Relation To Ohm's Law
In the context of resistive circuits and in light of conservation of energy and electrical potential, Joule's first law and Ohm's law are equivalent and derivable from each other (as explained by James Clerk Maxwell in 1881, by Mascart in 1883, and by Oliver Heaviside in 1894), though they were discovered independently and experimentally, before the notions of conservation of energy and electrical potential were well developed.
Joule's first law states that the rate of heat dissipation in a resistive conductor is proportional to the square of the current through it and to its resistance. That is, the power dissipated in a resistor, in terms of the current through it and its resistance, is:
Joule arrived at this result experimentally in 1841, using a calorimeter to measure heat, and a galvanometer to measure current, with a variety of resistive circuits.
The law applies to any circuit that obeys Ohm's law, that is, that conducts a current proportional to the voltage across it, or equivalently, that can be characterized by a resistance. Ohm's law states that for a voltage V across a circuit of resistance R the current will be:
By substituting this formula for current into one or both factors of current in Joule's law, the power dissipated can be written in the equivalent forms:
The relation is actually more generally applicable than either Joule's law or Ohm's law, as it represents the instantaneous power being applied to a circuit with voltage V across it and current I into it, whether the circuit is resistive or not. In combination with either Ohm's law or Joule's law, it may be used to derive the other.
Since the power dissipated by a resistor is the amount of energy used (electrical work applied) per unit time, the total energy consumed and dissipated in time t is:
Read more about this topic: Joule's Laws
Famous quotes containing the words relation to, relation and/or law:
“Any relation to the land, the habit of tilling it, or mining it, or even hunting on it, generates the feeling of patriotism. He who keeps shop on it, or he who merely uses it as a support to his desk and ledger, or to his manufactory, values it less.”
—Ralph Waldo Emerson (1803–1882)
“Much poetry seems to be aware of its situation in time and of its relation to the metronome, the clock, and the calendar. ... The season or month is there to be felt; the day is there to be seized. Poems beginning “When” are much more numerous than those beginning “Where” of “If.” As the meter is running, the recurrent message tapped out by the passing of measured time is mortality.”
—William Harmon (b. 1938)
““Teacher, which commandment in the law is the greatest?” He said to him, “You shall love the Lord your God with all your heart, and with all your soul, and with all your mind.’ This is the greatest and first commandment. And a second is like it: You shall love your neighbor as yourself.’ On these two commandments hang all the law and the prophets.””
—Bible: New Testament, Matthew 22:36-40.