A group of lamps having total power rating of $1000 \mathrm{~W}$ is supplied by an $\mathrm{AC}$ voltage of…

A group of lamps having total power rating of $1000 \mathrm{~W}$ is supplied by an $\mathrm{AC}$ voltage of $\mathrm{E}=200$ $\sin \left(310 t+60^{\circ}\right)$, the r.m.s. value of current flowing through the circuit is
  1. $10 \mathrm{~A}$
  2. $5 \sqrt{2} \mathrm{~A}$
  3. $20 \mathrm{~A}$
  4. $10 \sqrt{2} \mathrm{~A}$

Solution

Power: $\mathrm{P}=\frac{1}{2} \mathrm{~V}_0 \mathrm{I}_0 \cos \phi$ $\therefore \quad 1000=\frac{1}{2} \times 200 \times \mathrm{I}_0 \cos 60^{\circ}$ $\mathrm{I}_0=20 \mathrm{~A}$ $\therefore \quad \mathrm{I}_{\mathrm{mms}}=\frac{20}{\sqrt{2}}$ $\mathrm{I}_{\mathrm{rms}}=10 \sqrt{2} \mathrm{~A}$

Asked in: MHT CET 2023 (13 May Shift 2)

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