Chapter 2, Problem 2.30MCQ

Under balanced operating conditions, consider the three-phase complex power delivered by the three-phase source to the three-phase load. Match the following expressions, those on the left to those on the right.

(i) Realpower, ${\text{P}}_{3\varphi }$

(a) $\left(\sqrt{\text{3}}{\text{V}}_{\text{LL}}{\text{I}}_{\text{L}}\right)\text{VA}$

(ii) Reactive power, ${\text{Q}}_{3\varphi }$

(b) $\left(\sqrt{\text{3}}{\text{V}}_{\text{LL}}{\text{I}}_{\text{L}}\sin \varphi \right)\text{var}$

(iii) Total apparent power, ${\text{S}}_{3\varphi }$ (c) $\left(\sqrt{\text{3}}{\text{V}}_{\text{LL}}{\text{I}}_{\text{L}}\cos \varphi \right)\text{W}$

(iv) Complex power, ${\text{S}}_{3\varphi }$ (d) ${\text{P}}_{3\varphi }+j{\text{Q}}_{3\varphi }$

Note that ${\text{V}}_{\text{LL}}$ is the rms line-to-line voltage, ${\text{I}}_{\text{L}}$ is the rms line current, and $\varphi$ is the power-factor angle.