## Circuits and Transmission Lines - Dec 2012

### Electronics & Telecomm. (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) ** For maximum power transfer find the value of Z_{L} if

(i) Z_{L} is impedance

(ii) Z_{L} is pure resistance :

(5 marks)
** 1 (b) ** find initial value of, f(t)= 20-10t-e^{-25t}

verify using initial value theorem. (5 marks)
** 1 (c) ** In the network given below, initial value of I_{L} =4A and V_{C}=100. Find I_{C}(0^{+}):

(5 marks)
** 1 (d) ** Current I_{1} and I_{2} entering at 1 and port 2 respectively of two port network are given by following equation.

I_{1} =0.5V_{1} - 0.2V_{2}

I_{2} = -0.2V_{1} +V_{2}

Obtain T and Π(pi) representation. (5 marks)

### Attempt any FOUR from the following

** 1 (e) ** For network shown, find V_{C} /V and draw pole-zero plot.

(5 marks)
** 2 (a) ** Using mesh analysis find power supplied by the dependent source.

(10 marks)
** 2 (b) ** Find current supplied by source.

(10 marks)
** 3 (a) ** Write B and Q matrix for the Graph shown.

(10 marks)
** 3 (b) ** Draw Bode plot for the function G(s). Find gain margin, phase margin and comment on stability.

$$
G(s)=
\frac{2(s+0.25)}{s^2(s+1)(s+0.5)}
$$(10 marks)
** 4 (a) ** Switch is opened at t=0 with initial conditions as shown. Find

$$
v_1, \frac{dv_1}{dt}, \frac{dv_2}{dt}\ at \ time\ 0^+ $$

(10 marks)
** 4 (b) ** Find Y parameter using interconnection:

(10 marks)
** 5 (a) ** In the network key is closed at t=0. Find i_{1} (0^{+}), i_{2}(0^{+} and i_{3} (0^{+}).

(10 marks)
** 5 (b) ** Find i(t).

(10 marks)
** 6 (a) ** The circuit attain steady state with switch at position (a) & is moved to position (b) at t=0. Find V(t) for t ≥ 0.

(10 marks)
** 6 (b) ** Find Z_{11}, Z_{21} and G_{21}

(10 marks)
** 7 (a) ** Realize following functon in Foster II form

$$
Z(s)=\frac{(s^2+1)(s^2+3)}{s(s^2+2)(s^2+4)}
$$
(10 marks)
**7 (b)** Check following polynomials for Hurtwitz -

$$
\ \left(i\right)\ \ p\left(s\right)=S^4+4s^2+8
$$

$$ \left(ii\right)\ \ p\left(s\right)=s^4+s^3+5s^2+3s+4 $$(10 marks)