What is the diameter of the wire in the fuse?

Determining the diameter of the wire in the fuse

The diameter of the fuse wire is approximately 2 mm. This is calculated using the formula for current density and the area of a circle to first determine the cross-sectional area and then derive the diameter.

Explanation

The question asks for the diameter of the wire in a fuse that blows at a current of 1.0 A with a current density of 320 A/cm². The current density is defined as the current per unit area. Since the current and current density are given, we can first calculate the cross-sectional area of the fuse wire and then determine its diameter.

First, we convert the current density to the SI unit by multiplying with 10² (since 1 cm² = 10² mm²), which gives us 32000 A/m². The formula for current density (J) is J = I/A, where I is the current and A is the area. We can rearrange the formula to find the area (A = I/J).

For this fuse, the current (I) is 1 A and the current density (J) is 32000 A/m², so:

A = 1 A / 32000 A/m² = 3.125 × 10⁻⁵ m²

Now, using the area of a circle (A = πd²/4, where d is the diameter), we rearrange to solve for the diameter (d):

d = 2 √(A/π) = 2 √((3.125 × 10⁻⁵ m²)/π)

Using a calculator, we find the diameter is approximately 2 mm.