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In physics, power (symbol: P) is the amount of work W done per unit of time t. This can be modeled as an energy flow, equivalent to the rate of change of the energy in a system, or the time rate of doing work, as defined by
where
The units of power are therefore energy divided by time (e.g. foot-pounds per minute, joules per second). The SI unit of power is the watt, which is equal to one joule per second.
Non-SI units of power include horsepower (HP), Pferdestärke (PS) and the cheval vapeur (CV). 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 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. Professional cyclists have been measured at 2000 W output for short periods of time.
The instantaneous electrical power P delivered to a component is defined as:
where V is the potential difference (or voltage drop) across the component and I is the current flowing through it. If the component is a resistor with resistance R, then:
or
The average power consumed by a two-terminal electrical device is a function of the root mean square values of the sinusoidal voltage across the terminals and the sinusoidal current passing through the device. That is,
where I is the root mean square value of the sinusoidal alternating current (AC) and U is the root mean square value of the sinusoidal alternating voltage. φ is the phase angle between the voltage and the current sine functions. If I is in amperes and U is in volts then P is in watts.
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 reactive (VAR) and does not include the <math>\cos\phi<math> term due to the current and voltage being out of phase. For simple domestic appliances, 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.
The efficient transfer of electrical power is governed by the maximum power theorem, which states that for the transfer of maximum power from a source with a fixed internal resistance to a load, the resistance of the load must be equal to that of the source.
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