Conductor design principle: Does increasing a conductor’s cross-sectional area reduce its resistance and therefore affect how much it opposes current?
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AApplies — larger cross-sectional area lowers resistance (R ∝ 1/A).
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BDoes not apply — area has no effect; only length matters.
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CDoes not apply — resistance depends only on material resistivity.
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DDoes not apply — increasing area increases resistance.
Answer
Correct Answer: Applies — larger cross-sectional area lowers resistance (R ∝ 1/A).
Explanation
Introduction / Context:Wire sizing impacts voltage drop, heating, and efficiency. Understanding how geometry influences resistance helps in selecting conductors for power distribution and signal integrity.
Given Data / Assumptions:
- Uniform conductor of length L and cross-sectional area A.
- Material has resistivity ρ at the operating temperature.
- Direct current conditions (but the geometric relation holds for AC resistance ignoring skin effect).
Concept / Approach:The basic relationship for resistance is R = ρ * L / A. For fixed material (ρ constant) and length L, R is inversely proportional to area. Doubling area halves resistance, which reduces voltage drop and I^2R heating for a given current.
Step-by-Step Solution:
State the model: R = ρ * L / A.Hold ρ and L constant; vary A.Observe inverse relationship: as A increases, R decreases proportionally.Verification / Alternative check:Compare AWG tables: lower AWG numbers (thicker wires, larger area) exhibit lower resistance per unit length, confirming the formula.
Why Other Options Are Wrong:
- “Only length matters” (option b) contradicts R ∝ L / A.
- “Only resistivity matters” (option c) ignores geometry.
- “Increasing area increases resistance” (option d) reverses the proportionality.
Common Pitfalls:Overlooking temperature dependence of ρ and ignoring skin effect at high frequencies, which effectively reduces the conductive area.
Final Answer:Applies — larger cross-section reduces resistance (R ∝ 1/A).