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# power

Contributor(s): Jerome Kelly

Also see current, voltage, resistance,and Ohm's Law.

Electrical power is the rate at which electrical energy is converted to another form, such as motion, heat, or an electromagnetic field. The common symbol for power is the uppercase letter P. The standard unit is the watt,symbolized by W. In utility circuits, the kilowatt (kW) is often specified instead;1 kW = 1000 W.

One watt is the power resulting from an energy dissipation, conversion, or storage process equivalent to one joule per second. When expressed in watts, power is sometimes called wattage. The wattage in a direct current (DC) circuit is equal to the product of the voltage in volts and the current in amperes. This rule also holds for low-frequency alternating current (AC) circuits in which energy is neither stored nor released. At high AC frequencies, in which energy is stored and released (as well as dissipated or converted), the expression for power is more complex.

In a DC circuit, a source of E volts, deliveringIamperes, produces P watts according to the formula:

P = EI

When a current of I amperes passes through a resistance of Rohms, then the power in watts dissipated or converted by that component is given by:

P = I2R

When a potential difference of E volts appears across a component having a resistance of R ohms, then the power in watts dissipated or converted by that component is given by:

P = E2/R

In a DC circuit, power is a scalar (one-dimensional) quantity. In the general AC case, the determination of power requires two dimensions, because AC power is a vector quantity. Assuming there is no reactance (opposition to AC but not to DC) in an AC circuit, the power can be calculated according to the above formulas for DC, using root-mean-square values for the alternating current and voltage. If reactance exists, some power is alternately stored and released by the system. This is called apparent power or reactive power. The resistance dissipates power as heat or converts it to some other tangible form; this is called true power. The vector combination of reactance and resistance is known as impedance.

This was last updated in January 2008

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