Compare wire resistance when cross-sectional area changes
Explain qualitatively why a thicker matching metallic wire has lower resistance and distinguish transverse area from surface area.
Section 4.2.4 · Resistance
Core and Extended; Physics 0625, 2026–2028. Use the stated source, operating conditions and meter ranges. Written practice is self-checked.
Before you begin
- Explain mobile electrons in a metal.
- Identify a section perpendicular to the wire's length.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which cut gives a wire's cross-sectional area?
What you will learn
- State the qualitative cross-sectional-area relationship.
- Distinguish cross-section, surface area and changed material conditions.
Use the transverse conducting area
For metallic wires with the same material, length and temperature, a larger cross-sectional area gives lower resistance. The larger transverse conducting region provides more room for carrier flow. A thinner matching wire has greater resistance.
Cross-sectional area is the area of a cut perpendicular to the length. It is not the total outside surface area of the wire and not merely its circumference. For a round wire, diameter and area are related but are not the same quantity. Quantitative area and diameter scaling is handled in the Supplement sequence.
Make a controlled comparison
A thicker wire of a different material cannot be ranked by thickness alone. Likewise, strong heating may change resistance during a trial. Match material, conducting length and temperature, and use secure comparable contacts so contact changes do not masquerade as sample behaviour.
An insulating coating increases an object's outside diameter without necessarily changing the metal core's conducting cross-section. Compare the actual conducting material, not the whole coated outline. This lesson states a qualitative change rather than a calibrated drawing-thickness ratio.
Pause and explain
A plastic coating thickens a wire's outside outline without changing the metal core. Does this alone increase the conducting cross-section?
Worked example
Two metallic wires have the same material, length and temperature. One has greater conducting cross-sectional area. Which has lower resistance?
Show the worked solution
- The other relevant conditions match.
- Larger conducting area gives lower resistance.
- The thicker conducting wire has lower resistance.
Answer The wire with larger conducting cross-sectional area.
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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 thin and thick conducting wires with matching material, length and temperature.
Give me a hint
Use conducting cross-section rather than the outside coated outline.
Compare my reasoning
- The comparison holds the other influences fixed.
- The thicker conducting wire has greater transverse area.
- Its resistance is lower.
The thicker conducting wire has lower resistance.
Look for these in your work
- State the controls.
- Identify the conducting area.
Explain why a wire's outside surface area is not the area meant in the resistance comparison.
Give me a hint
Specify the direction of the relevant cut.
Compare my reasoning
- The relevant section is perpendicular to length.
- Outside surface area extends along the wire.
- These are different geometric quantities.
The relevant area is the transverse conducting cross-section, not the outside surface.
Look for these in your work
- Describe the cut.
- Distinguish the two areas.
A metal core gets a thicker plastic coat but keeps the same core, length and temperature. Can lower core resistance be inferred from the larger outside diameter?
Give me a hint
Ask whether more conducting metal has been added.
Compare my reasoning
- The plastic is an insulating coating.
- The metal conducting cross-section is unchanged.
- The controlled area relationship gives no lower core resistance from the coat alone.
No; the conducting core area has not changed.
Look for these in your work
- Identify the conducting region.
- Avoid using the coated diameter as metal area.
Common mistakes
- Use conducting cross-section, not outside surface area.
- Hold material, length and temperature fixed.
- An insulating coating need not change the metal area.
What can you explain now?
Under matched conditions, what happens when conducting cross-sectional area increases?
Compare with the explanation
Resistance decreases.
The qualitative relationship concerns the conducting core's transverse area.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Compare resistance by conducting cross-sectional area while retaining material, length and temperature controls.
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.