Electrical Impedance - Device Examples - Deriving The Device-specific Impedances - Capacitor

Capacitor

For a capacitor, there is the relation:

Considering the voltage signal to be

it follows that

And thus

This says that the ratio of AC voltage amplitude to AC current amplitude across a capacitor is, and that the AC voltage lags the AC current across a capacitor by 90 degrees (or the AC current leads the AC voltage across a capacitor by 90 degrees).

This result is commonly expressed in polar form, as

or, by applying Euler's formula, as