When the current is in phase with the pressure, it is a simple matter, because the power or
watts = amperes × volts
that is, the product of the ammeter and voltmeter readings will give the power. However, the condition of synchronism of current and pressure hardly ever exists in practice, there being more or less phase difference.
Fig. 1,358.—Method of obtaining the active component of the current; diagram illustrating why the power factor is equal to cos φ. If AB and AC be respectively the given current and pressure, or readings of the ammeter and voltmeter, and φ the angle of phase difference between current and pressure, then drawing from B, BD perpendicular to AC will give AD the active component. Now, true power = AC × AD, but AD = AB cos φ, hence true power = AC × AB cos φ. Again, apparent power = AC × AB, and since true power = apparent power × power factor, the power factor = cos φ.
When the current is not in phase with the pressure, it is considered as made up of two components at right angles to each other.
1. The active component, in phase with the pressure;
2. The wattless component, at right angles to the pressure.
With phase difference between current and pressure the product of ammeter and voltmeter readings do not give the true power, and in order to obtain the latter, the active component of the current in phase with the pressure must be considered, that is,