Electricity is an essential part of our daily life, and understanding how it interacts with materials is crucial. One fundamental principle that explains how electrical energy transforms into heat is Joule’s Law of Heating.
This law is vital in electrical engineering, physics, and everyday electrical appliances.
What is Joule’s Law of Heating?
Joule’s Law of Heating, also known as Joule’s heating law or simply Joule law, states that the heat produced in a conductor by an electric current is directly proportional to the square of the current, the resistance of the conductor, and the time for which the current flows.
In simpler terms, the more the current and resistance, and the longer the current flows, the more heat is generated.
Mathematically, it is expressed as:
H=I2Rt
Where:
- H = Heat produced (in joules)
- I = Current flowing through the conductor (in amperes)
- R = Resistance of the conductor (in ohms)
- t = Time for which current flows (in seconds)
Derivation of Joule’s Law of Heating Formula
Let’s derive Joule’s law step by step:
- Electric Work Done:
The work done by a current I through a conductor of resistance R over time t is: W = V × I × t, where V is the voltage across the conductor. - Ohm’s Law Relation:
Using Ohm’s law, V=I⋅R, the work done becomes:
W = V × I × t=(I × R) × I × t=I2Rt - Heat Produced:
This work done is converted entirely into heat energy in the conductor. Therefore: H=I2Rt Joules
This derivation clearly explains why the heat produced depends on current, resistance, and time.
Solved Example on Joule’s Heating Law
A current of 5 A flows through a resistor of 10 Ω for 2 minutes. Calculate the heat produced in the resistor.
Solution:
Given:
- Current, I=5 A
- Resistance, R=10 Ω
- Time, t=2 minutes=120 s
Using Joule’s law,
H=I2Rt
H=(5)2 x 10 x120=30,000 J
The heat produced is 30,000 joules.
Joule’s Law of Heating in Calories
The standard formula of Joule’s Law is:
H=I2Rt
Since 1 calorie = 4.186 joules,
The heat produced in calories can be calculated as:
Hcal=I2Rt / 4.186
Where:
- Hcal= Heat produced in calories
- I = Current in amperes
- R = Resistance in ohms
- t = Time in seconds
Example: Joules Law in Calories
Problem: A current of 2 A flows through a resistor of 5 Ω for 3 minutes. Find the heat produced in calories.
Given:
- Current, I=2 A
- Resistance, R=5 Ω
- Time, t=3 minutes
Solution:
- Convert time to seconds: t=3×60=180 s
- Using Joule’s law in joules:
H=I2Rt=(2)2 x 5 x 180=3600 J - Convert joules to calories:
Hcal=3600/4.186=860 cal
The heat produced is approximately 860 calories.
Practical Applications of Joule’s Law of Heating
Joule’s law of heating is not just theoretical—it has many practical applications:
- Electric Heaters:
Devices like room heaters, geysers, and irons use the principle of Joule heating law to convert electrical energy into heat. - Fuses:
Fuses rely on Joule’s law to melt and break the circuit when excessive current flows, preventing damage to appliances. - Incandescent Bulbs:
Filaments in traditional light bulbs produce light and heat because of the heat generated by electric current, explained by Joule’s law. - Electric Cooking Appliances:
Devices like electric stoves and toasters use the principle to generate controlled heat. - Industrial Applications:
Industrial heating processes, such as in furnaces and resistance welding, are designed using Joule law principles.
Conclusion
Joule’s Law of Heating explains the relationship between electric current, resistance, and heat. Its formula, H=I2Rt, is fundamental in electrical and electronic engineering. From household appliances to industrial machines, Joule’s law governs how electrical energy transforms into heat, ensuring safety and efficiency.
By understanding what is Joule’s law of heating, engineers and students can design electrical systems with precision and optimize energy usage effectively.
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