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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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In a circuit the voltage and current are given by v = (10 + j5) and i = (6 + j4) · Power of the circuit is
60 Watt
20 Watt
80 Watt
70 Watt
80 Watt
Given: Voltage v = (10 + j5) V, Current i = (6 + j4) A.
Voltage v = (10 + j5) V, Current i = (6 + j4) A.
P=Re{V×I∗}
Identify complex conjugate of current
To calculate real power in an AC circuit, we use the formula P=Re{V⋅I∗}. First, find the complex conjugate of i=(6+j4), which is i∗=(6−j4).
i∗=6−j4
Calculate the complex power (S)
Multiply the complex voltage v by the conjugate current i∗: S=(10+j5)(6−j4). Expanding this product: S=10(6)−10(j4)+j5(6)−j5(j4)=60−j40+j30−j2(20).
S=60−j10+20=80−j10
Extract Real Power
The real power P corresponds to the real part of the complex power S. From S=80−j10, the real component is 80.
P=Re{80−j10}=80 Watt
C is correct because the real part of the product V×I∗ yields a power of 80 Watt.
In AC circuits, remember that complex power S=P+jQ where P is real (active) power in Watts and Q is reactive power in VARs; this is analogous to finding the dot product of two vectors in physics.