The resistance of a conductor is directly proportional to its
2023
The resistance of a conductor is directly proportional to its
Answer: C. length — ConceptFor a uniform conductor, resistance is governed by R = ρL/A, where ρ is electrical resistivity, L is length, and A is cross-sectional area. Direct…
- A.
area of cross-section
- B.
density
- C.
length
- D.
More than one of the above
- E.
None of the above
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Correct answer: C
Concept
For a uniform conductor, resistance is governed by R = ρL/A, where ρ is electrical resistivity, L is length, and A is cross-sectional area.
Direct proportionality means that, with the other relevant quantities fixed, multiplying one quantity multiplies resistance by the same factor.
Application
Keep electrical resistivity ρ and cross-sectional area A fixed. The relation becomes R ∝ L.
If L is doubled, R is doubled, so resistance is directly proportional to length.
Cross-sectional area appears in the denominator, so R ∝ 1/A rather than R ∝ A.
Mass density is not electrical resistivity and is not a variable in this relation.
Contrast
Area of cross-section has an inverse relation with resistance.
Density is distinct from electrical resistivity.
Length has the direct-proportional relation stated in the question.
Therefore the compound choices “more than one” and “none” do not describe the relation.
Cross-check
For two wires of the same material and area, R₂/R₁ = L₂/L₁. Thus a wire three times as long has three times the resistance.
The required quantity is length.