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 (Ïr² 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 / (Ïr²)
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