GATE ECE 1997 | Question 23

Question

 

In the circuit of the figure is all currents and voltages are sinusoids of frequency $\omega \;  \mathrm{rad} / \mathrm{sec}$.

1. Find the impedance to the right of $(\mathrm{A}, \mathrm{B})$ at $(\omega) =0 \; \mathrm{rad} / \mathrm{sec}$ and $(\omega)=\infty \; \mathrm{rad} / \mathrm{sec}$.
2. If $\omega=\omega_{0} \; \mathrm{rad} / \sec$ and $i_{1}(t) = I \; \sin \left(\omega_{0} t\right) \mathrm{A}$, where $I$ is positive $\omega_{0} \neq 0, \omega_{0} \neq \infty$ then find $I$, $\omega_{0}$ and $i_{2}(t)$