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 Fig., the steady state output voltage corresponding to the input voltage $$\left( {3 + 4\sin \,\,100\,t} \right)$$ $$V$$ is

For the circuit in Fig. Which is in steady state,

(a)Find the frequency $${\omega _0}$$ at which the magnitude of the impedance across terminals a, b reaches maximum.

(b) Find the impedance across a, b at the frequency $${\omega _0}$$.

(c) If $${v_i}\left( t \right) = V\,\,\sin \left( {{\omega _0}t} \right),$$ find $${i_L}\left( t \right),\,\,{i_c}\left( t \right),{i_R}\left( t \right).$$

In the circuit of Fig., the value of the voltage source E is