What Size of Wire Should Be Used to Make a Fuse that Limits Current to 0.67 A?

When it comes to designing a fuse, the size of the wire plays a critical role in its functionality. In this scenario, we are tasked with determining the diameter of the cylindrical wire that should be used to make a fuse that limits the current to 0.67 A. This calculation involves considering the current density and the desired current limit to ensure that the fuse operates effectively.

Current density, which is the amount of current per unit area, is a key parameter in determining the size of wire for a fuse. In this case, the current density at which the fuse material melts is given as 390 A/cm². By setting the current limit at 0.67 A, we can calculate the diameter of the wire that will provide the necessary current-carrying capacity.

To calculate the diameter of the wire, we can use the formula d = √(4I/Jπ), where d is the diameter, I is the current, J is the current density, and π is the mathematical constant pi. Substituting the given values of I = 0.67 A, J = 390 A/cm², and π ≈ 3.14 into the formula, we can solve for the diameter of the wire.

By performing the calculations, we find that the diameter of the wire should be approximately 0.0468 cm or 4.68×10⁻⁴ m to limit the current to 0.67 A effectively. This precise sizing ensures that the fuse will activate at the specified current level and protect the circuit from potential damage due to overcurrent conditions.