If $I_1, I_2, I_3$ and $I_4$ are the respective $r.m.s$. values of the time varying currents as shown in the four cases $I, II, III$ and $IV$. Then identify the correct relations.

The r.m.s. voltage of domestic electricity supply is $220$ $volt$ . Electrical appliances should be designed to withstand an instantaneous voltage of......$V$

The maximum value of $a.c.$ voltage in a circuit is $707V$. Its rms value is.....$V$

The direct current which would give the same heating effect in an equal constant resistance as the current shown in figure, i.e. the $r.m.s.$ current, is.....$A$

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) $\frac{{{x_0}}}{{(2\sqrt 2 )}}$

A $40$ $\Omega$ electric heater is connected to a$ 200 V, 50 Hz$ mains supply. The peak value of electric current flowing in the circuit is approximately......$A$