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power, in mathematics
power,in mathematics: see exponentexponent,
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 x2 and xn, the number 2 and the letter n
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power, in physics
power,in physics, time rate of doing workwork,
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 energyenergy,
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 horsepowerhorsepower,
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 wattwatt
[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 joulejoule
, 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, electricpower, 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 ofenergy, 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.
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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.
powerThe rate at which energy is expended by a source or work is done. It is measured in watts, i.e. in joules per second.
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.
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 a2, is also known as the square of a, or a squared. The third power of a, written a3, is known as the cube of a, or a cubed. It should be noted that a2 is the area of a square with sides of length a and that a3 is the volume of a cube with edges of length a.
The fundamental operations on powers are given by the following formulas:
|an ÷ am||= an–m|
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 a0 = 1 when a ≠ 0. Negative exponents are also possible: a–n = 1/an. For fractional exponents, we have (seeBINOMIAL EQUATION and EXTRACTION OF A ROOT). In the case of an irrational exponent α,
where rn 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(1) Electricity. See current, volt, watt, AC and DC.
(2) The capability of a computer system. See computer power and throughput.
(3) (POWER) (Performance Optimization With Enhanced RISC) A family of RISC-based CPUs from IBM. See POWER CPU.