The heat produced in a resistor is proportional to the square of the current, the resistance, and the time for which current flows.
Every ampere pays a heat tax on its way through a resistance.
H = I² × R × t
H
heat energy (joules)
I
current (amperes)
R
resistance (ohms)
t
time (seconds)
In plain English: Current squared is the headline: double the current through a wire and it makes four times the heat. This is why fuses blow and why thick wires exist.
Where you'll meet it: Explains fuse ratings, wire gauge choices, and why a slightly overloaded resistor smells the way it does. It is Watt's law (I²R) accumulated over time.