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) Real power, \(\mathrm{P}_{3 \phi}\)

(a) \(\left(\sqrt{3} V_{L L} I_{L}ight)\) VA

(ii) Reactive power, \(\mathrm{Q}_{3 \phi}\)

(b) \(\left(\sqrt{3} V_{L L} I_{L} \sin \phiight)\) var

(iii) Total apparent power, \(\mathrm{S}_{3 \phi}\)

(c) \(\left(\sqrt{3} \mathrm{~V}_{\mathrm{LL}} \mathrm{I}_{\mathrm{L}} \cos \phiight) \mathrm{W}\)

(iv) Complex power, \(S_{3 \phi}\)

(d) \(\mathrm{P}_{3 \phi}+j \mathrm{Q}_{3 \phi}\)

\(\mathrm{V}_{\mathrm{LL}}\) is the rms line-to-line voltage, \(\mathrm{I}_{\mathrm{L}}\) is the rms line current, and \(\phi\) is the power-factor angle.