Question

The total instantaneous power absorbed by a three-phase motor (under balanced steady conditions) as well as balanced three-phase impedance load is

(a) A constant

(b) A function of time

Short answer

Answer

The correct option is (a); that is, a constant.

Step-by-step solution

Calculate the expression of power in the case of a three-phase circuit

For a balanced three-phase circuit, the per-phase power and the three-phase power are given respectively by the following expressions:

$$\begin{gathered} {\mathbf{P}}_{\mathbf{per}\mathbf{}\mathbf{phase}}\mathbf{=}{\mathbf{V}}_{\mathbf{P}}{\mathbf{I}}_{\mathbf{p}}\mathbf{}\mathbf{cosf} \\ {\mathbf{P}}_{\mathbf{3}\mathbf{f}}\mathbf{=}\mathbf{3}{\mathbf{V}}_{\mathbf{P}}{\mathbf{I}}_{\mathbf{p}}\mathbf{}\mathbf{cosf} \end{gathered}$$

It is clear from the above expressions that the power expression does not depend on the time.

Therefore, the sum of instantaneous powers in the case of a balanced three-phase circuit is constant.

Thus, the correct option is (a).

Explanation for option (b)

For the total instantaneous power to be a function of time, the expression of power must be dependent on time.

Thus, the option (b) is incorrect.