JEE Mains · Physics · STD 12 -7. Alternating current
In an a.c. circuit, voltage and current are given by: \(V=100 \sin (100 t)\ V\) and \(I=100 \sin \left(100 t+\frac{\pi}{3}\right)\ \mathrm{mA}\) respectively. The average power dissipated in one cycle is _______.
- A \(5 \mathrm{~W}\)
- B \(10 \mathrm{~W}\)
- C \(2.5 \mathrm{~W}\)
- D \(25 \mathrm{~W}\)
Answer & Solution
Correct Answer
(C) \(2.5 \mathrm{~W}\)
Step-by-step Solution
Detailed explanation
\( P_{\text {avg }}=V_{\text {rms }} I_{\text {rms }} \cos (\Delta \phi) \) \( =\frac{100}{\sqrt{2}} \times \frac{100 \times 10^{-3}}{\sqrt{2}} \times \cos \left(\frac{\pi}{3}\right) \) \( =\frac{10^4}{2} \times \frac{1}{2} \times 10^{-3} \) \( =\frac{10}{4}=2.5 \mathrm{~W}\)
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