An integral $${\rm I}$$ over a counter clock wise circle $$C$$ is given by $${\rm I} = \oint\limits_c {{{{z^2} - 1} \over {{z^2} + 1}}} \,\,{e^z}\,dz$$
If $$C$$ is defined as $$\left| z \right| = 3,$$ then the value of $${\rm I}$$ is

In the circuit shown, $$V$$ is a sinusoidal voltage source. The current $$I$$ is in phase with voltage $$V$$. The ratio $${{{\rm{Amplitude of voltage across the capacitor }}} \over {{\rm{Amplitude of voltage across the resistor }}}}$$ is ______.

Consider the circuit shown in the figure.

The Thevenin equivalent resistance (in Ω) across P – Q is _________.

The switch in the circuit, shown in the figure, was open for a long time and is closed at t = 0. The current i(t) (in ampere) at t = 0.5 seconds is ________