A resistor of resistance $R$, inductor of inductive reactance $2 R$ and a capacitor of capacitive reactance $X_C$ are connected in series to an AC source.If the series $L-C-R$ circuit is in resonance, then the power factor of the circuit and the value, $X_C$ are respectively

An inductor and a resistor are connected in series to an AC source of voltage $144 \sin \left(100 \pi t+\frac{\pi}{2}\right) \mathrm{V}$. If the current in the circuit is $6 \sin \left(100 \pi t+\frac{\pi}{6}\right) \mathrm{A}$, then the resistance of the resistor is

A resistance of $20 \Omega$ is connected to a source of an alternating potential $V=200 \sin (10 \pi t)$. If $t$ is the time taken by the current to change from the peak value to rms value, then $t$ is (in seconds)