Power (physics) In physics, power(symbol:P) is defined as the amount of energy consumed per unit time. In the MKS system, the unit of power is the joule per second (!s), "nown as the watt (in honor of ames #att, the eighteenth$century de%eloper of the steam engine). &or e'ample, the rate at which a light bulb con%erts electrical energy into heat and light is measured in wattsthe more wattage, the more power, or eui%alently the more electrical energy is used per unit time. *+*-nergy transfer can be used to do wor",so power is also the rate at which this wor" is performed. /he same amount of wor" is done when carrying a load up a flight of stairs whether the person carrying it wal"s or runs, but more power is e'pended during the running because the wor" is done in a shorter amount of time. /he output power of an electric motor is the product of the toruethe motor generates and the angular %elocity of its output shaft. /he power e'pended to mo%e a %ehicle is the product of the traction force of the wheels and the %elocity of the %ehicle. /he integral of power o%er time defines the wor"done. 0ecause this integral depends on the trajectory of the point of app lication of the force and torue, this calculation of wor" is said to be path dependent. Contents • + 1nits • - 2%er age powe r • 3 Mechanica l power o 3.+ Mecha nic al ad%ant age • 4 5ower in opt ics • 6 le ct ric al powe r • 7 5ea" power an d duty cycle • 8 See also • 9 e fe renc es Units 2nsel 2dams photograph of electrical wires of the 0oulder ;am 5ower 1nits, +<4+=+<4- /he dimension of power is energy di%ided by time. /he SIunit of power is the watt(#), which is eual to onejouleper second. >ther units of power includeergsper second
In physics, power (symbol: P ) is defined as the amount of energy consumed per unittime. In the MKS system, the unit of power is the joule per second (!s), "nown as the
watt (in honor of ames #att, the eighteenth$century de%eloper of the steam engine). &or
e'ample, the rate at which a light bulb con%erts electrical energy into heat and light is
measured in wattsthe more wattage, the more power, or eui%alently the moreelectrical energy is used per unit time.*+*-
nergy transfer can be used to do wor" , so power is also the rate at which this wor" is
performed. /he same amount of wor" is done when carrying a load up a flight of stairs
whether the person carrying it wal"s or runs, but more power is e'pended during therunning because the wor" is done in a shorter amount of time. /he output power of an
electric motor is the product of the torue the motor generates and the angular %elocity of
its output shaft. /he power e'pended to mo%e a %ehicle is the product of the tractionforce of the wheels and the %elocity of the %ehicle.
/he integral of power o%er time defines the wor" done. 0ecause this integral depends onthe trajectory of the point of application of the force and torue, this calculation of wor"
is said to be path dependent.
Contents
• + 1nits
• - 2%erage power
• 3 Mechanical power
o 3.+ Mechanical ad%antage
• 4 5ower in optics
• 6 lectrical power• 7 5ea" power and duty cycle
• 8 See also
• 9 eferences
Units
2nsel 2dams photograph of electrical wires of the 0oulder ;am 5ower 1nits, +<4+=
+<4-
/he dimension of power is energy di%ided by time. /he SI unit of power is the watt (#),
which is eual to one joule per second. >ther units of power include ergs per second
and foot$pounds per minute. >ne horsepower is eui%alent to 33,BBB foot$pounds per
minute, or the power reuired to lift 66B pounds by one foot in one second, and iseui%alent to about 847 watts. >ther units include d0m, a relati%e logarithmic measure
with + milliwatt as referenceC (food) calories per hour (often referred to as "ilocalories
per hour)C 0tu per hour (0tu!h)C and tons of refrigeration (+-,BBB 0tu!h).
Average power
2s a simple e'ample, burning a "ilogram of coal releases much more energy than does
detonating a "ilogram of /D/,*3 but because the /D/ reaction releases energy much
more uic"ly, it deli%ers far more power than the coal. If EW is the amount of wor" performed during a period of time of duration Et , the average power P a%g o%er that period
is gi%en by the formula
It is the a%erage amount of wor" done or energy con%erted per unit of time. /he a%erage
power is often simply called FpowerF when the conte't ma"es it clear.
/he instantaneous power is then the limiting %alue of the a%erage power as the timeinter%al Et approaches Gero.
In the case of constant power P , the amount of wor" performed during a period of
duration T is gi%en by:
In the conte't of energy con%ersion, it is more customary to use the symbol E rather thanW .
Mechanical power
5ower in mechanical systems is the combination of forces and mo%ement. In particular,
power is the product of a force on an object and the objectHs %elocity, or the product of a
torue on a shaft and the shaftHs angular %elocity.
Mechanical power is also described as the time deri%ati%e of wor". In mechanics, the
wor" done by a force F on an object that tra%els along a cur%e C is gi%en by the line
integral:
#hich, when the path is a straight line, can also be written as:
where x defines the path C and v is the %elocity along this path. 2pplying the gradienttheorem to the first euation (and remembering that force is the negati%e of the gradient
of the potential energy) yields:
#here 2 and 0 are the beginning and end of the path along which the wor" was done.
/hus the power de%eloped along a path is the time deri%ati%e of this:
In one dimension and with a constant %elocity, this can be simplified to:
In rotational systems, power is the product of the torue τ and angular %elocity ω,
where ω measured in radians per second.
In fluid power systems such as hydraulic actuators, power is gi%en by
where p is pressure in pascals, or D!m- and Q is %olumetric flow rate in m3!s in SI units.
Mechanical advantage
If a mechanical system has no losses then the input power must eual the output power.
/his pro%ides a simple formula for the mechanical ad%antage of the system.
et the input power to a de%ice be a force F A acting on a point that mo%es with %elocity
v A and the output power be a force F B acts on a point that mo%es with %elocity v B. If there
are no losses in the system, then
and the mechanical ad%antage of the system is gi%en by
2 similar relationship is obtained for rotating systems, where T A and ω A are the torue
and angular %elocity of the input and T B and ω B are the torue and angular %elocity of the
output. If there are no losses in the system, then
which yields the mechanical ad%antage
/hese relations are important because they define the ma'imum performance of a de%ice
in terms of %elocity ratios determined by its physical dimensions. See for e'ample gear
ratios.
Power in optics
In optics, or radiometry, the term power sometimes refers to radiant flu', the a%erage rateof energy transport by electromagnetic radiation, measured in watts. In other conte'ts, it
refers to optical power , the ability of a lens or other optical de%ice to focus light. It ismeasured in diopters (in%erse meters), and euals the in%erse of the focal length of the
optical de%ice.
Electrical power
Main article: lectric power
/he instantaneous electrical power P deli%ered to a component is gi%en by
where
P (t ) is the instantaneous power, measured in watts ( joules per second)
V (t ) is the potential difference (or %oltage drop) across the component, measuredin %olts
I (t ) is the current through it, measured in amperes
If the component is a resistor with time$in%ariant %oltage to current ratio, then:
In a train of identical pulses, the instantaneous power is a periodic function of time. /he
ratio of the pulse duration to the period is eual to the ratio of the a%erage power to the pea" power. It is also called the duty cycle (see te't for definitions).
In the case of a periodic signal of period , li"e a train of identical pulses, the
instantaneous power is also a periodic function of period . /he peak power is simply defined by:
.
/he pea" power is not always readily measurable, howe%er, and the measurement of the
a%erage power is more commonly performed by an instrument. If one defines the
energy per pulse as:
then the a%erage power is:
.
>ne may define the pulse length such that so that the ratios
are eual. /hese ratios are called the duty cycle of the pulse train.
