Difficulty: Easy
Correct Answer: Four times
Explanation:
Introduction / Context:The safe current a conductor can carry is often limited by allowable current density and temperature rise. For a given material and cooling condition, current capacity is proportional to the cross-sectional area when the same current density criterion is used.
Given Data / Assumptions:
Concept / Approach:Current I = J * A for a given current density J. The area of a circular cross-section is A = π (d^2) / 4. Doubling diameter multiplies area by 4, so the allowable current at the same J increases by the same factor.
Step-by-Step Solution:
Original area A₁ = π d^2 / 4.New area A₂ = π (2d)^2 / 4 = π * 4 d^2 / 4 = 4 A₁.At the same J_max, I₂ = J_max * A₂ = 4 * J_max * A₁ = 4 I₁.Verification / Alternative check:
Thermal limits also scale favorably with larger area for the same current density; practical ampacity tables reflect similar trends (with additional derating factors).Why Other Options Are Wrong:
One-fourth or half would imply reduced area, not increased; twice ignores the quadratic area change.Common Pitfalls:
Confusing diameter with radius or forgetting that area scales with the square of diameter.Final Answer:
Four times
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