Formula
The heat released by a conductor equals the square of the current times resistance times time: Q = I²Rt.
ENT-level problem
A resistor of resistance $R = 10$ ohm is connected to a source of voltage $U = 20$ V. Find the current flowing through the resistor.
Ohm's law for a circuit segment: $I = U/R$.
$$I = \frac{U}{R} = \frac{20}{10} = 2 \text{ A}$$
The Joule–Lenz law describes the heating of a conductor by an electric current: the greater the current, the resistance and the time, the more heat is released. The unit of heat is the joule (J).
The power of heat release is P = I²R, so Q = P · t. This underlies heating appliances and the filaments of incandescent lamps; excessive current also overheats fuses.
The heating power is P = I²R, and the heat over time t is Q = P · t = I²Rt.
Charge carriers collide with the lattice ions and transfer energy to them — macroscopically this appears as heating proportional to I²Rt.
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