A fuse in an electric circuit is a wire that is designed to melt, and thereby open the circuit, if the current exceeds a predetermined value. Suppose that the material to be used in a fuse melts when the current density rises to 520 A/cm2. What diameter of cylindrical wire should be used to make a fuse that will limit the current to 0.62 A

0.0389 cm

Explanation:

The current density in a conductive wire is given by

where

I is the current

A is the cross-sectional area of the wire

In this problem, we know that:

- The fuse melts when the current density reaches a value of

- The maximum limit of the current in the wire must be

I = 0.62 A

Therefore, we can find the cross-sectional area that the wire should have:

We know that the cross-sectional area can be written as

where d is the diameter of the wire.

Re-arranging the equation, we  find the diameter of the wire:

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y