Electric Potential Difference

Okay, let’s slow down and build this one up together. We already know current is charge on the move — but what actually pushes it around the circuit? That’s the job of potential difference, also called voltage. Grab a cup of tea, and let’s work through it step by step.

Let’s start with an everyday picture

Imagine you’re pushing a trolley up a small hill so it can roll back down again. To get it to the top, you have to do work on it — you’re giving it energy. Once it’s at the top, it has the potential to roll all the way back down, giving up that energy as it goes (maybe as heat from the wheels, or noise, or warming the ground).

A cell does exactly this, but to charge instead of a trolley. Inside the cell, chemical reactions do work on the charge and “lift” it to a higher electrical potential. As that charge then travels round the circuit and through components like resistors and lamps, it gives that energy back up again — mostly as heat and light. By the time it gets back to the negative terminal, it has “rolled all the way down” and is ready to be lifted again.

Turning that idea into a formula

So potential difference is really just: how much energy did each little bit of charge gain (or lose)? We write it like this:

Here, V is the potential difference in volts (V), W is the work done — or energy transferred — in joules (J), and q is the charge in coulombs (C). So a p.d. of 6 V simply means every coulomb of charge that passes through gets 6 joules of energy. Bigger voltage, bigger “push” of energy per bit of charge.

This also gives us a nice, simple way to think about the unit itself: 1 volt is just 1 joule per coulomb. If someone tells you a battery is “9 volts”, they’re really telling you it gives 9 joules of energy to every coulomb of charge that flows through it.

How do we actually measure it?

We use a voltmeter. But here’s the important bit — a voltmeter doesn’t sit “in the road” of the current like an ammeter does. Instead, it sits off to the side, connected across the two ends of the component you’re interested in, like it’s comparing the potential at one end with the potential at the other.

A little extra: the electronvolt

Here’s something neat. Electrons are tiny, so the energy they gain moving through a p.d. is a very small number of joules — awkward to write out every time. Physicists invented a friendlier unit for this: the electronvolt (eV), which is just the energy gained by a single electron moving through a p.d. of 1 volt.