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

Two incandescent light bulbs of $$40$$ $$W$$ and $$60$$ $$W$$ rating are connected in series across the mains. Then

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