Capacitor

Q. An alternating potential $V=V_0\sin \omega t$ is applied across a circuit. As a result the current $I=I_0\sin (\omega t-\frac{\pi }{3})$ flows through it. The average power consumed in the circuit is

1. $0.5V_0{I}_0$
2. $0.707V_0{I}_0$
3. $0.25V_0{I}_0$
4. $1.414V_0{I}_0$

Q. In a series $\text{CR}$ circuit shown in figure, the applied voltage is $10\text{V}$ and the voltage across capacitor is found to be $8\text{V}.$ Then the voltage across $R$, and the phase difference between current and the applied voltage will respectively be-

1. $6\text{V};{\tan }^{-1}\left(\frac{4}{3}\right)$
2. $3\text{V};{\tan }^{-1}\left(\frac{3}{4}\right)$
3. $6\text{V};{\tan }^{-1}\left(\frac{1}{2}\right)$
4. None

Q. An arc lamp requires a direct current of $10\text{A}$ at $80\text{V}$ to function. If it is connected to a $220\text{V}$ (rms), $50\text{Hz}$ AC supply, the series inductor needed for it to work is close to

1. $0.044\text{H}$
2. $80\text{H}$
3. $0.08\text{H}$
4. $0.065\text{H}$