A group of electric lamps having a total power rating of 1000 watt is supplied by an a.c. voltage             E = 200 sin (310 t + 60°). Then the r.m.s. value of the circuit current is

10A $10\sqrt 2 A$ 20 A $ 20\sqrt 2 A$

$10\sqrt 2 A$

$ Power(P) = E_{rms}I_{rms}cos\phi = \frac{E_0 I_0}{2} cos60^o = \frac{E_0I_0}{4}$ $\Rightarrow I_0 = 20A$ $I_{rms} = \frac{I_0}{\sqrt 2} = \frac{20}{\sqrt 2} = 10\sqrt 2 A$