¹¹The sole purpose of transforming voltage and current levels in a power grid is to minimize power losses due to the electrical resistance of the conductors. Recall from basic DC electrical theory that the amount of power dissipated by a current-carrying resistance is P = I²R. This means doubling the current through a resistive conductor will increase that conductor’s power dissipation four-fold, all other factors being equal. Metal wire is expensive, especially when thousands of miles of it must be run to form a power grid. In the interest of reducing this expense, transformers are used to maintain long-distance power line voltages high and currents low, permitting the use of smaller-gauge conductors to carry that current.