In an $ac$ circuit, the instantaneous voltage $e(t)$ and current $I(t)$ are given by $e(t)$ = $5[cos\ \omega t + \sqrt 3\ sin\ \omega t]\ volt$ $i (t)$ = $5[sin(\omega t +\frac {\pi}{4})]\ amp$ then

The mean and $rms$ value of an alternating voltage for half cycle as shown in figure are  respectively:-

An alternating voltage $v\left( t \right) = 220\,\sin \,100\pi l\,volt$ is applied to a purely resistive load of $50\,\Omega $ . The time taken for the current to rise from half of the peak value of the peak value is.....$ms$

A $110 \,V$ $d.c$. heater is used on an $a.c.$ source, such that the heat produced is same as it produces when connected to $110 \,V$ $dc$ in same time-intervals. What would be the $r.m.s.$ value of the alternating voltage is .......... $V$

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 peak value of an Alternating current is $ 6$ amp, then r.m.s. value of current will be