The network $$N$$ in Fig. consists only of two elements: a resistor of $$1\Omega $$ and an inductor of L Henry. $$A$$ $$5$$ $$V$$ source is connected at the input at $$t\, = \,0$$ seconds. The inductor current is zero at $$t\, = \,0$$. The output voltage is found to be $$5{e^{ - 3t}}\,\,V,$$ for $$t\, = \,0$$.

(a) Find the voltage transfer function of the network.
(b) Find L, and draw the configuration of the network.
(c) Find the impulse response of the network.

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.

The circuit shown in the figure, is initially in its steady state. Switch is opened at t = 0.
(1) Determine the initial voltage, V_C(0^-), across the capacitor, and the initial current, i_L(0^-) , through the indicator.
(2) Calculate the voltage, V_L(t) , across the inductance for t > 0.

In the following circuit the capacitance varies as C = KQ, where K is a constant equal to 0.5 Farads/Coulomb and Q, the charge on the capacitor in Coulombs. Determine the current through the circuit and sketch the voltage waveform across the capacitor (V_C) for a step input V_i as shown in figure.