A segment of a circuit is shown in figure. $${v_R} = 5\,\,V,\,\,{v_C} = 4\sin 2t.$$ The voltage $${V_L}$$ is given by

Fig. shows the waveform of the current passing through an inductor of resistance $$1\,\Omega $$ and inductance $$2$$ $$H.$$ The energy absorbed by the inductor in the first four seconds is

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