Compare wire resistance when length changes
Explain qualitatively why a longer metallic wire has greater resistance when material, cross-section and temperature are controlled.
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
- Describe metallic charge carriers.
- Distinguish wire length and cross-sectional area.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What dimension describes distance along the conducting wire?
What you will learn
- State the qualitative length relationship for a metallic wire.
- Identify conditions needed for a fair comparison.
Compare the conducting path
For metallic wires of the same material, cross-sectional area and temperature, a longer wire has greater resistance. The carriers encounter a longer conducting path through the material. A shorter matching wire has lower resistance. The Core requirement is this qualitative relationship.
The comparison concerns the actual conducting length, not the straight distance between endpoints if a wire is coiled. Coiling an unchanged wire into a compact shape does not by itself shorten its conducting path. A label saying 'larger wire' is ambiguous unless length and thickness are distinguished.
Hold other influences fixed
Different materials or temperatures can change resistance independently of length. Stronger heating during one measurement can confound a wire comparison. Keep current effects suitable and use matched temperature conditions rather than attributing every observed difference to length.
Cross-sectional area is a separate influence: a longer but much thicker wire cannot be ranked from length alone. Numerical direct-proportion calculations belong to the Supplement sequence. This lesson requires a direction of change under controlled conditions, not an unsupported numerical factor.
Sources for this lesson
Pause and explain
Two wires differ only in conducting length. Which has greater resistance?
Worked example
Wire B is longer than wire A; both have the same material, uniform area and temperature. Compare their resistance qualitatively.
Show the worked solution
- Only conducting length is changed.
- The longer metallic path has greater resistance.
- B therefore has greater resistance than A.
Answer B has greater resistance under the stated matched conditions.
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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.
Compare a short and long wire with matching material, uniform area and temperature.
Give me a hint
Use the qualitative length relationship under the stated controls.
Compare my reasoning
- The material, area and temperature match.
- The long wire has a longer conducting path.
- Its resistance is greater.
The longer wire has greater resistance.
Look for these in your work
- State the controls.
- Give the direction of change.
An unchanged wire is coiled without stretching, heating or changing contacts. Does its shorter endpoint separation establish lower resistance?
Give me a hint
Compare the actual wire path before and after coiling.
Compare my reasoning
- The conducting length is unchanged.
- Material, area and temperature remain the same.
- The length comparison gives no reduction from endpoint separation alone.
No; the same conducting length remains under the stated conditions.
Look for these in your work
- Use path length.
- Do not equate coil size with wire length.
Wire B is longer but also thicker and at a different temperature than A. Can length alone decide which has greater resistance?
Give me a hint
Identify the uncontrolled area and temperature influences.
Compare my reasoning
- Length favours a greater resistance for B.
- Area and temperature also changed.
- The net comparison needs more information or matched controls.
No; the additional area and temperature changes prevent a length-only ranking.
Look for these in your work
- Name the confounders.
- Require controlled or quantitative evidence.
Common mistakes
- Compare actual conducting length.
- Hold material, area and temperature fixed.
- Do not rank a longer and thicker wire from length alone.
What can you explain now?
At fixed material, area and temperature, how does resistance change for a longer wire?
Compare with the explanation
It increases.
The conducting path is longer in the controlled comparison.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
State the qualitative wire-length relationship with conducting-path and fair-comparison conditions.
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.