In an ac circuit , an alternating voltage `e = 200 sqrt2 sin 100 t` volts is connected to a capacitor of capacitance `1 mu F`. The rms value of the current in the circuit is :

Options

A. 10mA
B. 100mA
C. 200mA
D. 20mA

Answer

D

Explanation

The given equation of alternating voltage is
`e = 200sqrt2 sin 100t` ….(i)
The standard equation of alternating voltage is
`e = e_0 sin omega t ` …..(ii)
Comparing (i) and (ii) , we get
`e_0 = 200sqrt2 V, omega = 100 rad s^(-1)`
The capacitive reactance is
`X_C = (1)/(omega C) = (1)/(100 xx 1 xx 10^(-6)) Omega `
The rms value of the current in the circuit is
`i_(rms) = (V_(rms))/(X_C) = (e_0 //sqrt2)/(1//omega C) = ((200sqrt2 //sqrt2))/((1//100 xx 10^(-6)) )`
`= 200 xx 100 xx 10^(-6) A = 2 xx 10^(-2) A = 20 mA `