# Three phase induction motors

1. Jun 1, 2008

### Aaron321

hey does anyone know the effiency and power factor of a typical three phase induction motor?

cheers,

Last edited: Jun 1, 2008
2. Jun 1, 2008

### konthelion

Well, it's always a good thing to start off with the definitions of efficiency, power, and power factor.

Let $$\eta$$ be the efficiency, then $$\eta = \frac{P_{out}}{P_{in}}$$
Let P= power, then P=VI.

Therefore the average Power = $$VIcos(\theta)$$
By definition of power factor, it is the ratio of average power/VI.
Thus, the definition of power factor = $$\frac{VIcos(\theta)}{VI}=cos(\theta)$$

From here, use the Pythagorean theorem to solve for power factor of a three phase