Joule's Law Example

When an electric current circulates, part of the energy is converted to work, and part of it is converted to heat. This heat is produced because when the electric current passes through the circuit, it must overcome the resistance offered by the conductor. This energy applied to overcome resistance is released in the form of heat.

This phenomenon was observed by the English scientist James Prescott Joule, who also observed the relationships that exist between the time that the current, as well as the intensity of that current, with the heat or with the work generated, and he used different methods of measuring the current and the heat generated. The statement of Joule's Law is as follows:

The heat produced in a conductor by the passage of current is directly proportional to the resistance, to the square of the current and to the time it is connected.

Current, measured in Amps, passes through the conductors; the more resistance to the passage of current a conductor has, the more difficult it will be for electrons to move through the conductor. The energy used to move the flow of electrons is dissipated as heat.

Joule's observations are synthesized in the following formula:

J = I²* R * t
J = It is the measure of the heat produced, which is measured in Joules. One joule equals 0.24 calories.
I = It is the Current. It is measured in amps.
R = Resistance of the conductor or load, measured in Ohms (W)
t = It is the time that the current circulates through the conductor, or also the time that the circuit remains connected. It is measured in seconds.

From this formula, we can calculate any of the other quantities:

I = √ (J) / (R * t)
R = (J) / (I²* t)
t = (J) / (I²* R)

Examples of Joule's Law

Example 1. Calculate the heat produced by a current of 2A on a resistance of 150 W, for 7 seconds.

J =?
I = 2 A
R = 150 W
t = 7 s
J = I²* R * t
J = (2²) (150) (7) = (4) (150) (7) = 4200 J

4200 Joules of heat are produced.

Example 2. Calculate the current that circulates through a circuit, if we know that on a resistance of 150 W, 1500 J.

J = 1500 J
I =?
R = 80 W
t = 3 s
I = √ (J) / (R * t)
I = √ (1500) / (80 * 3) = √ (1500) / (240) = √6.25 = 2.5 A

The Circuit Current is 2.5 Amps.

Example 3. Calculate the resistance of the conductor, if we know that the current is 1.25 A, the time is 4.5 seconds and the heat produced is 1458 J.

J = 1458 J
I = 1.2 A
R =?
t = 4.5 s
R = (J) / (I²* t)
R = (1458) / (1.2²) (4.5) = (1458) / (1.44) (4.5) = (1458) / (6.48) = 225 W

The resistance of the conductor is 225 Ohms.

Example 4. Calculate how long a circuit is connected, if the current is 500 mA, the resistance of the conductor is 125 W and the heat produced is 31.25 J.

J = 31.25 J
I = 500 mA = 0.5 A
R = 125 W
t =?
t = (J) / (I²* R)
t = (31.25) / (0.5²) (125) = (31.25) / (0.25) (125) = (31.25) / (31.25) = 1 s

The circuit is connected for 1 second.