Chapter 11, Problem 1RQ

The average power absorbed by an inductor is zero,

1. (a) True
2. (b) False

To determine

Choose the correct option to check whether the average power absorbed by an inductor $L$ is zero or not.

Answer to Problem 1RQ

The correct option from the given choices is $\left(\text{a}\right)\text{True}$.

Explanation of Solution

Calculation:

Write the general expression to find the average power $P$.

$P=\frac{1}{2}{V}_m{I}_m\cos \left({\theta }_v-{\theta }_i\right)$ (1)

Here,

$V_m$ is the amplitude of the voltage,

$I_m$ is the amplitude of the current,

${\theta }_v$ is the phase angle of the voltage, and

${\theta }_i$ is the phase angle of the current.

For a purely reactive circuit, ${\theta }_v-{\theta }_i=\pm 90°$.

Substitute $90°$ for ${\theta }_v-{\theta }_i$ in equation (1) to find the average power $P$ absorbed by the reactive load $\left(L\text{or}C\right)$.

$\begin{array}{c}P=\frac{1}{2}{V}_m{I}_m\cos \left(90°\right)\\ =\frac{1}{2}{V}_m{I}_m\left(0\right)\end{array}$

$P=0$ (2)

Equation (2) shows that a purely reactive circuit absorbs no average power.

Therefore, the average power absorbed by an inductor is zero. Hence, option (a) is correct and option (b) is incorrect.

Conclusion:

Thus, the correct option from the given choices is $\left(\text{a}\right)\text{True}$.