Ohm's law, explained with examples
Ohm's law links the three most important quantities in a circuit: potential difference, current and resistance. Almost every GCSE electricity question uses it, so it is worth making completely automatic.
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The equation
V = I R
- V is the potential difference (voltage), in volts (V);
- I is the current, in amps (A);
- R is the resistance, in ohms (Ω).
Rearranged: I = V/R and R = V/I. For GCSE Physics and Combined Science exams in 2025, 2026 and 2027, an equations sheet is provided in the exam, including the equations students previously had to recall; check the arrangements for your exam year, but learn it anyway, because fluent recall saves time.
In words: the current through a component depends on the potential difference across it and its resistance. Increase the potential difference and more current flows. Increase the resistance and less current flows for the same potential difference.
What Ohm's law really says
Strictly, Ohm's law says that for a metal conductor at constant temperature, the current is directly proportional to the potential difference. Components that obey this, such as a fixed resistor, are called ohmic conductors: their resistance stays the same whatever the current. The equation V = IR can be used for any component at a given moment, but only ohmic components have a constant R.
I-V graphs
- Fixed resistor (at constant temperature): a straight line through the origin. Current is directly proportional to potential difference, so resistance is constant.
- Filament lamp: an S-shaped curve. As the current increases, the filament gets hotter, its metal ions vibrate more, electrons collide with them more often, and resistance increases. So the graph gets less steep at higher voltages.
- Diode: current flows in one direction only. In the forward direction, current rises steeply once the potential difference passes a small threshold. In reverse, the resistance is very high and almost no current flows.
Worked examples
Example 1: finding current
A 12 V supply is connected across a 4 Ω resistor. Find the current.
- I = V/R = 12/4 = 3 A.
Example 2: finding resistance
A lamp has 6.0 V across it and a current of 0.25 A. Find its resistance.
- R = V/I = 6.0/0.25 = 24 Ω.
Example 3: finding potential difference
A current of 200 mA flows through a 47 Ω resistor. Find the potential difference.
- Convert: 200 mA = 0.2 A.
- V = IR = 0.2 × 47 = 9.4 V.
Example 4: kilohms
A 3.0 V cell drives current through a 1.5 kΩ resistor. Find the current in milliamps.
- 1.5 kΩ = 1500 Ω. I = 3.0/1500 = 0.002 A.
- I = 2 mA.
Example 5: resistors in series
A 9 V battery is connected to a 2 Ω and a 4 Ω resistor in series. Find the current and the potential difference across each resistor.
- In series, resistances add: R = 6 Ω. I = 9/6 = 1.5 A, the same through both.
- V across 2 Ω = 1.5 × 2 = 3 V; across 4 Ω = 6 V. Together they make 9 V.
Example 6: resistors in parallel
A 6 V supply is connected across a 3 Ω and a 6 Ω resistor in parallel. Find the total current.
- Each branch has the full 6 V. Currents: 6/3 = 2 A and 6/6 = 1 A.
- Total current = 3 A, so the total resistance is 6/3 = 2 Ω, less than either resistor.
Example 7: reading an I-V graph
On a graph, a resistor carries 0.4 A at 2.0 V. What current flows at 5.0 V?
- A fixed resistor is ohmic: R = 2.0/0.4 = 5 Ω.
- At 5.0 V, I = 5.0/5 = 1.0 A.
Thermistors and LDRs
Two components change their resistance on purpose. A thermistor's resistance falls as its temperature rises, so it is used in thermostats and digital thermometers. A light-dependent resistor (LDR) has a resistance that falls as light gets brighter, so it is used in automatic night lights. Use V = IR exactly as before: if the resistance falls while the potential difference stays the same, the current rises. Exam questions often ask you to explain, step by step, what happens to the current or to a voltmeter reading when the temperature or light level changes.
The resistance required practical
To investigate how the length of a wire affects its resistance, connect the wire in series with an ammeter and a power supply, with a voltmeter in parallel across the chosen length of wire. Use crocodile clips to select lengths such as 10 cm, 20 cm, up to 100 cm. For each length, record V and I, and calculate R = V/I.
- Result: resistance is directly proportional to length; a graph of R against length is a straight line through the origin.
- Control variables: the same wire material and thickness, and a constant temperature.
- Improving accuracy: use a low current and switch off between readings, so the wire does not heat up and change its resistance.
A second version of the practical builds series and parallel circuits of resistors and compares their total resistances. Adding resistors in series increases the total resistance, while adding them in parallel decreases it, because each extra branch gives the current another path.
Common mistakes
- Forgetting to convert mA to A or kΩ to Ω.
- Assuming a filament lamp has constant resistance.
- Putting the voltmeter in series instead of in parallel.
- Adding resistances in parallel as if they were in series.
Practice questions
Try each one before opening the answer.
Q1. Find the current through a 10 Ω resistor with 5 V across it.
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Q2. A heater draws 10 A from a 230 V supply. Find its resistance.
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Q3. Why does a filament lamp's resistance increase as it gets brighter?
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Q4. Two 8 Ω resistors are in parallel. Find the combined resistance.
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Frequently asked questions
Is V = IR given in the GCSE exam?
For GCSE exams in 2025, 2026 and 2027, an equations sheet is provided with the Physics and Combined Science papers, including the equations students previously had to recall. Check the arrangements for your exam year, and learn the equation anyway, because using it fluently saves time.
Is Ohm's law the same as V = IR?
Not quite. V = IR defines resistance and works for any component. Ohm's law is the stronger statement that, for some conductors at constant temperature, R does not change.
Key takeaways
- V = IR; learn all three rearrangements.
- Convert to volts, amps and ohms first.
- Ohmic conductors give straight-line I-V graphs through the origin.
- Filament lamps get hotter, so their resistance rises.
- Diodes let current flow in one direction only.