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.
- 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.