Calculate resistance from potential difference and current
Use R = V/I with matching component measurements and distinguish an operating-point resistance from constant resistance.
Section P4.2.4 · Resistance
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Distinguish current and p.d.
- Convert volts and amperes and divide.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is 600 mA in amperes?
What you will learn
- Calculate resistance using R = V/I.
- Match the p.d. and current to the same component and operating state.
Use matching measurements
Resistance is calculated from R = V/I, where V is the p.d. across the component and I the current through it. The unit is the ohm, Ω. A component at 3.0 V carrying 0.60 A has resistance 5.0 Ω at that operating state.
The numerator and denominator must belong to the same component at the same time and conditions. A source voltage combined with a different branch current is not automatically that component's resistance. Convert milliampere readings to amperes before dividing by a voltage in volts.
State the limit of the quotient
A resistance found at one operating point does not prove constant resistance at all voltages. A heated filament lamp can have a different V/I at another operating state. The constant-resistance model is a further condition, not a consequence of one quotient.
For non-zero V and zero observed current, no finite R follows by division; instrument sensitivity and an open path must be considered. If both measured V and I are zero, 0/0 does not determine a resistance. A zero-origin graph point alone therefore cannot be used to claim that a component has zero resistance.
Sources for this lesson
Pause and explain
3.0 V across a component gives 0.60 A through it. What resistance follows?
Worked example
A component has p.d. 3.0 V and current 0.60 A at the same state. Find its resistance.
Show the worked solution
- Use R = V/I.
- Divide 3.0 by 0.60.
- R = 5.0 Ω at this state.
Answer 5.0 Ω at the stated operating point.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find resistance at V = 3.0 V and I = 0.60 A for one component.
Give me a hint
Divide the matching p.d. by the current through that component.
Compare my reasoning
- R = V/I.
- 3.0/0.60 = 5.0.
- The resistance is 5.0 Ω.
5.0 Ω.
Look for these in your work
- Use matching measurements.
- State ohms.
Find resistance for 6.0 V and 250 mA at a stated component state.
Give me a hint
Convert the milliampere current before dividing.
Compare my reasoning
- 250 mA = 0.250 A.
- R = 6.0/0.250.
- R = 24 Ω.
24 Ω.
Look for these in your work
- Convert current.
- Do not use 250 as an ampere value.
At an unpowered state V = 0 and I = 0. A learner claims R = 0 Ω. Assess the calculation.
Give me a hint
Check whether the ratio 0/0 determines a unique resistance.
Compare my reasoning
- R = V/I would give 0/0.
- That quotient is indeterminate.
- Other suitable operating measurements are needed.
No resistance is determined by the zero-voltage, zero-current point alone.
Look for these in your work
- Identify the indeterminate ratio.
- Do not claim zero resistance from the origin.
Common mistakes
- Use the same component and state.
- Convert mA to A.
- One quotient does not prove constant resistance everywhere.
What can you explain now?
What is the equation for resistance?
Compare with the explanation
R = V/I.
The voltage must be across and the current through the same component.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Calculate resistance from matching component data and recognise when a quotient is indeterminate or only local.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.