watt
SI coherent derived unit with special name and symbol
Name | Symbol | Derived quantity | Expressed in terms of SI base units | |
watt | W | power, radiant flux |
kg m^{2} s^{‑3} | |
DefinitionThe watt, symbol W, is the SI coherent derived unit of power, or rate of energy transfer. It is the special name for the joule per second, symbol J/s. One watt is equal to the transfer of one joule in one second. |
The watt, symbol W, is named after the Scottish engineer James Watt (1737 – 1819).
Power
Power is the rate at which work is done, or heat is transferred. It is equal to the amount of energy transferred or converted per unit time. Thus:
Using SI coherent units:
- power, P, is measured in watts, symbol W,
- energy, E, is measured in joules, symbol J,
- time, T, is measured in seconds, symbol s.
Electrical power
Joule heating, also known as resistive heating, is the process of heat dissipation by which the passage of an electric current through a conductor increases the internal energy of the conductor, converting thermodynamic work into heat. Joule’s first law states that the rate of heat production, or resistive heating power P, of a conductor is directly proportional to the product of the square of the current I and its electrical resistance R.
Using SI coherent units, the proportionality constant is 1. Thus:
where
- power, P, is measured in watts, symbol W,
- current, I, is measured in amperes, symbol A,
- resistance, R, is measured in ohms, symbol Ω.
Ohm’s law states that the current, I, through a conductor between two points is directly proportional to the voltage, V, across the two points. The current is also indirectly proportional to the resistance of the conductor.
Using SI coherent units, the proportionality constant is 1. Thus:
where:
- current, I, is measured in amperes, symbol A,
- voltage, V, is measured in volts, symbol V,
- resistance, R, is measured in ohms, symbol Ω.
Substituting in the equation for Joule’s first law gives a method for evaluating electrical power in terms of current and voltage:
Using SI coherent units,
Radiant power
Power is related to intensity at a radius, r; the power emitted by a source can be written as: