Discussion
A capacitor of 50 µF offers a reactance of 50 Ω against AC supply of 100 V. The frequency of the supply is :
Answer: A
The supply frequency is about 63.6 Hz.
The reactance of a capacitor is \(X_{C} = 1/(2\pi f C)\), so the frequency follows directly; the 100 V supply voltage is not needed.
\[ \begin{aligned} f &= \frac{1}{2\pi C X_{C}} \\ &= \frac{1}{2\pi \times 50 \times 10^{-6} \times 50} \\ &= \frac{1}{0.0157} = 63.66\ \text{Hz} \end{aligned} \]
At 50 Hz the reactance of 50 µF would be about 63.7 Ω, not 50 Ω. A capacitor at zero frequency (dc) has infinite reactance.
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