So far the case when a battery has been connected to charge the capacitor and disconnected and a resistor applied to charge it up have been considered. If an alternating waveform, which by its nature is continually changing is applied to the capacitor, then it will be in a continual state of charging and discharging.
For this to happen a current must be flowing in the circuit. In this way a capacitor will allow an alternating current to flow, but it will block a direct current. As such capacitors are used for coupling an AC signal between two circuits which are at different steady state potentials.
It is found that when the sine-wave is first applied first applied, the rate of change of the voltage is at its greatest and this means that the charge is increasing at its fastest rate and hence the current flowing into the capacitor will be at its greatest. In other words the current is at its maximum.
As the voltage on the capacitor increases, the rate of change of voltage decreases and as a result the increase in charge and hence the current falls. Eventually the peak of the voltage sine-eave is reached where there is no change in voltage and accordingly the current at this point is zero.
After the voltage peak, the voltage starts to decreases, and accordingly the level of charge falls and this means that current flows out of the capacitor from this point.
The remainder of the waveform follows in a similar fashion. As a result it can be seen that the voltage and current are not in phase with each other. The current lags the voltage by a quarter of a cycle, i.e. 90°.
It is possible to express the current and voltage relationship for a perfect capacitor as:
Vt = sin(ωt)
It = sin(ωt+90)