In a purely capacitive ac circuit, we get,(adsbygoogle = window.adsbygoogle || []).push({});

I_{m}= V_{m}*ω*C, ....(1)

Where, I_{m}= Amplitude of the current

V_{m}= Amplitude of the voltage

Now, what I think is,

We know that in a purely capacitive circuit, voltage lags behind current by a phase difference of ∏/2 rad. So, at any time 't',

I = I_{m}sin(ωt+∏/2)

V = V_{m}sinωt

Using Kirchhoff's Loop Rule,

V = V_{m}sinωt = q/C

Where q = charge on the capacitor at time 't',

To find the current, I = dq/dt,

dq = Idt,

q = ∫Idt

q = ∫I_{m}cosωt dt

q = I_{m}∫cosωt dt

q = I_{m}*ω*sinωt

So, V_{m}sinωt = I_{m}*ω*sinωt /C

V_{m}= I_{m}*ω/C

I_{m}= V_{m}*C/ω, which is apparently, not equal to equation (1).

Am I wrong in my approach?

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# AC applied to a capacitor.

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