Hence, the energy delivered to the capacitor over an interval of time from to will be:From this derivation it can be seen that the change in energy only depends on the value of the capacitor voltage at times and and not on the specific voltage waveform in the interval (the voltage variation over time). The instantaneous energy of a capacitor is defined as:
assuming that a capacitor with zero voltage has zero energy.
Hence, the energy delivered to the inductor over an interval of time from to will be:From this derivation it can be seen that the change in energy only depends on the value of the inductor current at times and and not on the specific current waveform in the interval. The instantaneous energy of an inductor is defined as:
assuming that an inductor with zero current has zero energy.