles and zeros of impedance of the network shown in figure (c)

(5 marks)
**1 (d)** State the properties of prf(5 marks)
**2 (a)** Find the Thevin equivalent network of figure (c)

(10 marks)
**2 (b)** Find the current I_{2} using mesh analysis of figure (d)

(10 marks)
**3 (a)** The switch is closed at t=0, find values of I, dI/dt , d^{2}I/dt^{2} at t=0^{+}. Assume all initial current of inductor to be zero for circuit (e)
(10 marks)
**3 (b)** Calculate the twig voltage using KVL equations for network shown in figure (f)(10 marks)
**4 (a)** Determine Y-parameter for network an figure (g)

(10 marks)
**4 (b)** In the network figure (h). Determine the currents i_{1}(t) and i_{2}(t) when the switch 'k' is closed at t=0
(10 marks)
**5 (a)** The pole-zero diagram of driving point impedance function of network figure (i). At d.c. the input impedance is resistive and equal to 2?. Determine the values of R-L and C
(10 marks)
**5 (b)** Test whether the following polynomial are Hurwitz. Use continuous fraction expansion method :-

(i) s^{4}+2s^{2}+2

(ii) s^{7}+2s^{6}+2s^{5}+s^{4}+4s^{3}+8s^{2}+8s+4

(10 marks)
**6 (a)** Determine the node voltage at 1 and 2 of the network shown in figure (f). Use nodal analysis
(10 marks)
**6 (b)** Find the response of V_{0} (t) for network shown in figure (k)
(10 marks)
**7 (a)** Realize the given expression in Foster I, Foster II, Cauer-I and Cauer-II form

$$z\left(s\right)=\frac{s\left(s+4\right)\left(s+8\right)}{\left(s^2+7s+6\right)}$$(20 marks)