The frequency of $AC$ mains in India is (in $\text{ Hz}$)

At time $t=0 \text{ s}$, the voltage of an $AC$ generator starts from $0 \text{ V}$ and becomes $2 \text{ V}$ at time $t=\frac{1}{100 \pi} \text{ s}$. The voltage increases up to $100 \text{ V}$, after which it starts to decrease. Find the frequency of the generator. (in $\text{ Hz}$)

The instantaneous values of current and voltage in an $AC$ circuit are given by $I = 6 \sin(100 \pi t + \frac{\pi}{4})$ and $V = 5 \sin(100 \pi t - \frac{\pi}{4})$. Then,

In an a.c. circuit $I=100 \sin 200 \pi t$. The time required for the current to achieve its peak value will be

The frequency of an alternating voltage is $50 \ Hz$. The time taken for the instantaneous voltage to increase from zero to half of its peak voltage is:

For a domestic $AC$ supply of $220 \ V$ at $50 \ \text{cycles per sec}$, the potential difference between the terminals of a two-pin electric outlet in a room is given by