ExamBro
ExamBro
MHT CET · Physics · Alternating Current

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. A \(10 \mathrm{~A}\)
  2. B \(5 \sqrt{2} \mathrm{~A}\)
  3. C \(20 \mathrm{~A}\)
  4. D \(10 \sqrt{2} \mathrm{~A}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(10 \sqrt{2} \mathrm{~A}\)

Step-by-step Solution

Detailed explanation

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