Curioustab Logo Curioustab
Home » Electronics and Communication Engineering » Materials and Components

If the diameter of a circular wire is doubled while using the same permissible current density, its current-carrying capacity becomes what multiple of the original value?

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:

  • Uniform, circular wire; same material and environment.
  • Permissible current density J_max is unchanged.
  • Original diameter d; new diameter 2d.


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
← Previous Question Next Question→

More Questions from Materials and Components

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion