# 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/cmÂ²

**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 (ÏrÂ² 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 / (ÏrÂ²)

r = â(I / (JÏ))

## Final Calculation

Plugging in the given values:

r = â(0.57 / (540Ï))

r â 0.0183 m

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

Diameter â 2 Ã 0.0183 â 0.0366 m