A voltage of 100 V is applied to an impedance of Z = (3 + j4) Ω. What are the values of active power, reactive power and volt-amperes respectively?

Concept:

The power triangle is as shown below.

P = Active power (or) Real power in W = Vrms Irms cos ϕ

Q = Reactive power in VAR = Vrms Irms sin ϕ

S = Apparent power in VA = Vrms Irms

S = P + jQ

\(S = \sqrt {{P^2} + {Q^2}}\)

ϕ is the phase difference between the voltage and current

Power factor \(\cos \phi = \frac{P}{S}\)

Calculation:

V = 100 V

Impedance, Z = 3 + j4

Power factor, \(\cos \phi = \frac{R}{Z} = \frac{3}{{\sqrt {{3^2} + {4^2}} }} = 0.6\)

Current (I) = V/Z = 100/5 = 20 A

Real power (P) = 100 × 20 × 0.6 = 1200 W

Reactive power (Q) = 100 × 20 × 0.8 = 1600 W

Apparent power (S) = 100 × 20 = 2000 W

The corresponding power triangle is as shown below.