Electric Circuits and Networks

8.9 APPARENT POWER, ACTIVE POWER, REACTIVE POWER AND POWER FACTOR

Consider a sinusoidal voltage source v(t) = V_m cosωt delivering power to a resistive load R. The current in the resistor is i(t) = I_m cosωt, where I _m = V_m/R.

The instantaneous power is p(t) = V_mI_m cos²ωt = 0.5 V_mI_m + 0.5 V_mI_m cos2ωt W. The first term is a constant and the second term produces an average of zero over a cycle. Therefore, the average power delivered to the resistor is 0.5 V_mI_m = 0.5V_m²/R = 0.5I_m²R. The average power can be expressed as V_rmsI_ms in terms of rms values of voltage and current. Thus, a sinusoidal voltage/current is only as effective as a DC voltage/current of magnitude that is only 70.7% of the amplitude of the sinusoid. The presence of the second term ...