Page 321 - Basic Electrical Engineering
P. 321
v = V Sin ωt
m
i = I Sin (ωt + ϕ) as I leads V
m
Power is the product of voltage and current. The instantaneous power is
P = v × i
= V Sin ωt × I Sin(ωt + ϕ)
m
m
= V I [2sin ωt sin(ωt + ϕ)]
m m
= V I [cos (−ϕ)− cos(2ωt + ϕ)]
m m
= V I
m m
as cos(−ϕ) = cos ϕ
The second term is a cosine term whose average value over a complete
cycle is zero. Hence, average power consumed by the circuit is
The power triangle has been shown in Fig. 3.24 (b).
Thus, various powers are
Apparent power S = VI Volt Amperes or VA
Active power P = VI cos ϕ W
Reactive power Q = VI sinϕ VAR
