## Circuits and Transmission Lines - May 2013

### 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) ** Determine K for the given network.

(4 marks)
** 1 (b) ** The reduced incidence matrix of an oriented graph is -

$$ A=\begin{bmatrix}
0 &-1 &1 &0 &0 \\
0&0 &-1 &-1 &-1 \\
-1&0 &0 &0 &1
\end{bmatrix} $$ Draw oriented graph and how many trees are possible for this graph.(4 marks)
** 1 (c) ** For the circuit shown, V_{c} is 0 at t= 0 sec. Find I_{cc}tj for t > 0

(4 marks)
** 1 (d) ** For the circuit shown below, find current I:

(4 marks)
** 1 (e) ** Derive the expression for transmission parameters in terms of Z parameters. (4 marks)
** 2 (a) ** Linear graph of a network is shown below. For the given tree (shown with firm lines) obtain -

(i) Fundamental cutset matrix

(ii) Fundamental tieset matrix

(10 marks)
** 2 (b) ** A series R-L circuit has a constant voltage 25V applied at t = 0. At what time does V_{R} = V_{L}

(10 marks)
** 3 (a) ** Find the voltage across 6Ω resistor using mesh analysis.

(10 marks)
** 3 (b) ** In the given circuit, switch is charged from position 1 to position 2 at t= 0, steady state has been reached before switching. Find the values of

$$ i, \dfrac{di}{dt} \ and \ \dfrac{d^2i}{dt^2} at t=0^+ $$

(10 marks)
** 4 (a) ** Find the current through 50Ω resistor using Thevenin's theorem.

(10 marks)
** 4 (b) ** Find the h-parameter for the network shown below.

(10 marks)
** 5 (a) ** Determine whether following functions are positive real. $$ (i)\ \dfrac {s(s+3)(s+5)}{(s+1)(s+4)} \\
(ii)\ \dfrac {2s^2+2s+4}{(s+1)(s^2+2)}
$$ (10 marks)
** 5 (b) ** Check whether following polynomials are Hurwitz or not

$$
(i) s^3+4s^2+5s+2 \\
(ii) s^4+s^3+2s^2+3s+2
$$ (4 marks)
** 5 (c) ** For the network shown below, find $$ \dfrac {V_C}{Y} $$

(6 marks)
** 6 (a) ** Realise the following function in Cauer-I and Cauer-II from

$$
Z(s)=\dfrac {(s+1)(s+3)}{(s+2)(s+6)}
$$ (10 marks)
** 6 (b) ** Find Z parameter for the network shown below.

(10 marks)
** 7 (a) ** Find V_{2}/V_{1} and I_{2}/I_{1} for the network shown below

(10 marks)
** 7 (b) ** For the network shown below reaches steady with switch K opened. At t=0, the switch is closed, find i(t) for t> 0.

(10 marks)