# Power and power factor

This is one more post about basic concepts directed to students and beginners in the area. Also will talk about the power factor, an important parameter in AC systems.

Electric power

$i$ is the electrical current produced by a voltage source, the quantity of electric charge $dQ$ which moves between the terminals is $i dt$ because:

$i=\frac{\left | Q \right |}{\Delta t}$

$d$ is the derived symbol which represents the instant variation rate, $\Delta t$ is the time interval. Therefore:

$i=\frac{d Q}{d t}$

$dU=V\cdot dQ=V\cdot idt$

$P=\frac{dU}{dt}$

$P=V\cdot i$

Dissipated power due to the resistance:

$P=i^2R=\frac{V^2}{R}$

Calculate electric energy consumption

The consumption $E$ is measured in kilowatt-hour and the formula to the calculation is:

$E=P\cdot \Delta t$

And the cost:

$Cost=unitary value\cdot E$

Power in alternate current

In alternate current exist three types of power: apparent, active and reactive. The active power is the really used power by the load, the reactive “return” to the source, making an analogy the active power is the liquid and the reactive is soft drink’s foam. The apparent power $S$(VA) is:

$S=\sqrt{P^2+Q^2}$ $P$(kW) is the active power and $Q$(var) is the reactive.

A 100% resistive load has zero reactive power. The reactive power can be capacitive or inductive. The right triangle is for inductive loads and the left triangle is for capacitive loads.

The power factor $F_{p}$ is:

$F_{p}=cos(\theta)=\frac{P}{S}$

The electrical energy standards require that the products and equipment have a minimum power factor of 0.98, in some countries is 0.92. To correct the power factor of inductive load machines, which use motors, are employed capacitors bank in parallel with the inductive load to have the minimum power factor. After correction, the angle of power triangle becomes smaller.