R = V ÷ I is a definition that works for every component at every point. Ohm’s law is a description of one kind of component: current is proportional to p.d. when the temperature is constant. Keep them apart and most “true or false” questions in this topic become routine.
This lesson builds on reading a current-voltage graph and belongs to potential difference, resistance and circuits.
What is the difference?
| Statement | Applies to | Says |
|---|---|---|
| R = V ÷ I | any component | what resistance means at one point |
| Ohm’s law | ohmic components at constant temperature | I is proportional to V, so R is constant |
A test for an ohmic component: compute V ÷ I for several readings. If the value is constant, the component is ohmic over that range. If it changes, the component is non-ohmic, but R = V ÷ I still gives its resistance at each reading.
How do I work through a question?
- Write down the claim you are asked to judge.
- Decide whether it is a definition or a law about a type of component.
- Compute V ÷ I at each data point, or check whether doubling V doubles I.
- State the conclusion for the component, using the numbers.
- Give the reason, for example a change in temperature.
Worked example
Two components were tested. (Invented example data.)
| V (V) | 2.0 | 4.0 | 6.0 |
|---|---|---|---|
| I for component A (A) | 0.20 | 0.40 | 0.60 |
| I for component B (A) | 0.50 | 0.80 | 1.00 |
Which component obeys Ohm’s law?
Step 1, component A: V ÷ I = 2.0 ÷ 0.20 = 10 Ω, 4.0 ÷ 0.40 = 10 Ω, 6.0 ÷ 0.60 = 10 Ω. The value is constant.
Step 2, component B: 2.0 ÷ 0.50 = 4.0 Ω, 4.0 ÷ 0.80 = 5.0 Ω, 6.0 ÷ 1.00 = 6.0 Ω. The value increases.
Step 3, check by doubling: for A, doubling V from 2.0 V to 4.0 V doubles I from 0.20 A to 0.40 A. For B, I rises from 0.50 A to 0.80 A, a factor of 1.6.
Step 4, conclusion: A obeys Ohm’s law (resistance 10 Ω). B does not, and R = V ÷ I still gives its resistance at each point.
The mistake to watch for
A common slip is to say that a component which is not ohmic “does not obey V = I × R”.
Mistaken answer: “Component B breaks V = I × R because its resistance changes.”
The student confused the definition with the law. V = I × R is true for B at every point. What B fails is the proportionality between I and V.
The correction is to say exactly what fails: “Component B is non-ohmic because V ÷ I is not constant, so I is not proportional to V.”
Check yourself
Try these, then open each answer.
1. True or false: “R = V ÷ I only works for ohmic components.” Explain.
Show answer
False. R = V ÷ I defines resistance and works for any component at any point. Only the statement that R stays constant is special to ohmic components.
2. A component gives I = 0.10, 0.20, 0.30 A at V = 1.0, 2.0, 3.0 V. Is it ohmic? Give its resistance.
Show answer
V ÷ I = 1.0 ÷ 0.10 = 10 Ω, 2.0 ÷ 0.20 = 10 Ω, 3.0 ÷ 0.30 = 10 Ω. It is ohmic, with a resistance of 10 Ω.
3. Another component gives I = 0.10, 0.15, 0.18 A at V = 1.0, 2.0, 3.0 V. Is it ohmic? Give the trend.
Show answer
V ÷ I = 10 Ω, 2.0 ÷ 0.15 ≈ 13 Ω, 3.0 ÷ 0.18 ≈ 17 Ω. It is non-ohmic, and its resistance increases as V rises.
Where this leads next
Next, apply all of this to a circuit diagram in meter placement. The circuit reasoning simulator can show how current changes as you change a component, and the practice set includes a data-comparison question.
Students who can do each calculation but are unsure how to phrase a conclusion can benefit from a teacher reading their sentences as a marker would. That is part of our online one-to-one Physics tuition.