Electric Potential: What Voltage Really Is

The electric potential is the electric potential energy per unit charge, and that is the rigorous way to understand what voltage really means.

We all use the word “volts” quite naturally. We know there’s 230V in the wall socket and 5V in a USB port. The “water pressure” analogy is often used, and it can work as a start, but it falls short when we want to truly understand what’s happening with the energy.

To understand voltage, we first need to understand Potential Energy. And for that, nothing better than going back to gravity.

Potential Energy: the cost of climbing the mountain

Suppose you have a rock on the floor and you want to lift it onto a shelf two meters high.

• You have to exert a force against gravity.
• You have to do work ().

That work you’ve done is not lost. It is “stored” in the rock. Now the rock has Gravitational Potential Energy. If you let it go, that energy will be released (probably breaking something along the way).

Something similar happens in electricity. If you have an electric field (created by a positive charge) and you try to bring another positive charge closer:

1. A repulsive force will appear (Coulomb’s law).
2. You will have to push to get it closer and do work.
3. That work is stored in the charge as Electric Potential Energy (). It is measured in Joules (J).

Electric Potential: the “height” of the terrain

The problem with only talking about potential energy is that it depends on the size of the charge. That’s why physicists defined a more useful quantity: the potential energy per unit charge.

Thus, the Electric Potential was born.

In other words, we define how much work it would cost to bring a unit charge (1 Coulomb) to that point.

• Potential Energy is what the charge has.
• Potential is a property of the point in space.

Analogy:

• The Potential is the height of the mountain. The mountain measures the same whether you or a truck climbs it.
• The Potential Energy is the effort required to climb. The truck will use much more energy than you to reach the same height.

Why does current flow?

Going back to the mountain analogy: things tend to move towards states of lower potential energy.

1. In a circuit, the power supply creates a sort of “electric mountain”.
2. It generates a point of high potential and another of low potential.
3. The charges feel that slope (which is physically related to the Electric Field) and move, releasing energy in the process.

That released energy is what will light up the bulb, heat a resistor, or run a motor.

Potential Difference or Voltage

In the real world, the absolute value of the potential at a point doesn’t matter much to us. What interests us is the height difference between two points.

If I put a ball on a flat table, it doesn’t move, even if the table is 100 meters high. The ball only rolls if there is a slope.

We call that electrical slope the Potential Difference or Voltage.

Rigorous definition of the volt

Here is the definition worth engraving in memory. The unit of voltage is the Volt (V). According to the previous formula:

What does this really mean? It means that if we have a potential difference of 12 Volts (like in a car battery), that battery is capable of delivering 12 Joules of energy to each Coulomb of charge that passes through it.

• High Voltage: Each charge carries a lot of energy.
• Low Voltage: Each charge carries little energy.

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