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AC Voltage Applied to a Capacitor


A circuit which has only a capacitor and an AC power source (such as a wall outlet). A capacitor is a device for storing charg.

It turns out that there is a 90o phase difference between the current and voltage, with the current reaching its peak 90o (1/4 cycle) before the voltage reaches its peak.

Put another way, the current leads the voltage by 90o in a purely capacitive circuit.

The current flowing in the AC source is :

i = dQ/dt

The source voltage or applied voltage V = Vm sin ωt .

Where Vm = amplitude of voltage and ω = angular frequency.

Relationship between voltage and charge for a capacitor: CV = Q

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V = voltage across the plates of the capacitor

Q = charge on the capacitor.


Can be written as:

Q = C × Vm × sin (ω × t)

The current flowing in the AC source :

i = dQ/dt

i = d(Vm × sin (ω × t))/dt

i = C × Vm × ω × cos(ω × t)

i = (Vm × sin(ω × t + π/2))(1/(ω × c))

The current varies sinusoidally having a phase difference of 90 degree.

i = im × sin(ω × t + π/2)

The amplitude of the current can be written as:

im = ωCVm

Capacitors do not behave the same as resistors. Whereas resistors allow a flow of electrons through them directly proportional to the voltage drop, capacitors oppose changes in voltage by drawing or supplying current as they charge or discharge to the new voltage level.

AC Voltage Applied to a Capacitor

The flow of electrons “through” a capacitor is directly proportional to the rate of change of voltage across the capacitor.

This opposition to voltage change is another form of reactance, but one that is precisely opposite to the kind exhibited by inductors.

Role of the Capacitor in AC circuit

The capacitors are used to store energy on their conductive plates in the form of an electrical charge. The capacitor that is linked in an AC circuit blocks the power supply when get fully charged. When there is an AC power supply in the circuit, the capacitor will charge and discharge alternatively at a rate determined by the supplied frequency.

Function of Capacitor in AC Circuit

The capacitors are used to buildup voltage above the input voltage and rectifier circuits to level the current fluctuations. The capacitors are used to block the DC static voltage and allow AC signals to pass from one circuit area to another and known as coupling capacitors. The decoupling capacitors are used to eliminate any AC signal at the DC bias point. The starting torque can be improved using capacitors and used to improve the power factor in power systems.

The principle of charging and discharging of capacitor

In the capacitor charging process, the current flows towards the positive plate in this process positive charge gets added to that plate.

In the case capacitor is fully charged, no current flows in the circuit due to potential difference across the capacitor is equal to the source-voltage.This means the charging current drops to zero (capacitor voltage = source voltage).

In the capacitor discharging process, current flows away from the positive plate and towards negative plate, that is in the opposite direction.