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Encyclopedia > Power (physics)

In physics, power (symbol: P) is the rate at which work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time. As a rate of change of work done or the energy of a subsystem, power is: A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... In physics, mechanical work is the amount of energy transferred by a force. ...

where

P is power
W is work
t is time.

The average power (often simply called "power" when the context makes it clear) is the average amount of work done or energy transferred per unit time. The instantaneous power is then the limiting value of the average power as the time interval Δt approaches zero. In physics, mechanical work is the amount of energy transferred by a force. ... Look up time in Wiktionary, the free dictionary. ...

When the rate of energy transfer or work is constant, all of this can be simplified to

,

where W and E are, respectively, the work done or energy transferred in time t (usually measured in seconds).

## Mechanical power

In mechanics, the work done on an object is related to the forces acting on it by For other uses, see Mechanic (disambiguation). ... In physics, mechanical work is the amount of energy transferred by a force. ...

where

F is force
Δs is the displacement of the object.

This is often summarized by saying that work is equal to the force acting on an object times its displacement (how far the object moves while the force acts on it). Note that only motion that is along the same axis as the force "counts", however; motion in the same direction as force gives positive work, and motion in the opposite direction gives negative work, while motion perpendicular to the force yields zero work. For other uses, see Force (disambiguation). ... In Newtonian mechanics, displacement is the vector that specifies the position of a point or a particle in reference to an origin or to a previous position. ...

.

The average power is then

.

This formula is important in characterizing engines—the power put out by an engine is equal to the force it exerts times its velocity. For other uses, see Engine (disambiguation). ...

In rotational systems, power is related to the torque (τ) and angular velocity (ω): For other senses of this word, see torque (disambiguation). ... Angular frequency is a measure of how fast an object is rotating In physics (specifically mechanics and electrical engineering), angular frequency &#969; (also called angular speed) is a scalar measure of rotation rate. ...

.

The average power is therefore

.

## Electrical power

Main article: Electric power For delivered electrical power, see Electrical power industry. ...

### Instantaneous electrical power

The instantaneous electrical power P delivered to a component is given by

where

P(t) is the instantaneous power, measured in watts (joules per second)
V(t) is the potential difference (or voltage drop) across the component, measured in volts
I(t) is the current flowing through it, measured in amperes

If the component is a resistor, then: For other uses, see Watt (disambiguation). ... The joule (IPA: or ) (symbol: J) is the SI unit of energy. ... This article is about the unit of time. ... Potential difference is a quantity in physics related to the amount of energy that would be required to move an object from one place to another against various types of force. ... Josephson junction array chip developed by NIST as a standard volt. ... In electricity, current refers to electric current, which is the flow of electric charge. ... For other uses, see Ampere (disambiguation). ... Resistor symbols (non-European) Resistor symbols (Europe, IEC) Axial-lead resistors on tape. ...

where

is the resistance, measured in ohms. Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... The ohm (symbol: Î©) is the SI unit of electric resistance. ...

If the component is reactive (e.g. a capacitor or an inductor), then the instantaneous power is negative when the component is giving stored energy back to its environment, i.e., when the current and voltage are of opposite signs. See Capacitor (component) for a discussion of specific types. ... An inductor is a passive electrical device employed in electrical circuits for its property of inductance. ...

### Average electrical power for sinusoidal voltages

The average power consumed by a sinusoidally-driven linear two-terminal electrical device is a function of the root mean square (rms) values of the voltage across the terminals and the current passing through the device, and of the phase angle between the voltage and current sinusoids. That is, In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... Electric current is the flow (movement) of electric charge. ...

where

P is the average power, measured in watts
I is the root mean square value of the sinusoidal alternating current (AC), measured in amperes
V is the root mean square value of the sinusoidal alternating voltage, measured in volts
φ is the phase angle between the voltage and the current sine functions.

The amplitudes of sinusoidal voltages and currents, such as those used almost universally in mains electrical supplies, are normally specified in terms of root mean square values. This makes the above calculation a simple matter of multiplying the two stated numbers together. For other uses, see Watt (disambiguation). ... For other uses, see Ampere (disambiguation). ... Josephson junction array chip developed by NIST as a standard volt. ... The phase angle of a point on a periodic wave is the distance between the point and a specified reference point, expressed using an angular measure. ...

This figure can also be called the effective power, as compared to the larger apparent power which is expressed in volt-amperes (VA) and does not include the cos φ term due to the current and voltage being out of phase. For simple domestic appliances or a purely resistive network, the cos φ term (called the power factor) can often be assumed to be unity, and can therefore be omitted from the equation. In this case, the effective and apparent power are assumed to be equal. See Real power for detailed explanation In alternating current power transmission and distribution, effective power (also true power or real power) is the actual power delivered to a system. ... Usually hidden to the unaided eye, the 60Hz blinking of (non-incandescent) lighting powered by AC mains is revealed in this motion-blurred long exposure of city lights. ... In the United States the term (Volt-amps) in Electrical terms, means watts. ... The power factor of an AC electric power system is defined as the ratio of the real power to the apparent power, and is a number between 0 and 1. ...

### Average electrical power for AC

Where v(t) and i(t) are, respectively, the instantaneous voltage and current as functions of time.

For purely resistive devices, the average power is equal to the product of the rms voltage and rms current, even if the waveforms are not sinusoidal. The formula works for any waveform, periodic or otherwise, that has a mean square; that is why the rms formulation is so useful.

For devices more complex than a resistor, the average effective power can still be expressed in general as a power factor times the product of rms voltage and rms current, but the power factor is no longer as simple as the cosine of a phase angle if the drive is non-sinusoidal or the device is not linear.

### Peak power and duty cycle In a train of identical pulses, the instantaneous power is a periodic function of time. The ratio of the pulse duration to the period is equal to the ratio of the average power to the peak power. It is also called the duty cycle (see text for definitions).

In the case of a periodic signal s(t) of period T, like a train of identical pulses, the instantaneous power p(t) = | s(t) | 2 is also a periodic function of period T. The peak power is simply defined by: Image File history File links Download high resolution version (1200x900, 12 KB)Plot of the instantaneous power p(t) of periodic signal of period T. The peak power and average power are also shown. ... Image File history File links Download high resolution version (1200x900, 12 KB)Plot of the instantaneous power p(t) of periodic signal of period T. The peak power and average power are also shown. ...

P0 = max(p(t)).

The peak power is not always readily measurable, however, and the measurement of the average power Pavg is more commonly performed by an instrument. If one defines the energy per pulse as:

then the average power is:

.

One may define the pulse length τ such that P0τ = εpulse so that the ratios

are equal. These ratios are called the duty cycle of the pulse train.

## Power in optics

Main article: Optical power

In thermodynamics, motive power is an agency, as water or steam, used to impart motion. ... This page lists examples of the power in watts produced by various different sources of energy. ... Pulsed power is the term used to describe the science and technology of accumulating energy over a relatively long period of time and releasing it very quickly thus increasing the instantaneous power. ... In physics, intensity is a measure of the time-averaged energy flux. ... Results from FactBites:

 Power (physics) - Wikipedia, the free encyclopedia (973 words) The power consumption of a human is on average roughly 100 watts, ranging from 85 W during sleep to 800 W or more while playing a strenuous sport. The average power consumed by a sinusoidally-driven linear two-terminal electrical device is a function of the root mean square (rms) values of the voltage across the terminals and the current passing through the device, and of the phase angle between the voltage and current sinusoids. The ratio of the pulse duration to the period is equal to the ratio of the average power to the peak power.
 Power - Wikipedia, the free encyclopedia (407 words) Power (physics) is the amount of work done or energy transferred per unit of time. In optics, the optical power of a lens is the inverse of its focal length. Reserve power, a power that may be exercised by the head of state of a country in certain exceptional circumstances.
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