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.

.