Answer to Question #117658 in Electric Circuits for Sam

Question

Describe how AC electricity is transferred from the hydroelectric plant to homes and industry. Mathematically account for the need of transformers and high voltages. You should include:

Answer 1

The process is quite easy if we do not go into too much details.

There are electrical generators at the hydroelectric plant. They convert potential and kinetic energy of water into electrical energy.

The generators are connected to transformers. The transformers increase the value of voltage to reduce power loss and increase the efficiency of power transmission. Therefore, transformers convert the same power from one value of voltage and current to another.

The transformers pass the energy to loads (cities) through power transmission lines and substations (point where one line may split into several lines). As cables and wires reach homes, they are connected to smaller local transformers that reduce the voltage until common 230 or 120V.

Why does the transmission over long distances is more efficient at high voltage? Remember that the heat generated as an electric current flows in a wire is

$$P_h=I^2R.$$

It is very expensive to reduce the resistance to make heat power loss lower. It is much more efficient to reduce the value of current.

Assume that we have power $P$ generated. In terms of voltage and current it can be expressed as

$$P=VI.$$

For constant value of generated power, if we increase the voltage, the current decreases. That easy! As the current decreases, the heal loss $P_h$ also decreases.