In a circuit, voltage and current are given by V = 10 sin(ωt - 30°), i = 10 sin (ωt + 30) calculate the power consume in this circuit:

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:

i = 10 sin (ωt + 30)

v = 10 sin (ωt – 30)

ϕ = - 30 – (30) = - 60°

Real power consumed, \(P = \frac{{10}}{{\sqrt 2 }} \times \frac{{10}}{{\sqrt 2 }} \times \cos 60^\circ = 25\;W\)