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Show that the Current Leads the Voltage in Phase By π/2 in an Ac Circuit Containing an Ideal Capacitor ? - Physics

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ConceptAc Voltage Applied to a Capacitor

Question

Show that the current leads the voltage in phase by π/2 in an AC circuit containing an ideal capacitor ?

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)))`

Hence, the current leads the voltage in phase by π/2.
  Is there an error in this question or solution?
Solution Show that the Current Leads the Voltage in Phase By π/2 in an Ac Circuit Containing an Ideal Capacitor ? Concept: Ac Voltage Applied to a Capacitor.
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