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

An alternating voltage is represented by $V = 80 \sin(100 \pi t) \cos(100 \pi t) \text{ V}$. The peak voltage is (in $\text{ V}$)

Voltage and current in an $ac$ circuit are given by $V = 5\sin(100\pi t - \frac{\pi}{6})$ and $I = 4\sin(100\pi t + \frac{\pi}{6})$. Which of the following statements is correct?

In an $A.C.$ circuit,the instantaneous current and $E.M.F.$ are represented as $i = i_0 \sin(\omega t - \frac{\pi}{6})$ and $E = E_0 \sin(\omega t + \frac{\pi}{3})$ respectively. The voltage leads the current by

An $AC$ source rated $220\, V, 50\, Hz$ is connected to a resistor. The time taken by the current to change from its maximum value to the $rms$ value is:

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 $\text{ Hz}$)