An $a.c.$ of frequency $f$ is flowing in a circuit containing only an ideal choke coil of inductance $L$. If $V_0$ and $i_0$ represent peak values of the voltage and the current respectively,the average power given by the source to the choke coil is equal to

$A$ coil has inductance $L$. The ratio of its reactance when it is connected first to an $A.C.$ source and then to a $D.C.$ source is

An alternating voltage of $22 \, V$ is applied across an inductance coil of reactance $11 \, \Omega$. If the inductance of the coil is $0.07 \, H$, the frequency of the alternating voltage is: (in $ \, Hz$)

Explain why the reactance provided by a capacitor to an alternating current decreases with increasing frequency.

Given below are two statements:
Statement-$I$: In an $AC$ circuit,the current through a capacitor leads the voltage across it.
Statement-$II$: In $AC$ circuits containing pure capacitance only,the phase difference between the current and the voltage is $\pi$.
In the light of the above statements,choose the most appropriate answer from the options given below:

The equation of current in a purely inductive circuit is $i = 5 \sin (49 \pi t - 30^{\circ})$. If the inductance is $30 \, mH$,then the equation for the voltage across the inductor will be. (Let $\pi = \frac{22}{7}$)