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NEET PHYSICSEasy

A 40μF40 \mu\text{F} capacitor is connected to a 200 V200\text{ V}, 50 Hz50\text{ Hz} AC supply. The RMS value of the current in the circuit is, nearly:

A

2.05 A

B

2.5 A

C

25.1 A

D

1.7 A

Step-by-Step Solution

To find the RMS current (IrmsI_{rms}), we first calculate the capacitive reactance (XCX_C) using the formula XC=12πfCX_C = \frac{1}{2\pi fC}. Given C=40×106 FC = 40 \times 10^{-6}\text{ F} and f=50 Hzf = 50\text{ Hz}, XC=12×3.14×50×40×10679.6 ΩX_C = \frac{1}{2 \times 3.14 \times 50 \times 40 \times 10^{-6}} \approx 79.6 \ \Omega. According to the sources, the RMS current is given by Irms=VrmsXCI_{rms} = \frac{V_{rms}}{X_C} . Substituting the given RMS voltage (200 V200\text{ V}), we get Irms=20079.62.51 AI_{rms} = \frac{200}{79.6} \approx 2.51\text{ A}. Therefore, the RMS current is nearly 2.5 A.

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