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Question
Show that the current leads the voltage in phase by π/2 in an AC circuit containing an ideal capacitor ?
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Solution
Let us consider a capacitor C connected to an AC source as shown below.
Let the AC voltage applied be
`v = v_msinωt`
`∴ v = q/C`
Applying Kirchhoff’s loop rule, we have:
` v_msinωt q/C`
`i = (dq)/dt`
`∴ i = (d)/dt( v_mCsinωt) `
`ωCv_mcos(ωt)`
`cos ωt = sinωt+π/2`
`∴ i = i_msin(ωt+π/2)`
`i_m = ωCv_m`
`i =(v_m)/((1/(ωC)))`
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