In an AC circuit, an alternating voltage $straight e space equals space 200 square root of 2$ 100t volt is connected to a capacitor of capacity 1μF. The rms value of the current in the circuit is

100 mA

200 mA

20 mA

10 mA

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Solution

20 mA

Given space straight e equals space 200 square root of 2 space sin space 100 space straight t and space space straight C space equals space 1 space μF straight E subscript rms space equals space 200 space straight V straight X subscript straight C space equals space 1 over ωC space equals space fraction numerator 1 over denominator 1 space straight x space 10 to the power of negative 6 end exponent space straight x space 100 space end fraction space equals space 10 to the power of 4 space straight capital omega straight i subscript rms space equals space straight E subscript rms over straight X subscript straight C straight i subscript rms space equals 200 over 10 to the power of 4 space equals space 2 space straight x space 10 to the power of negative 2 end exponent space straight A space equals space 20 space mA

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