What is the maximum voltage of $220\, V$ (in $, V$)?

An alternating current is given by $i = 2 \sin \omega t + 6 \cos \omega t$. The $R.M.S.$ current in amperes is,

$A$ bulb of resistance $280 \Omega$ is supplied with a $200 V$ $AC$ supply. What is the peak current?

Match the following:
Currents $r.m.s.$ values
$(1) x_0 \sin \omega t$ $(i) x_0$
$(2) x_0 \sin \omega t \cos \omega t$ $(ii) \frac{x_0}{\sqrt{2}}$
$(3) x_0 \sin \omega t + x_0 \cos \omega t$ $(iii) \frac{x_0}{2\sqrt{2}}$

In an $a.c.$ circuit,the instantaneous current and $emf$ are represented as $I = I_0 \sin(\omega t - \pi / 6)$ and $E = E_0 \sin(\omega t + \pi / 3)$ respectively. The voltage leads the current by

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