>>12883816>>12883816Power = Voltage * Current
The power being the same is a statement of conservation of energy since P = E/t. Step up or step down transformers must necessarily step down or step up, respectively, the currents. The transformers actually modulate the currents via number of coils, and this is what steps the voltage up or down.
There's a subtlety though. The voltage in this equation is actually a voltage drop. Physically only changes in potential are meaningful (as a proxy to energy). The way to view power = V*I is that the current flow over some voltage drop determines the power. If the current flows more strongly, then it can't deliver as much of a voltage drop.
Think of it like a waterfall. You can either have a very fast river falling a short distance, or a slow river falling a very far distance. Both generate the same amount of energy, or in this case power. Transformers basically just alter the height of the waterfall, which has advantageous properties.
Joule heating is P = I^2 * R. Power lines lose energy by delivering electricity such far distances. If you can decrease the current flow along these very long wires, you lose less energy to heat. Equivalently, this is solved by stepping up the voltage. This is also why room temperature superconductors are such a big deal. If we can find them, we can transmit electricity along power lines without losing any energy.
