# Joule’s Law of Heating - Electrical Laws

Posted by Circuits Arena on Monday 6 February 2023

Joule’s Law of Heating - Electrical Laws is the artlcle explaining Joule’s Law: Joule's Law states that the heat generated by an electrical current flowing through a conductor is proportional to the p...

## Joule’s Law:

**Joule's Law** states that the heat generated by an electrical current flowing through a conductor is proportional to the product of the current squared and the resistance of the conductor. Mathematically, it is expressed as Q = I^2 * R, where Q is the heat generated, I is the current, and R is the resistance. This law forms the basis for Ohm's Law, which relates the current, voltage, and resistance in an electrical circuit

### Joule’s Law of Heating

The heat which is produced due to the flow of current within an electric wire, is expressed in unit of Joules. Now the mathematical representation and explanation of Joule’s law is given in the following manner.

i.e. H α i²[ When R and t are constant]

The amount of heat produced is proportional to the electrical resistance of the wire when the current in the wire and the time of current flowing are constant.

i.e. H α R[ When i and t are constant]

The heat generated due to the flow of current is proportional to the time of current flowing, when the electrical resistance and the amount of current is constant.

i.e. H α t[ When R and i are constant]

When these three conditions are merged, the resulting formula is like this

i.e. H α i².R.t[ When i,R and t all are variables]

Here, ‘H’ is the heat generated in Joules, ‘i’ is the current flowing through the conducting wire in ampere and ‘t’ is the time in seconds. There are four variables in the equation. When any three of these are known the other one can be calculated.

Here, 'J' is a constant, known as Joule's mechanical equivalent of heat. Mechanical equivalent of heat may be defined as the number of work units which, when completely converted into heat, furnishes one unit of heat.

Obviously the value of J will depend on the choice of units of work and heat.

It has been found that

J = 4.2 joules/cal (1 joule = 107 ergs) = 1400 ft. lbs./CHU = 778 ft. lbs/B Th U

It should be noted that the above values are not very accurate but are good enough for general work.

Now according to Joule's law I2Rt = work done in joules electrically when I ampere of current are maintained through a resistor of R ohms for t second.

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