Calculating the Diameter of a Fuse Wire

Understanding Fuse Wire Diameter Calculation

A fuse in an electric circuit serves as a safety measure to protect the circuit from damage due to excessive current flow. When the current in the circuit exceeds a certain limit, the fuse wire melts, breaking the circuit and preventing further damage. In this scenario, we are tasked with calculating the diameter of a cylindrical wire for a fuse based on specific parameters.

Given Parameters

Current Density (J): 540 A/cm²

Current (I): 0.57 A

Formula for Current Density

The formula for current density (J) is J = I/A, where A is the cross-sectional area of the wire (πr² for a cylindrical wire).

Calculating the Wire Diameter

Using the formula for current density and rearranging it to find the diameter (d) of the wire, we get:

J = I / (πr²)

r = √(I / (Jπ))

Final Calculation

Plugging in the given values:

r = √(0.57 / (540π))

r ≈ 0.0183 m

Since the diameter is equal to twice the radius, the diameter of the cylindrical wire for the fuse should be:

Diameter ≈ 2 × 0.0183 ≈ 0.0366 m