Calculating the Diameter of a Wire in a Fuse

What is the diameter of the wire in the fuse?

6.5 mm

Answer:

The diameter of the wire in the fuse is approximately 0.191 cm.

A certain fuse "blows" if the current in it exceeds 4.0 A. The fuse contains a wire that melts when the current density is 110.0 A/cm² or more. To calculate the diameter of the wire in the fuse, we can use the formula for current density. The current density is defined as the current passing through a conductor per unit area. The formula for current density is J = I/A, where J is the current density, I is the current, and A is the cross-sectional area of the wire.

We are given that the fuse "blows" if the current exceeds 4.0 A, meaning that the current passing through the wire is 4.0 A. Additionally, the wire melts when the current density is 110.0 A/cm² or more.

Let's assume that the diameter of the wire is d. The radius of the wire is then half of the diameter, which is d/2. Using the formula for the cross-sectional area of a wire, A = πr², we can substitute the radius into the formula to get A = π(d/2)² = πd²/4.

By rearranging the formula for current density to solve for the diameter, we find that the diameter of the wire in the fuse is approximately 0.191 cm.