ELECTRIC POWER

ELECTRIC POWER

Electric power is the rate, per unit time, at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second.

Electric power is usually produced by electric generators, but can also be supplied by sources such as electric batteries. It is usually supplied to businesses and homes (as domestic mains electricity) by the electric power industry through an electric power grid.

Symbol	Meaning
J	joule
kg	kilogram
m	metre
s	second
N	newton
Pa	pascal
W	watt
C	coulomb
V	volt
Ω	ohm
A	ampere

Electric power can be delivered over long distances by transmission lines and used for applications such as motion, light or heat with high efficiency.

1 Passive devices (loads)

2 Active devices (power sources)

3 Passive sign convention

4 Resistive circuits

5 Alternating current

6 Electromagnetic fields

Definition

Electric power, like mechanical power, is the rate of doing work, measured in watts, and represented by the letter P. The term wattage is used colloquially to mean "electric power in watts." The electric power in watts produced by an electric current I consisting of a charge of Q coulombs every t seconds passing through an electric potential (voltage) difference of V is

Where 

Q is electric charge in coulombs

t is time in seconds

I is electric current in amperes

V is electric potential or voltage in volts

Resistive circuits

where

Vp is the peak voltage in volts

Ip is the peak current in amperes

Vrms is the root-mean-square voltage in volts

Irms is the root-mean-square current in amperes

θ is the phase angle between the current and voltage sine waves

Engineers use the following terms to describe energy flow in a system (and assign each of them a different unit to differentiate between them):

Active power, P, or real power: watt (W);

Reactive power, Q: volt-ampere reactive (var);

Complex power, S: volt-ampere (VA);

Apparent power, |S|: the magnitude of complex power S: volt-ampere (VA);

Phase of voltage relative to current, φ: the angle of difference (in degrees) between current and voltage; 

The Power Triangle

The complex power is the vector sum of active and reactive power. The apparent power is the magnitude of the complex power.

  Active power, P

  Reactive power, Q

  Complex power, S

  Apparent power, |S|

  Phase of voltage relative to current, 

These are all denoted in the adjacent diagram (called a Power Triangle).

Power triangle: The components of AC power

The relationship between real power, reactive power and apparent power can be expressed by representing the quantities as vectors. Real power is represented as a horizontal vector and reactive power is represented as a vertical vector. The apparent power vector is the hypotenuse of a right triangle formed by connecting the real and reactive power vectors. This representation is often called the power triangle. Using the Pythagorean Theorem, the relationship among real, reactive and apparent power is:

Real and reactive powers can also be calculated directly from the apparent power, when the current and voltage are both sinusoids with a known phase angle θ between them:

The ratio of real power to apparent power is called power factor and is a number always between 0 and 1. Where the currents and voltages have non-sinusoidal forms, power factor is generalized to include the effects of distortion.