Solution for Question 5 : IES Conventional 1998 : Electronics & Telecommunication Engineering : Paper I

Q.5 (a): The switch closes in the circuit of Fig. 5 (a) at t = 0. Assuming a relaxed circuit at the time of switching, determine the current i for t > 0. Also find the voltage VL  across the inductances for t > 0.

Sol: For t < 0- (Initial Condition)

the circuit becomes as:

      i (0-) = 0 Amp

Vc(0-) = 0 V

at t = 0+,

  i (0+) = 0 Amp

Vc(0+) = 100 V

at t = infinity, (final condition)

       i (00) = 0 Amp

Vc(00) = 0 V

        Since,  X(t) = X(final) + ( X(initial) - X(final)).e(-t/RC)

       Hence,   I (t) = 0 + 0.e(-t/RC) = 0 Amp

       &,          V(t) = 0 + (100 - 0).e(-t/RC) = 100.e(-2500t)

Q.5 (b): Find the Z-parameters of the two port in Fig. 5 (b).

Sol: By using cascading theorem, we can divide the circuit in three different sections as shown in figure below:

And inner delta circuit can be converted in to the star circuit as:

Now, its too easy to find out the Z-parameters.