Current tells you how fast charge flows — but something has to push it round the loop first. That push is potential difference, better known as voltage. It’s really a story about energy: how much a cell gives to each little chunk of charge, and how that energy gets spent along the way. Let’s build it up in plain language, with one neat equation and a bonus energy unit at the end.
📘 What you need to know
Potential difference (p.d.), or voltage, is the work done per unit charge as charge moves between two points
It’s measured in volts (V), and 1 volt = 1 joule per coulomb (1 V = 1 J C−1)
The equation is V = W / q
A cell or battery is the source of p.d. — it gives energy to the charge
A voltmeter measures p.d. and is connected in parallel, across a component
The electronvolt (eV) is a tiny energy unit: 1 eV = 1.6 × 10−19 J
What is potential difference?
Think of a cell as a little energy pump. As charge passes through it, the cell hands each coulomb a packet of energy — a shove. That energised charge then travels round the circuit and “spends” its energy in the components: lighting a lamp, spinning a motor, warming a resistor.
Potential difference measures exactly how much energy is handed over per unit of charge between two points. Formally:
Potential difference — definition
The work done per unit charge in moving charge between two points
“Work done” is just physics-speak for “energy transferred”. So p.d. is really energy per coulomb. That immediately tells you the units: joules per coulomb — which we call the volt.
Charge goes in with little energy and comes out with more. The p.d. across the cell is the energy given to each coulomb.
Here’s the mental picture that makes voltage click: think of a water slide. The cell is the pump that lifts water up to the top (giving it energy). The p.d. is how high the pump lifts each bucket. Then the water rushes down the slide (the circuit), spending that energy on the way. High voltage = a taller lift = more energy per bucket of charge.
The equation
Putting the definition into symbols:
Potential difference equationV = W / q
Where:
V = potential difference, in volts (V)
W = work done (energy transferred), in joules (J)
q = charge, in coulombs (C)
Because V = W/q, one volt is one joule shared out over one coulomb:
The volt
1 V = 1 J C−1 (one joule per coulomb)
WE 1
A cell does 12 J of work moving a charge of 3.0 C through a lamp. Calculate the potential difference across the lamp.
Step 1 — write the equationV = W / qStep 2 — substituteV = 12 ÷ 3.0V = 4.0 VEach coulomb of charge gave up 4 joules to the lamp. That’s what “4 volts” means.
WE 2
A charge of 5.0 C passes through a component with a potential difference of 6.0 V across it. Calculate the energy transferred.
Step 1 — rearrange for energyV = W/q, so W = q × VStep 2 — substituteW = 5.0 × 6.0W = 30 JMore charge, or a bigger p.d., means more energy transferred. Here, 30 joules get delivered to the component.
Measuring potential difference
To measure the p.d. across a component, you use a voltmeter. Since p.d. is the difference between two points, the voltmeter has to touch both ends of the component at once. That means wiring it in parallel — a little side-branch across the component.
An ideal voltmeter has very high (infinite) resistance, so hardly any current sneaks through it. That way it reads the p.d. without disturbing the circuit.
The voltmeter (V) branches across the lamp, touching both ends, to read the potential difference between them.
Work done joules, J
÷ charge (per coulomb)
Potential diff. volts, V
The electronvolt — a tiny energy unit
When we deal with single electrons, the joule is a clumsy, oversized unit — like measuring a grain of rice in kilograms. So physicists invented a bite-sized energy unit that fits particles: the electronvolt (eV).
Electronvolt — definition
The energy gained by one electron moving through a potential difference of one volt
We can work out its size in joules straight from W = qV. The charge is one electron (e = 1.6 × 10−19 C) and the p.d. is 1 V:
Push one electron through a p.d. of exactly 1 volt and it gains one electronvolt of energy.
WE 3
Show that one electronvolt is equal to 1.6 × 10−19 J. (Charge of an electron e = 1.6 × 10−19 C.)
Step 1 — use the energy equationW = qV, with q = e and V = 1 V
Step 2 — substituteW = (1.6 × 10⁻¹⁹) × 11 eV = 1.6 × 10⁻¹⁹ JThe charge of an electron is on your data sheet, so you never have to memorise this — just multiply it by 1 volt.
💡 Top tips
Voltage = energy per coulomb. Say that sentence and most p.d. questions unlock.
1 V = 1 J C−1 — the volt is secretly “joules per coulomb”.
Voltmeter goes in parallel, across the component — never in series.
Rearrange freely:V = W/q also gives W = qV and q = W/V.
The charge of an electron is on your data sheet — use it for electronvolt conversions.
⚠ Common mistakes
Confusing p.d. with current — p.d. is the energy-per-charge push, current is the flow rate
Connecting a voltmeter in series instead of parallel
Forgetting that “work done” just means “energy transferred”
Mixing up the electronvolt (energy) with the volt (potential difference) — different quantities
Leaving charge in the wrong units — keep q in coulombs and W in joules
Quick recap: Potential difference is the work done per unit charge, V = W/q, measured in volts (1 V = 1 J C−1). A cell is the source of p.d.; a voltmeter measures it in parallel. The electronvolt is a tiny energy unit: 1 eV = 1.6 × 10−19 J.
So current is the flow, and potential difference is the push behind it. Put those two together and a natural question appears: for a given push, how much current do you get? The answer depends on how much the component resists the flow. That’s exactly where we head next, in Electrical Conductors & Insulators — why some materials let charge stroll through while others block it almost completely.
Want voltage to finally make sense?
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