Joule’s Law of Heating

Contents

💡

Key learnings:

Joule’s Law Definition: Joule’s Law of Heating is defined as the principle that the heat produced in a wire is proportional to the square of the current, the resistance of the wire, and the time the current flows.
Formula of Joule’s Law: The formula H = I²Rt describes the heat produced, where H is heat in joules, I is current in amperes, R is resistance in ohms, and t is time in seconds.
Current and Heat: The amount of heat generated is proportional to the square of the current flowing through the wire.
Resistance Impact: The electrical resistance of the wire is directly proportional to the heat produced when current flows.
Practical Applications: Joule’s Law of Heating explains heat generation in electrical systems, which is crucial for designing safe electrical appliances.

When current flows through an electric circuit, electrons collide with atoms in the wire, causing heat. How much heat is generated depends on several conditions and parameters. James Prescott Joule, an English physicist, created a formula to explain this phenomenon accurately, known as Joule’s law.

What is Joule’s Law of Heating

The heat produced by the current flowing through a wire is measured in joules. Joule’s law is explained mathematically as follows.

The heat produced in a wire is proportional to the square of the current flowing through it, given that the electrical resistance of the wire and the time the current flows 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.
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.

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

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 seconds.