Design Your Circuit with the Right Fuse Diameter for Maximum Safety!
How can we determine the diameter of a cylindrical wire needed to create a fuse that limits the current to 0.50A?
Given the current density threshold of 440A/cm², what calculations do we need to make to ensure the safety and efficiency of our electric circuit?
Calculating the Diameter of the Wire for the Fuse
To determine the diameter of the cylindrical wire required to create a fuse that limits the current to 0.50A, we need to consider the current density threshold and the desired current limit.
When designing an electric circuit, safety is paramount. Using the right fuse diameter is crucial to prevent any mishaps due to excessive current flow. In this scenario, we are given that the material used in the fuse melts when the current density reaches 440A/cm².
To calculate the diameter of the wire needed for the fuse, we start by utilizing the formula I = J * A, where I is the current (0.50A), J is the current density (440A/cm²), and A is the cross-sectional area of the wire in cm². By rearranging the formula, we can solve for A: A = I / J.
Plugging in the values, we find that the minimum cross-sectional area required is approximately 0.0011364 cm². To determine the diameter (d) of the wire, we can use the formula for the area of a circle: A = π * (d/2)².
Rearranging the formula for d, we find that the diameter should be approximately 0.0674 cm. Therefore, a cylindrical wire with a diameter of around 0.0674 cm should be used to create a fuse that limits the current to 0.50A, ensuring the safety and efficiency of the electric circuit.