The residues of a function $$f\left( z \right) = {1 \over {\left( {z - 4} \right){{\left( {z + 1} \right)}^3}}}$$ are

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 ______.

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 ________

Consider the circuit shown in the figure.

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