Joule law.

Joule’s law,  in electricity, mathematical description of the rate at which resistance in a circuit converts electric energy into heat energy. The English physicist James Prescott Joule discovered in 1840 that the amount of heat per second that develops in a wire carrying a current is proportional to the electrical resistance of the wire and the square of the current. He determined that the heat evolved per second is equivalent to the electric power absorbed, or the power loss.

A quantitative form of Joule’s law is that the heat evolved per second, or the electric power loss, P,equals the current I squared times the resistance R, or P = I2R. The power P has units of watts, or joules per second, when the current is expressed in amperes and the resistance in ohms.

Power of electric current.

Electric power, like mechanical power, is the rate of doing work, measured in watts, and represented by the letter P. The term wattage is used colloquially to mean "electric power in watts." The electric power in watts produced by an electric current I consisting of a charge ofQ coulombs every t seconds passing through an electric potential (voltage) difference of V is

where

Q is electric charge in coulombs

t is time in seconds

I is electric current in amperes

V is electric potential or voltage in volts

Ohm's law for non-uniform segments of electric circuit. Ohm's law for closed circuit.

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance,[1] one arrives at the usual mathematical equation that describes this relationship:[2]

where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units ofvolts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.