Power (physics) - Citizendia

For other uses, see Power (disambiguation).

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. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Physics, mechanical work is the amount of Energy transferred by a Force. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός As a rate of change of work done or the energy of a subsystem, power is:

$P = \frac{W}{t}\,$

where P is power, W is work and t is time. In Physics, mechanical work is the amount of Energy transferred by a Force. For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of

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.

$P = \lim_{\Delta t\rightarrow 0} \frac{\Delta W}{\Delta t} = \lim_{\Delta t\rightarrow 0} P_\mathrm{avg}\,$

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

$P = \frac{W}{t} = \frac{E}{t}$ ,

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

1 Units
2 Mechanical power
3 Electrical power
4 Power in optics
5 See also
6 References
7 External links

Units

The units of power are units of energy divided by time. The SI unit of power is the watt (W), which is equal to one joule per second. The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second. Non-SI units of power include ergs per second (erg/s), horsepower (hp), metric horsepower (Pferdestärke (PS) or cheval vapeur (CV)), and foot-pounds per minute. The foot-pound force, or simply foot-pound (symbol ft·lbf or ft·lb) is a unit of work or Energy (a scalar One unit of horsepower is equivalent to 33,000 foot-pounds per minute, or the power required to lift 550 pounds one foot in one second, and is equivalent to about 746 watts. The pound or pound-mass (abbreviation lb, lbm, or sometimes in the United States #) is a unit of Mass Other units include dBm, a logarithmic measure with 1 milliwatt as reference; (food) calories per hour (often referred to as kilocalories per hour); Btu per hour (Btu/h); and tons of refrigeration (12,000 Btu/h). For other uses see DBM (disambiguation dbm was the first of a family of simple Database engines originally written by Ken This article is about the unit of energy For its use in Nutrition and Food labelling regulations, see the article on Food energy. This article is about the unit of energy For its use in Nutrition and Food labelling regulations, see the article on Food energy. An air conditioner is an Appliance, System, or mechanism designed to extract Heat from an area via a Refrigeration cycle

Mechanical power

In mechanics, the work done on an object is related to the forces acting on it by

$W = F \cdot \Delta s \,$

where

F is force

Δs is the displacement of the object. Mechanics ( Greek) is the branch of Physics concerned with the behaviour of physical bodies when subjected to Forces or displacements In Physics, mechanical work is the amount of Energy transferred by a Force. In Physics, a force is whatever can cause an object with Mass to Accelerate. In Physics, displacement is the vector that specifies the position of a point or a particle in reference to a previous position or to the origin of the chosen

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.

Differentiating by time gives that the instantaneous power is equal to the force times the object's velocity v(t):

$P(t) = \mathbf{F}(t) \cdot \mathbf{v}(t) \,$ . In Physics, velocity is defined as the rate of change of Position.

The average power is then

$P_\mathrm{avg} = \frac{1}{\Delta t}\int\mathbf{F} \cdot \mathbf{v}\;\mathrm{d}t \,$ .

This formula is important in characterizing engines—the power put out by an engine is equal to the force it exerts times its velocity. An engine is a mechanical device that produces some form of output from a given input

In rotational systems, power is related to the torque (τ) and angular velocity (ω):

$P(t) = \mathbf{\tau}(t) \cdot \mathbf{\omega}(t) \,$ . A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about Do not confuse with Angular velocity In Physics (specifically Mechanics and Electrical engineering) angular frequency

The average power is therefore

$P_\mathrm{avg}=\frac{1}{\Delta t}\int\mathbf{\tau} \cdot \mathbf{\omega}\;\mathrm{d}t \,$ .

Electrical power

Main article: Electric power

Instantaneous electrical power

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

$P(t) = I(t) \cdot V(t) \,$

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:

$P=I^2 \cdot R = \frac{V^2}{R} \,$

where

$R = V/I \,$

is the resistance, measured in ohms. Electric power is defined as the rate at which Electrical energy is transferred by an Electric circuit. The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second. The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units In Physics, the potential difference or pd between two points is the difference of the points' Scalar potential, equivalent to the line integral The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. The ampere, in practice often shortened to amp, (symbol A is a unit of Electric current, or amount of Electric charge per second |- align = "center"| |width = "25"| | |- align = "center"| || Potentiometer |- align = "center"| | | |- align = "center"| Resistor| | Electrical resistance is a ratio of the degree to which an object opposes an Electric current through it measured in Ohms Its reciprocal quantity is The ohm (symbol Ω) is the SI unit of Electrical impedance or in the Direct current case Electrical 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. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors An inductor is a passive electrical component designed to provide Inductance in a circuit e. , when the current and voltage are of opposite signs.

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. In Mathematics, the root mean square (abbreviated RMS or rms) also known as the quadratic mean, is a statistical measure of the Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. That is,

$P = I \cdot V \cdot \cos \varphi \,$

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 watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second. The ampere, in practice often shortened to amp, (symbol A is a unit of Electric current, or amount of Electric charge per second The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. In the context of vectors and phasors, the term phase angle refers to the angular component of the Polar coordinate representation

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.

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. An alternating current ( AC) is an Electric current whose direction reverses cyclically as opposed to Direct current, whose direction remains constant This article deals with power in AC systems See Mains electricity for information on utility supplied AC power A volt-ampere in electrical terms means the amount of Apparent power in an Alternating current circuit equal to a current of one Ampere at an 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. 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 In this case, the effective and apparent power are assumed to be equal.

Average electrical power for AC

$P = {1 \over T} \int_{0}^{T} i(t) \cdot v(t)\, dt \,$

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:

P 0 = max(p (t))

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

$\epsilon_\mathrm{pulse} = \int_{0}^{T}p(t) \mathrm{d}t \,$

then the average power is:

$P_\mathrm{avg} = \frac{1}{T} \int_{0}^{T}p(t) \mathrm{d}t = \frac{\epsilon_\mathrm{pulse}}{T} \,$ .

One may define the pulse length $τ$ such that $P 0 τ = ε pulse$ so that the ratios

$\frac{P_\mathrm{avg}}{P_0} = \frac{\tau}{T} \,$

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

Power in optics

Main article: Optical power

In optics, or radiometry, the term power sometimes refers to radiant flux, the average rate of energy transport by electromagnetic radiation, measured in watts. Optical power ( dioptric power or refractive power) is the degree to which a lens or Mirror converges or diverges light In Optics, radiometry is the field that studies the Measurement of Electromagnetic radiation, including Visible light. In Radiometry, radiant flux or radiant power is the measure of the total power of Electromagnetic radiation (including Infrared, The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second. The term "power" is also, however, used to express the ability of a lens or other optical device to focus light. A lens is an optical device with perfect or approximate Axial symmetry which transmits and refracts Light, converging or diverging In Geometrical optics, a focus, also called an image point, is the point where Light rays originating from a point on the object converge. It is measured in dioptres (inverse metres), and equals the inverse of the focal length of the optical device. A dioptre, or diopter, is a Unit of measurement of the Optical power of a lens or curved Mirror, which is equal to the reciprocal The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The focal length of an optical system is a measure of how strongly it converges (focuses or diverges (diffuses Light.

References

External links

Unit Converter Tool also for Power

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Contents

Units

Mechanical power

Electrical power

Instantaneous electrical power

Average electrical power for sinusoidal voltages

Average electrical power for AC

Peak power and duty cycle

Power in optics

See also

References

External links