The sine of 90 degrees is 1 and the sine of 0 degrees is 0. Thus, at 90 degrees of angular phase displacement (no real power), apparent power (VA) equals reactive power (VAR). Thus:

0 = 90° ^ VAR = VA sin 90° = VA (1) = VA Q = 0 ° ^ VAR = VA sin 0 ° = VA (0) = 0 0 = 30° ^ VAR = VA sin 60° = VA (0.5) = 0.5VA

These relationships can also be expressed as a function of the Pythagorean theorem: A2 + B2 = C2. VA is C (the hypotenuse) and A and B (the legs of the triangle) are W and VAR. Thus:

VA = (W2 + VAR2)112 W = (VA2 - VAR2)112 VAR = (VA2 - W2)1/2

Power Factor

Power factor (PF) is a common measure of this angle of displacement of current from voltage. The cosine of the angle of current lag behind or lead ahead of voltage is the power factor of the circuit. This is quantified as the ratio of kW to kVA. The greater the phase displacement, the lower the power factor. Power factor is expressed as:

Real po

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