# power

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## power, in mathematics

## power,

in mathematics: see exponent**exponent,**

in mathematics, a number, letter, or algebraic expression written above and to the right of another number, letter, or expression called the base. In the expressions

*x*

^{2}and

*x*

^{n}, the number 2 and the letter

*n*

**.....**Click the link for more information. .

## power, in physics

## power,

in physics, time rate of doing work**work,**

in physics and mechanics, transfer of energy by a force acting to displace a body. Work is equal to the product of the force and the distance through which it produces movement.

**.....**Click the link for more information. or of producing or expending energy

**energy,**

in physics, the ability or capacity to do work or to produce change. Forms of energy include heat, light, sound, electricity, and chemical energy. Energy and work are measured in the same units—foot-pounds, joules, ergs, or some other, depending on the system of

**.....**Click the link for more information. . The unit of power based on the English units of measurement is the horsepower

**horsepower,**

unit of power in the English system of units. It is equal to 33,000 foot-pounds per minute or 550 foot-pounds per second or approximately 746 watts. The term

*horsepower*

**.....**Click the link for more information. , devised for describing mechanical power by James Watt, who estimated that a horse can do 550 ft-lb of work per sec; a foot-pound is the work done when a weight (force) of 1 lb is moved through a distance of 1 ft. The unit of power in the metric system is the watt

**watt**

[for James Watt], abbr. W, unit of power, or work done per unit time, equal to 1 joule per second. It is used as a measure of electrical and mechanical power. One watt is the amount of power that is delivered to a component of an electric circuit when a current of 1 ampere

**.....**Click the link for more information. , named in honor of James Watt and equal to 1 joule

**joule**

, abbr. J, unit of work or energy in the mks system of units, which is based on the metric system; it is the work done or energy expended by a force of 1 newton acting through a distance of 1 meter. The joule is named for James P. Joule.

**.....**Click the link for more information. per sec; the watt is used for measuring electric power in most countries, even those still using English units for other quantities. In common usage, the terms

*power*and

*energy*have become synonymous; for example, electrical energy is usually referred to as electric power (see power, electric

**power, electric,**

energy dissipated in an electrical or electronic circuit or device per unit of time. The electrical energy supplied by a current to an appliance enables it to do work or provide some other form of energy such as light or heat.

**.....**Click the link for more information. ). See also energy, sources of

**energy, sources of,**

origins of the power used for transportation, for heat and light in dwelling and working areas, and for the manufacture of goods of all kinds, among other applications.

**.....**Click the link for more information. .

## Power

The time rate of doing work. Like work, power is a scalar quantity, that is, a quantity which has magnitude but no direction. Some units often used for the measurement of power are the watt (1 joule of work per second) and the horsepower (550 foot-pounds of work per second). *See* Work

Power is a concept which can be used to describe the operation of any system or device in which a flow of energy occurs. In many problems of apparatus design, the power, rather than the total work to be done, determines the size of the component used. Any device can do a large amount of work by performing for a long time at a low rate of power, that is, by doing work slowly. However, if a large amount of work must be done rapidly, a high-power device is needed. High-power machines are usually larger, more complicated, and more expensive than equipment which need operate only at low power. A motor which must lift a certain weight will have to be larger and more powerful if it lifts the weight rapidly than if it raises it slowly. An electrical resistor must be large in size if it is to convert electrical energy into heat at a high rate without being damaged.

## power

The rate at which energy is expended by a source or work is done. It is measured in watts, i.e. in joules per second.## Power

a physical quantity measured as the ratio of work to the time interval during which the work is done. If the work is done at a uniform rate, power is defined by the formula *N* = *A/t*, where *A* is work done during the time *t*. In the general case *N* = *dA/dt*, where *dA* is the elementary work done during an elementary time interval *dt* (usually 1 sec). Power is measured in watts and sometimes (for engineering applications) in horse power.

## Power

Originally, the term “power” in arithmetic and algebra meant the product of a specified number of equal factors. The product of *n* equal factors *a* is denoted by *a*”. Here, *a* is called the base, and *n* is called the exponent. In English, the term “power” is sometimes used in the sense of “exponent.”

The second power of a, written *a*^{2}, is also known as the square of *a*, or *a* squared. The third power of *a*, written a^{3}, is known as the cube of a, or a cubed. It should be noted that *a ^{2}* is the area of a square with sides of length

*a*and that a

^{3}is the volume of a cube with edges of length

*a*.

The fundamental operations on powers are given by the following formulas:

a^{n}^{m} | = a^{n+m} |

a ÷ ^{n}a^{m} | = a^{n–m} |

(a)^{n}^{m} | = a^{nm} |

The concept of power came to be extended to cases where the exponent is not a positive integer. Thus, if the exponent is zero, we have *a*^{0} = 1 when a ≠ 0. Negative exponents are also possible: *a ^{–n}* = 1/

*a*. For fractional exponents, we have (

^{n}*see*BINOMIAL EQUATION and EXTRACTION OF A ROOT). In the case of an irrational exponent α,

where *r _{n}* is an arbitrary sequence of rational numbers that approaches a. The rules of operations given above also hold for powers where the exponent is not a positive integer.

The theory of analytic functions deals with powers that have imaginary bases and exponents.

## power

[′pau̇·ər]*x*-

*a*)

^{2}+ (

*y*-

*b*)

^{2}-

*r*

^{2}, where

*x*and

*y*are the coordinates of the point,

*a*and

*b*are the coordinates of the center of the circle, and

*r*is the radius of the circle.

*x*-

*a*)

^{2}+ (

*y*-

*b*)

^{2}+ (

*z*-

*c*)

^{2}-

*r*

^{2}, where

*x*,

*y*, and

*z*are the coordinates of the point;

*a*,

*b*, and

*c*are the coordinates of the center of the sphere; and

*r*is the radius of the sphere.

## power

## Power

Force, The*Star Wars*and sequels]

## power

**1.**control or dominion or a position of control, dominion, or authority

**2.**a state or other political entity with political, industrial, or military strength

**3.**

**a.**legal authority to act, esp in a specified capacity, for another

**b.**the document conferring such authority

**5.**

*Physics*

*Engineering*a measure of the rate of doing work expressed as the work done per unit time. It is measured in watts, horsepower, etc.

**6.**

**a.**the rate at which electrical energy is fed into or taken from a device or system. It is expressed, in a direct-current circuit, as the product of current and voltage and, in an alternating-current circuit, as the product of the effective values of the current and voltage and the cosine of the phase angle between them. It is measured in watts

**b.**(

*as modifier*):

*a power amplifier*

**7.**

**a.**mechanical energy as opposed to manual labour

**b.**(

*as modifier*):

*a power mower*

**8.**

**a.**a measure of the ability of a lens or optical system to magnify an object, equal to the reciprocal of the focal length. It is measured in dioptres

**b.**another word for magnification

**9.**the sixth of the nine orders into which the angels are traditionally divided in medieval angelology

## POWER

## power

**(1)**Electricity. See current, volt, watt, AC and DC.

**(2)**The capability of a computer system. See computer power and throughput.

**(3)**(POWER) (

**P**erformance

**O**ptimization

**W**ith

**E**nhanced

**R**ISC) A family of RISC-based CPUs from IBM. See POWER CPU.