Answer to Question #167608 in Electric Circuits for andrew brown

Question

An AC load exhibits a lagging power factor of 0.73 at 230 VAC and 315 amps. If the

system frequency is 60 Hz, calculate the following:

Apparent power (S) =?

A. 72.45 kVA B. 724.5 kVA C. 7.245 kVA

True power (P) =?

A. 5.289 kW B. 52.89 kW C. 528.9 kW

Reactive power (Q) =?

A. 4.952 kVAR B. 495.2 kVAR C. 49.52 kVAR

Answer 1

$V=230 V\newline I=315A\newline Powerfactor=cos\phi=0.73\implies\phi=43.11\degree\newline\newline \newline 1) Apparant \space power=VI=230\times315\newline=72.45kVA$

$2)True\space power=VIcos\phi=230\times315\times0.73\newline=52.89kW$

$3) Reactive\space Power=VIsin\phi=\newline230\times315\times sin43. 11=49.52kVAR$