An $AC$ source is rated $222 \,V, 60 \,Hz$. The average voltage is calculated in a time interval of $16.67 \,ms$. It

Match the following:

Currents	$r.m.s.$ values
$(A) \ x_0 \sin \omega t$	$(i) \ x_0$
$(B) \ x_0 \sin \omega t \cos \omega t$	$(ii) \ \frac{x_0}{\sqrt{2}}$
$(C) \ x_0 \sin \omega t + x_0 \cos \omega t$	$(iii) \ \frac{x_0}{2\sqrt{2}}$

The alternating current is given by $i = \left\{\sqrt{42} \sin \left(\frac{2 \pi}{T} t\right) + 10\right\} \text{ A}$. The $r.m.s.$ value of this current is $\text{A}$.

$A$ 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.

The average value of an $A$.$C$. voltage given by $V = V_{m} \sin(\omega t)$ over the time interval $t = 0$ to $t = \frac{\pi}{\omega}$ is:

The $AC$ voltage across a resistance can be measured using a