The power lost as heat in a transmission wire, due to its resistance, is proportional to:

1. Joule heating in a wire of resistance R carrying current I follows the relationship P_loss = I²R. 2. The text states: "which is proportional to the current squared in the transmission wire." 3. This is precisely why engineers push current down (via step-up transformers) rather than leaving current high on long transmission lines. 4. So the resistive power loss scales with the square of the current flowing through the wire, not simply with voltage or resistance alone. _Source: OpenStax Physics Ch 20 "Magnetism", p.691 §20.2 Motors, Generators, and Transformers_