Question

For the following voltage and current phasors, calculate the complex power, apparent power, real power, and reactive power. Determine whether the power factor is leading or lagging.

V= 220 ∠ 30⁰ V rms, I= 0.5∠ 60⁰ A rms
a. The value of apparent power is_____VA
b. The value of real power is____VA
c. The value of reactive power is___VAR
d. The power factor is (Click to select)

Answer 1

To calculate the complex power, multiply the voltage and current phasors conjugate, S = VI*. The values of apparent power, real power, and reactive power are 110 VA, 0 W, and 110 VAR respectively. The power factor is lagging.

Step-by-step explanation:

To calculate the complex power, we multiply the voltage and current phasors conjugate, S = VI*, where * denotes the complex conjugate.

For the given voltage V = 220 ∠ 30° V rms and current I = 0.5∠60° A rms,

• The complex power is S = (220 ∠ 30°)(0.5∠-60°) = 110∠90° VA
• The apparent power is the magnitude of the complex power, so the value is 110 VA
• The real power is the real part of the complex power, so the value is 110 cos(90°) = 0 W
• The reactive power is the imaginary part of the complex power, so the value is 110 sin(90°) = 110 VAR

Since the reactive power is positive, the power factor is lagging.