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In an ac circuit an alternating voltage e = 200 √2 sin 100 t volts is connected to a capacitor of capacity 1 μF. The r.m.s. value of the current in the circuit is:

1. 10mA
2. 100mA
3. 200mA
4. 20mA

Correct answer: 20mA

Solution

The rms value of the voltage is given by E_rms = E_peak / √2 = 200 V. The capacitive reactance is X_c = 1 / (ωC), where ω = 100 rad/s and C = 1 μF. Substituting, X_c = 1 / (100 × 1 × 10⁻⁶) = 10⁴ Ω. The rms current is I_rms = E_rms / X_c = 200 / 10⁴ = 0.02 A = 20 mA.

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