A $40 \mu ext{F}$ capacitor is connected to a $200 ext{ V}$, $50 ext{ Hz}$ AC supply. The RMS value of the

Question

A $40 \mu	ext{F}$ capacitor is connected to a $200	ext{ V}$, $50	ext{ Hz}$ AC supply. The RMS value of the current in the circuit is, nearly:

Accepted Answer

To find the RMS current ($I_{rms}$), we first calculate the capacitive reactance ($X_C$) using the formula $X_C = \frac{1}{2\pi fC}$. Given $C = 40 	imes 10^{-6}	ext{ F}$ and $f = 50	ext{ Hz}$, $X_C = \frac{1}{2 	imes 3.14 	imes 50 	imes 40 	imes 10^{-6}} \approx 79.6 \ \Omega$. According to the sources, the RMS current is given by $I_{rms} = \frac{V_{rms}}{X_C}$ . Substituting the given RMS voltage ($200	ext{ V}$), we get $I_{rms} = \frac{200}{79.6} \approx 2.51	ext{ A}$. Therefore, the RMS current is nearly **2.5 A**.

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