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GUJCET · Physics · Alternating Current
What is the average power dissipation in an ideal capacitor in AC circuit ?
- A \(\frac{1}{2} \mathrm{CV}^{2}\)
- B \(\mathrm{CV}^{2}\)
- C \(2 \mathrm{CV}^{2}\)
- D Zero
Answer & Solution
Correct Answer
(D) Zero
Step-by-step Solution
Detailed explanation
(D) Zero
for only capacitive circuit \(\phi=\frac{\pi}{2}\) rad
\(
\begin{aligned}
\mathrm{P} & =\frac{v_{m} i_{m}}{2} \cos \phi \\
\therefore \mathrm{P} & =\frac{v_{m} i_{m}}{2} \cos \frac{\pi}{2} \\
\therefore \mathrm{P} & =0 \qquad\left(\because \cos \frac{\pi}{2}=0\right)
\end{aligned}
\)
for only capacitive circuit \(\phi=\frac{\pi}{2}\) rad
\(
\begin{aligned}
\mathrm{P} & =\frac{v_{m} i_{m}}{2} \cos \phi \\
\therefore \mathrm{P} & =\frac{v_{m} i_{m}}{2} \cos \frac{\pi}{2} \\
\therefore \mathrm{P} & =0 \qquad\left(\because \cos \frac{\pi}{2}=0\right)
\end{aligned}
\)
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