Power transmission, transformer efficiency and the DC motor

Power stations send energy along long wires, and the wires have resistance R. A current I in a line of resistance R turns the power I²R into heat, and that power is wasted. The power sent is P = VI, so for the same power a higher line voltage means a smaller current: I = P ÷ V. Because the loss depends on the square of the current, ten times the voltage gives one tenth of the current and only one hundredth of the loss. This is why a step-up transformer raises the voltage at the power station, and step-down transformers lower it to 220 V near the homes. A real transformer is not perfect. Its efficiency is η = (Vs·Is) ÷ (Vp·Ip) × 100 %, the output power over the input power. Energy is lost as heat in the wires of the two coils, as heat from eddy currents in the iron core (thin insulated sheets reduce them), and in the repeated magnetising of the core, which also causes the hum. The voltage ratio always follows the turns, Vs ÷ Vp = Ns ÷ Np, whatever the efficiency. The losses show up in the currents: Is = η·Vp·Ip ÷ Vs, with η written as a fraction. Never climb or fly a kite near power lines or poles.