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.
Practise getting I or R on its own from V = IR in the Equation Rearranger.
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.
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.