A small signal voltage $V\left(t\right)=V_0$ sin $\omega t$ is applied across an ideal capacitor $C:$

The potential differences across the resistance, capacitance and inductance are $80 \mathrm{V}\text{,} 40 \mathrm{V}$ and $100 \mathrm{V}$, respectively in an $\mathrm{LCR}$ circuit. The power factor of this circuit is,

In the circuit shown, switch is connected to position 1 for a very long time. What is maximum current through inductor when switch is taken to position 2 ?

Time constant of the given circuit is $\tau$. If the battery is replaced by an ac source having voltage $V = V_{\circ }\cos \omega t$, power factor of the circuit will be :-