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Examoogle • User • info@examoogle.com • EE-2024-8821
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In a circuit the voltage and current are given by v = (10 + j5) and i = (6 + j4) · Reactive power of the circuit is
70 VAR
60 VAR
– 10 VAR
10 VAR
10 VAR
Given: Voltage phasor V = 10 + j5 V, Current phasor I = 6 + j4 A.
Voltage phasor V = 10 + j5 V, Current phasor I = 6 + j4 A.
S=V×I∗=P+jQ
Calculate the complex conjugate of current
The complex conjugate of current I=6+j4 is found by changing the sign of the imaginary part.
I∗=6−j4
Calculate the complex power S
Compute the product of voltage V and the conjugate of current I∗: S=(10+j5)(6−j4).
S=10(6)−10(j4)+j5(6)−j2(5)(4)
Simplify the expression
Since j2=−1, the term −j2(20) becomes +20. Expanding the terms gives S=60−j40+j30+20.
S=(60+20)+j(30−40)=80−j10
Identify reactive power Q
The complex power is expressed as S=P+jQ. Comparing 80−j10 with P+jQ, the reactive power Q is −10 VAR.
Q=−10 VAR
D is correct because the imaginary part of the complex power S=VI∗ yields the reactive power, which in this case calculates to −10 VAR.
In AC circuit analysis, remember that Q represents the reactive power; a negative value signifies that the circuit is capacitive (or supplying reactive power), while positive represents inductive behavior.