Joule’s Law of Heating Effect

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Joule’s Law is a mathematical representation of the rate at which the resistance in a circuit turns electric energy into heat energy. Students might already know the impact of electric heating current. The heat is created due to the collision among electrons in the wire. Students often have questions about the volume of heat generated from current flowing through a wire and also want to learn the parameters and conditions on which the law is based. To answer these questions, Joule derived a formula precisely describing the phenomenon called the Joule’s Law.

The amount of heat that is created inside the electric wire due to the transfer of current is represented in the unit of Joules. Joule’s Law says that during the flow of a current in a conductor, the amount of heat created is directly proportional to the resistance, current, and time in the current that is flowing.

Mathematical Representation of Joule’s Law

When the time of the current flowing and the resistance of the wire is constant in a wire carrying the current, the amount of heat that is produced and the square of the amount of the flowing current in the wire are directly proportional to each other.

H is directly proportional to i2 (where resistance and time are constant)

When a wire is conducting a current, the time of the current and current are constant, and the amount of heat produced and the amount of electrical resistance of the wire are proportional to each other.

H is directly proportional to R (where resistance and time are constant)

When the amount of the electrical resistance and the amount of current are constant in a current conducting wire, the heat thus generated and the time of the flowing current are directly proportional.

H is directly proportional to t (where R and current flowing are constant)

The English physicist James Prescott found that the amount of heat per second generated in a conductor carrying a current is directly proportional to the electrical resistance of the wire and the square of this passing current.

The heat that is created because of the flow of current in an electric wire is represented in Joules. Below is the mathematical expression of Joule’s Law:

Joule’s First Law

As per the Joule’s first law, the relationship between heat that is generated from the flowing electric current through a conductor is expressed as:

Q = I² R T

Where,

Q represents the amount of heat flowing
I represents the electric current
R is the electric resistance in the conductor
T represents time
The amount of heat generated is directly proportional to the electrical resistance of the wire when the current is flowing in the circuit and the flow of current has been constant.
The amount of heat that is generated in a conductor carrying the current, is directly proportional to the square of the flow of current passing through the circuit when both the electrical resistance and the supply of current are constant.
The amount of heat generated due to the flow of current is directly proportional to the time of the current flow when both the resistance and current flow are kept constant.

Solved Examples of Joule’s Law of Heating Effect

Question: Calculate the heat (energy) generated in resistance of 4 Ω when 3 A current flows through it for 2 minutes.

The amount of heat generated by the conductor is given by the formula:

Q = I² R T

By putting the values in the above mathematical equation we get,

Q = 3² × 4 × 60 = 2160 J

Question: A heater having resistance 200 Ω is connected to the main supply of power for 20 minutes. If a 10 A current flows through the conductor of the heater, then calculate the heat generated in the heater.

The amount of heat that is generated by the heater can be calculated as follows:

Q = I² R T

substituting the values in the equation, we get

Q = 10² × 200 × 20 × 60 = 24000000 J or 24 MJ.

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