Find the time required for $50\,Hz$ alternating current to change its value from zero to maximum value.

Match the following current $\text{r.m.s.}$ 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 $AC$ voltage across a resistance can be measured using a

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 $\text{A}$.

The peak value of an alternating current is $5 \ A$ and its frequency is $60 \ Hz$. Find its $rms$ value and the time taken to reach the peak value of current starting from zero.

What is $rms$ (root mean square) value? Write the formula of $rms$ current for an alternating current.