The self-inductance of a choke coil is $10\, mH$. When it is connected to a $10\, V$ $dc$ source,the power loss is $20\, W$. When it is connected to a $10\, V$ $ac$ source,the power loss is $10\, W$. The frequency of the $ac$ source is......$Hz$.

Give the name of the physical quantity in an $LCR$ circuit that corresponds to mass $m$ in forced oscillations.

At a particular angular frequency,the reactance of a capacitor and that of an inductor are the same. If the angular frequency is doubled,the ratio of the reactance of the capacitor to that of the inductor will be:

Statement-$I$: $A$ capacitor can be used in an $a.c.$ circuit in place of a choke coil.
Statement-$II$: $A$ capacitor blocks $d.c.$ and allows $a.c.$ to pass.

$A$ resistor $R$, an inductor $L$, and a capacitor $C$ are connected in series with an a.c. source. When $L$ is removed from the circuit, the phase difference between voltage and current in the circuit is $\pi/3$. If instead, $C$ is removed from the circuit, the phase difference is again $\pi/3$. The power factor of the circuit is

In domestic electric mains supply,the voltage and the current are