Question

What is the average power consumed/cycle in the ideal capacitor?

Answer 1

Ideal capacitor:

1. An ideal capacitor is defined as a purely reactive device with no resistive effect.
2. The ideal capacitor is not affected by atmospheric conditions.
3. It has a high resistance to temperature change.

Mathematically, it can be represented as:

$$\begin{gathered} {\mathrm{p}}_{\mathrm{c}}=\mathrm{iv} \\ =({\mathrm{i}}_{\mathrm{m}}\cos \mathrm{\omega t})({\mathrm{v}}_{\mathrm{m}}\sin \mathrm{\omega t}) \\ ={\mathrm{i}}_{\mathrm{m}}{\mathrm{v}}_{\mathrm{m}}(\cos \mathrm{\omega t}\sin \mathrm{\omega t}) \\ =\frac{{\mathrm{i}}_{\mathrm{m}}{\mathrm{v}}_{\mathrm{m}}}{2}\sin 2\mathrm{\omega t} \end{gathered}$$

We know that, $\sin 2\mathrm{\omega t}=0$

Therefore, in an ideal capacitor, the average power consumed per cycle is $0$.