The effective value ($RMS$ value) of the current $i = 2\sin(100\pi t) + 2\sin(100\pi t + 30^\circ)$ is:

What is the $r.m.s.$ value of an alternating current which,when passed through a resistor,produces heat that is thrice the heat produced by a direct current of $2 \ A$ in the same resistor (in $A$)?

The current flowing through an $AC$ circuit is given by $I = 5 \sin(120 \pi t) \text{ A}$. How long will the current take to reach the peak value starting from zero?

The voltage of an $AC$ source varies with time according to the equation,$V = 100 \sin(100 \pi t) \cos(100 \pi t)$. Where $t$ is in seconds and $V$ is in volts. Then:

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,

An $AC$ current is given by the expression,$I(t) = 50 \sin(200 \pi t)$ in amperes. The frequency and $RMS$ value of the current respectively are