Class 12 Physics Alternating Current Capacitive AC Circuit

Capacitive AC Circuit

Capacitive AC circuit has an AC voltage and only circuit element present is capacitor.

AC voltage applied to a Capacitor:-

  • In this circuit an alternating voltage is applied to  a  
  • The source voltage or applied voltage V = Vm sinωt .
  • In this circuit the capacitor  will continuously  get charged  and discharged  in each  half 
  • Therefore the applied voltage V =  voltage  across  the  plates  of the capacitor.
  • => V = (q/C)
    • Where q = charge  on the capacitor.
  • => Vm sinωt = (q/C)
  • By differentiating the above equation,
  • => C Vm d(sinωt)/dt = dq/dt
  • => I = C Vm ω cosωt
  • In terms of sine function :- I = C Vm ω sin(ωt + (∏/2)) (equation(1))
  • Putting C Vm ω = Im  =  current amplitude  in equation(1),
  • I = Im sin(ωt + ∏/2). This is  the  expression for current through capacitive circuit.

 

Capacitive Reactance:-

  • Current amplitude Im = C Vm ω
  • => Vm = (1/ ω C)  Im   (equation(a)) ,comparing equation(a) with V = IR , the term (1/ ω C)  acts as a  resistance in case of capacitive circuit.
  • (1 / ω C)  is  known as capacitive reactance. Capacitive reactance is the resistance associated with a  pure Capacitive AC circuit.
  • It is denoted by Xc.
  • SI  unit is  ohm(Ω).
  • Therefore Xc = (1/ ω C).
  • => Xc  ∝  (1/ ω)  and  Xc  ∝  (1/C).

Graphical representation of Voltage and Current

  • Voltage and current are out of phase by (∏/2). The current is ahead of voltage by (∏/2).
  • Average current over  a complete cycle  is  zero.
  • Average voltage  over  a complete cycle is  zero.

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