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Home / Physics / Joules Law

Joule’s Law: Know Statement, Formula, Derivation, Applications with Solved Examples

Last Updated on Jun 24, 2025
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An English physicist James Prescott Joule in 1840 discovered that the heat developed in an electrical circuit is directly proportional to the electrical resistance of the wire/ This is known as Joule’s law or Joule's law of heating. He also proposed that heat is a form of energy irrespective of the material used in the heating process.

In this article, we will understand Joule’s law of heating, its different applications and solved examples.

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Joule’s Law of Heating

Joule’s law establishes the relationship between the amount of heat flowing in an electric circuit and electrical energy.

Joule's Law- The heat produced in a conductor is directly proportional to the square of the current passing through it, the resistance of the conductor, and the time for which the current flows

The mathematical formula of Joule’s law is given by,

Where H = heat produced by the conductor.

I = electric current flowing through the conductor.

R = electrical resistance.

t = time elapsed.

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Derivation of Joule’s Law of Heating

The amount of work done in an electrical circuit is

W = Q x V – equation A

Q = It – equation 1

And V =IR – equation 2 (From Ohm’s law)

Substituting equation 1 and 2 in equation A ,

W = I x t x I x R

This work done is converted into heat energy and the equation becomes,

.

Electrical Power

Electrical power refers to the rate at which electrical energy is transferred or used in an electrical circuit. It is also referred to as work done in an electrical circuit.


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Application of Joule’s Law

The following are the applications of Joule’s law of heating

  • Electric Heaters: Electric heaters, including space heaters, water heaters, and heating elements in appliances, rely on Joule's Law to produce heat. Electric current flows through a resistive element, such as a coil or wire, which heats up and radiates warmth into the surrounding space or medium.
  • Incandescent Light Bulbs: Traditional incandescent light bulbs work based on Joule's Law. The electric current passes through a filament, which becomes so hot that it emits visible light along with heat. However, incandescent bulbs are inefficient because much of the energy is wasted as heat rather than light.
  • Electric Kettles: Electric kettles heat water by passing an electric current through a heating element, following Joule's Law. The resistance of the element causes it to become hot, boiling the water.
  • Toasters: Toasters use electrical resistance to generate heat that toasts bread slices. The heating elements in toasters are designed to follow Joule's Law to achieve the desired toasting effect.

Solved Examples
on Joule’s Law

Example 1. Find the heat energy produced in an electrical circuit with resistance 20Ω and current 10A flowing through it in time = 5 minutes.

Solution 1. Given data,

Resistance (R) = 20Ω

Current (I) = 10A

Time (t) = 5 minutes = 300 seconds

.

H = 10 x 10 x 20 x 300

H = 600000 J

H = 600 KJ.

The total heat energy produced is 600 KJ.

Example 2. If 4500J heat is produced in 10 seconds with 9Ω resistance, find the potential difference in the circuit.

Solution 2. Given data,

Heat produced (H) = 4500J.

Time (t) = 10 seconds.

Resistance (R) = 9Ω.

.

I = 7.07 A

According to Ohm’s law,

V = IR

V = 7.07 x 9

Potential difference = 6.708 V

The potential difference in the circuit is 6.708V.

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Joule's Law FAQs

The heat developed in an electrical circuit is directly proportional to the electrical resistance of the wire. This is known as Joule’s law.

Joule’s law is used to calculate the heat energy generated in an electrical circuit.

Yes, Joule’s law does involve the conservation of energy.

is the formula for Joule’s law.

It is used in domestic heating appliances, microwaves and ovens, electrical heating tops, etc.
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