How can we determine the diameter of the cylindrical wire needed to make a fuse that limits the current to 0.53 A?
Determining the Diameter of the Cylindrical Wire for the Fuse
To determine the diameter of the cylindrical wire needed to make a fuse that limits the current to 0.53 A, we can use the formula for current density, which is current divided by cross-sectional area. The current density is given as 510 A/cm2 and the desired current is 0.53 A. We can rearrange the formula to solve for the cross-sectional area and then use it to find the diameter.
First Step: Finding Cross-Sectional Area
Current density = Current / Cross-sectional area
510 A/cm2 = 0.53 A / Cross-sectional area
Cross-sectional area = 0.53 A / 510 A/cm2
Second Step: Calculating Diameter
Now, we can use the formula for the area of a circle to find the diameter:
Area of a circle = π * (diameter/2)2
Cross-sectional area = π * (diameter/2)2
Substituting the cross-sectional area we found:
0.53 A / 510 A/cm2 = π * (diameter/2)2
Solving for diameter, we have:
diameter = √((0.53 A / 510 A/cm2) / π) * 2