Question

Determine the complex power, apparent power, average power absorbed, reactive power, and power factor (including whether it is leading or lagging) for a load circuit whose voltage and current at its input terminals are given by:

a. v(t)= 100cos(377t - 30°) V
i(t)= 2.5cos(377t- 60°) A

b. Vrms= 110e^j60 , Irms= 3e^j45 A

Answer 1

Answer:

A) complex power = apparent  power =  ( 108.253 + 62.5 i ) VA  

    active power = 108.25 watts

   reactive power = 62.5 VAR'S

    power factor = cos ∅ = cos 30° = 0.866 ( lagging )

also ; current lags voltage by 30°

B) your question is not well written hence no answer

Explanation:

A) v(t) = 100 cos (377t - 30° ) v

    Vrms = $\frac{100}{\sqrt{2} }$ ∠ -30°

    I(t) = 2.5cos(377t- 60°) A

  Irms = $\frac{2.5}{\sqrt{2} }$ ∠ -60°

determine complex power apparent power . ......  power factor

Note : complex power = apparent power

=( Irms ) * Vrms

=  ( $\frac{2.5}{\sqrt{2} }$ ∠ -60° ) * ( $\frac{100}{\sqrt{2} }$ ∠ -30° )  

= 125 ∠ 30°

= ( 108.253 + 62.5 i ) VA   ( complex power )

active power = 108.25 watts

reactive power = 62.5 VAR'S

power factor = cos ∅ = cos 30° = 0.866 ( lagging )

current lags voltage by 30°