The phase difference between the voltage and the current in an ac circuit is $\pi /4$. If the frequency is $50\, Hz$ then this phase difference will be equivalent to a time of

The peak value of an Alternating current is $ 6$ amp, then r.m.s. value of current will be

An $AC$ current is given by $I = I _{1} \sin \omega t + I _{2} \cos \omega t$. A hot wire ammeter will give a reading

The mean value of current for half cycle for a current variation shown by the graph is

An alternating voltage is given by : $e = e_1\, \sin \omega t + e_2\, \cos \omega t$. Then  the root mean square value of voltage is given by :-

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