# watt

##### SI coherent derived unit with special name and symbol
Name Symbol Derived quantity Expressed in terms of SI base units
watt W power,
kg m2 s‑3

### Definition

The 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:

$P = \dfrac{E}{T}$

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.

$1 \ \text{W} = 1 \ \text{J s}^{-1}$

### 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.

$P \propto I^2 R$

Using SI coherent units, the proportionality constant is 1. Thus:

$P = I^2 R$

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.

$1 \ \text{W} \mspace{4mu} = 1 \ \text{A}^2 \ \Omega$

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.

$I \propto \dfrac{V}{R}$

Using SI coherent units, the proportionality constant is 1. Thus:

$I = \dfrac{V}{R}\\ \\ \\R = \dfrac{V}{I}$

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:

$P = I^2 R\\ \\ P = I^2 \left ( \dfrac{V}{I} \right )\\ \\ \\P = I V$

Using SI coherent units,

$1 \ \text{W} \mspace{4mu} = 1 \ \text{A V}$

$P(r)=I(4 \pi r^2)$