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_cctj 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 V₂/V₁ and I₂/I₁ 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)