Given two coupled inductors $${L_1}$$ and $${L_2}$$, their mutual inductance $$M$$ satisfies

A voltage wafeform $$v\left( t \right) = 12\,{t^2}$$ is applied across a $$1$$ $$H$$ inductor for $$t \ge 0,$$ with initial current through it being zero. The current through the inductor for $$t \ge 0$$ is given by:

For the circuit shown in Figure, the capacitance measured between terminals $$B$$ and $$Y$$ will be

In the circuit shown in Figure, it is desired to have a constant direct current $$i(t)$$ through the ideal inductor $$L.$$ The nature of the voltage source $$v(t)$$ must be