Potential difference equation: V = IR
Potential difference = current × resistance. In symbols, V = I R. V is the potential difference in volts (V), I is the current in amperes (A) and R is the resistance in ohms (Ω). It appears on the recall list of every AQA, Edexcel and OCR physics specification, and the exam's equation sheet prints it for you.
Equation
V = I R
| Symbol | Quantity | Unit |
|---|---|---|
V | potential difference | V |
I | current | A |
R | resistance | Ω |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | V = I R |
| AQA Combined Science (8464) | Recall | V = I R |
| Edexcel Physics (1PH0) | Recall | V = I R |
| Edexcel Combined Science (1SC0) | Recall | V = I R |
| OCR Gateway Physics A (J249) | Recall | V = I R |
| OCR Twenty First Century Physics B (J259) | Recall | V = I R |
Calculator: V = I R
The three quantities
Potential difference, often called p.d. or voltage, is the push that drives charge round a circuit. A battery or the mains supply provides it. You measure it with a voltmeter placed across a component.
Resistance is how hard it is for current to get through a component. A long, thin wire has more resistance than a short, thick one. For a fixed p.d., more resistance means less current.
So V = I R says that to push a current through a resistance, you need a p.d. equal to the two multiplied together.
In a practical, you set up a resistor with an ammeter in series and a voltmeter in parallel. You change the p.d., read the current each time, and plot a graph. A straight line through the origin shows the resistance does not change.
What the boards print
AQA, Edexcel and OCR all print V = I R with the same letters, for both Physics and Combined Science. Each specification calls it a recall equation. The sheet you get in the exam from 2025 onwards lists it anyway.
OCR Twenty First Century (J259) also lists a second p.d. equation: potential difference = work done ÷ charge, V = W/Q. No other board prints that form. The OCR Twenty First Century page shows it next to V = I R.
Rearranging and linking
- I = V ÷ R
- R = V ÷ I
V = I R connects to the power equations. Put it into P = VI and you get P = I²R. Current itself comes from how much charge flows each second.
Resistance stays fixed for a resistor at a steady temperature. A filament lamp is different: its resistance rises as it heats up. V = I R still works at any one moment, but R is not a constant.
Worked examples
V
- V = I R
- V = 0.2 × 45
- V = 9 V
9 V
R
- Change the current to amps: 40 mA = 0.04 A
- R = V ÷ I
- R = 12 ÷ 0.04
- R = 300 Ω
300 Ω
I
- I = V ÷ R
- I = 230 ÷ 46
- I = 5 A
5 A
Common mistakes
- Writing R = V × I. Resistance is p.d. divided by current, so a bigger current for the same p.d. means a smaller resistance.
- Leaving a resistance in kilohms. 2.2 kΩ is 2200 Ω, and using 2.2 makes the p.d. 1000 times too small.
- Reading the p.d. of the whole battery when the question asks about one component. In a series circuit the components share the p.d.
- Confusing the letter V with the unit V. The quantity is potential difference and the unit is the volt; they share a letter.
Practise getting I or R on its own from V = IR in the Equation Rearranger.
Questions people ask
Is potential difference the same as voltage?
Yes. Voltage is the everyday word. Exam papers use potential difference, or p.d. for short.
What does one ohm mean?
A component has a resistance of 1 Ω if a p.d. of 1 V drives a current of 1 A through it.