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Math and Arithmetic

Why the power factor is not more than unity?

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April 29, 2013 11:22PM

The power factor is defined as the cosine of an angle.

(It's the phase angle between voltage and current.)

The magnitude of the cosine is never greater than ' 1 '.

The theory of Unity Gain states that you cannot get more out than you put in.

If the current maximum of a cycle lags (or leads) the voltage maximum by a fraction x of a cycle, then if you think of the situation where the voltage and current are rotating vectors at an angle x degrees apart, then the only useful power is gained by the component of the current which is in phase with the voltage. So, resolve the current vector into two components, one in the direction of the voltage vector, (Icos(x)) and the other component perpendicular the the voltage vector, (Isin(x)). Then the useful power is gotten by multiplying the bits of voltage and current which are in phase: V times I cos(x). So the power obtained is a factor cos(x) down on the value if V and I were in perfect sync. That's why it's called power factor. It is why Power stations don't like inductive or capacitative loads: they have to supply heavy currents that actually deliver no power. Finally, cos(x) never gets above 1.