In the circuit of figure, the switch $$'S'$$ has remained open for a long time. The switch closes instantaneously at $$ t = 0$$. n

(a) Find $${V_0}$$ for $$t \le 0$$ and as $$t \to \infty $$.
(b) Write an expression for $${V_0}$$ as a function of time for $$0 \le t \le \infty $$.
(c) Evaluate $${V_0}$$ at $$t = 25\,\,\mu $$sec.

A coil with a quality factor $$(Q)$$ of $$10$$ is put in series with a capacitor $${C_1}$$ of $$10\,\,\mu F,$$ and the combination is found to draw maximum current when a sinusoidal voltage of frequency $$50$$ $$Hz$$ is applied. A second capacitor $${C_2}$$ is now in parallel with the circuit. What should be the capacitance of $${C_2}$$ for combined circuit to act purely as a resistance for a sinusoidal excitation at a frequency of $$100$$ $$Hz$$? Calculate the rms current drawn by the combined circuit at $$100$$ $$Hz$$ if the applied voltage is $$100V$$ (rms).

A 2-port network is shown in figure. The parameter $${h_{21}}$$ for this network can be given by

The Thevenin equivalent voltage V_TH appearing between the terminals A and B of the network shown in Fig. is given by