Question

The average power/cycle associated with the inductor is?

Answer 1

Explanation:

1. Average power dissipated is the amount of energy lost due to unwanted means in an electronic device or circuit.
2. This waste occurs because the energy gets converted to another form which is an unnecessary by-product, for example, heat, sound, etc.

Work done or power over a complete cycle in an inductor is given by,

$W={\int }_0^{T}EIdt$

Where $E$ is instantaneous voltage and $I$ is instantaneous current

We know, in an inductor,

$$\begin{gathered} I=I_0\sin \left(\omega t-\frac{\mathrm{\pi }}{2}\right) \\ \Rightarrow I=-I_0\cos \omega t \end{gathered}$$

here, $I_0$ is the amplitude of current, $\omega$ is angular frequency and $t$ is time

$$\begin{gathered} \Rightarrow W=-{\int }_0^T{E}_0\sin \omega t{I}_0\cos \omega tdt \\ \Rightarrow W=-E_0{I}_0{\int }_0^T\sin \omega t\cos \omega tdt \\ \Rightarrow W=-\frac{E_0{I}_0}{2}{\int }_0^{T}2\sin \omega t\cos \omega tdt \\ \Rightarrow W=-\frac{E_0{I}_0}{2}{\int }_0^T\sin 2\omega tdt \\ \Rightarrow W=0 \end{gathered}$$

i.e., the average power/cycle associated with the inductor is zero.