Page 316 - Basic Electrical Engineering

i = I sin (ωt – ϕ)
m

Sinusoidal waveforms of voltage and current are shown in Fig. 3.20. It is

seen that the current wave is lagging the voltage wave by an angle, ϕ which is
the power factor angle.

Fig. 3.20 clearly shows that current in an R–L circuit lags voltage by an
angle ϕ, which is called the power factor angle.

The expression for the voltage and current in series R–L circuit is,

v = V sin ωt
m

i = I sin (ωt − ϕ), as I lags V

The power is product of instantaneous values of voltage and current,

p = v × i
= V sin ωt × I sin (ωt − ϕ)
m
m

= V I [2 sin ωt sin (ωt − ϕ)
m m

= V I [cos ϕ − cos (2ωt − ϕ)
m m

= V I cos ϕ − v I cos (2ωt − ϕ)
m m
m m

The average power over a complete cycle is calculated as