Joule's Law of Heating
Simple Explanation
Joule's law of heating states that the heat generated by current flowing through a resistance is H=I²Rt — growing with the SQUARE of the current, directly with the resistance, and directly with time.
Why Do We Need It?
This is the specific physics behind every electrical heating device — and also behind unwanted heating in wires and components, which is why wiring must be rated to handle a circuit's expected current safely.
Formula
Joule's Law of Heating
H = I²Rt
When current flows through a resistor, electrical energy is converted into heat at a rate that grows with the SQUARE of the current — the total heat generated over a time t is I²Rt.
- H
- — heat generated, in joules (J)
- I
- — current through the resistor, in amperes (A)
- R
- — resistance, in ohms (Ω)
- t
- — time current flows, in seconds (s)
When to use it: Whenever the heat generated by current flowing through a resistance over a given time needs to be found.
Worked Example
Find the heat generated by a current
A current of 2 A flows through a 10 Ω resistor for 60 seconds. Find the heat generated.
Why Does This Work?
This is a direct consequence of P=I²R (electrical power dissipated as heat in a resistor) combined with E=Pt (energy equals power times time) — substituting P=I²R into E=Pt gives exactly H=I²Rt.
Real-Life Example
Why household wiring is rated for a maximum current
Electrical wiring and circuit breakers are rated for a specific maximum current (like 15 or 20 amps), not a maximum power or voltage.
Because heat generated grows with the SQUARE of current (H=I²Rt), even a modest increase in current above the rated limit can generate dangerously excessive heat in the wiring — exactly why current, not voltage, is the critical safety limit.
Practice
A current of 3 A flows through a 5 Ω resistor for 30 seconds. Find the heat generated.
MediumCommon mistake
Forgetting to square the current — since I is squared in the formula, DOUBLING the current QUADRUPLES the heat generated, not just doubles it.
Quick Review
- H = I²Rt.
- Heat grows with the SQUARE of current.
- The physics behind both intentional heating devices and unwanted wiring heating.