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Power transmission over long distances from power plants to local power grids is often done over DC with relatively high voltages/tensions. The argument for this is that since, by Joule's law, power dissipation due to heat by a resistive element is given by I^2 * R, lowering the current as a result of upping the voltage results in less power loss. But what is really puzzling me is that, by Ohm's law, I^2 * R is equal to (V^2)/R (since I = V/R), in which case upping the voltage will result in *increased* loss of power through heat generation.

I must be missing something, but I feel this isn't as clear as most people make it out to be with repeated quotes of I^2 * R without considering other equivalent forms..

Thanks a lot!