Basic electricity – resistance dependence: For a metallic conductor, resistance R is proportional to which geometric parameter(s), given length l and cross-sectional area A?

Introduction / Context:
Designing conductors and busbars requires understanding how resistance scales with geometry and material properties. The standard relationship for a uniform conductor is R = ρ * l / A, where ρ is resistivity. This question assesses recognition of the proportionalities to l and A.

Given Data / Assumptions:

• Uniform material with constant resistivity ρ at a fixed temperature.
• Conductor of length l and cross-sectional area A.
• DC or low-frequency regime where skin effect is negligible.

Concept / Approach:
From R = ρ * l / A, resistance increases linearly with length and decreases inversely with area. Therefore, R is proportional to l (directly) but not to A or A^2. Option 'both a & b' is incorrect because it implies direct proportionality to area as well.

Step-by-Step Solution:
Start with R = ρ * l / A.Hold ρ constant: R ∝ l and R ∝ 1/A.Identify which option reflects a direct proportionality: only 'l'.Thus, choose option (b).

Verification / Alternative check:
Doubling l doubles R; doubling A halves R. Experimental measurements on metal wires confirm linearity within elastic ranges and constant temperature.

Why Other Options Are Wrong:
Option (a): suggests R increases with A; false (it decreases).

Option (c): area squared has no basis here.

Option (d): incorrectly mixes a true and a false direct proportionality.

Common Pitfalls:

• Forgetting temperature dependence: ρ rises with temperature for metals.
• Ignoring skin effect at high frequency, which alters effective area.

Final Answer:
l (length of the conductor)