The circuit of Fig. represents a

For the circuit in Fig., write the state equations using v_c and i_L as state variables.

For the circuit in Fig.

(a) Find the Thevenin equivalent of the sub circuit faced by the capacitor across the terminals a, b.

(b) Find $$v_c\left(t\right),\;t>0,\;given\;v_c(0)\;=\;0.$$

(c) Find i(t), t>0.

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.