The heat produced in a resistor by an $AC$ current is three times the heat produced by a $2 \, A$ $DC$ current. What is the $rms$ value of the $AC$ current in $A$?

$A$ light bulb is rated at $100\;W$ for a $220\;V$ supply. Find
$(a)$ the resistance of the bulb;
$(b)$ the peak voltage of the source; and
$(c)$ the rms current through the bulb.

$A$ current in a circuit is given by $i = 3 + 4 \sin \omega t$. The effective value of the current is

The ratio of the peak value to the root mean square (r.m.s.) value of an alternating current is:

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:

$A$ resistance of $40 \,\Omega$ is connected to a source of alternating current rated $220 \,V, 50 \,Hz$. Find the time taken by the current to change from its maximum value to its $rms$ value.