**Simple representation**

We can represent this by a mine cart on a railway. There is a rope attached to it at the front. If you stand in front of the mine cart and pull the rope, the cart will go forward on the rails. If you stand next to the rails and pull the rope, you will notice that it takes more force to pull the mine cart. You are pulling the rope at an angle, this angle can be compared with the angle ‘phi’ (φ). The wider the angle, the harder it gets to pull the mine cart at the same speed. Therefore, you will have to use more power as the angle widens.

**Theoretical representation**

The cos phi is a power factor. It is the ratio between active power and apparent power.

With alternating voltages, the apparent power S (in VA) of an inductive load is stronger than the active power P (in W) which is actually used by the load.

The cos phi equals active power P divided by the apparent power S.

cos φ = P/S

Examples:

*Resistive loads:*

Incandescent light bulbs and heating elements cos φ = 1

*Inductive loads:*

Electric hand tools | cos φ ~ 0.97 |

Electromotors | cos φ = 0.7 – 0.8 |

Fluorescent tubes, welding transformer | cos φ ~ 0.5 |

List of appliances