The frequency for which a $5 \mu F$ capacitor has a reactance of $\frac{1}{1000} \Omega$ is given by

An alternating voltage given as $V = 100 \sqrt{2} \sin(100t) \text{ V}$ is applied to a capacitor of $1 \mu\text{F}$. The current reading of the ammeter will be equal to . . . . . . $\text{mA}$.

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:

Obtain the formula for current when an $AC$ voltage is applied to a capacitor and draw the graphs of $V$ and $I$ versus $\omega t$.

In a pure inductive circuit, the curve between frequency $f$ and the reciprocal of inductive reactance $1/X_L$ is:

Obtain an equation for the current when an $AC$ voltage is applied to an inductor and draw a graph of $V$ and $I$ versus time.