A 14-gauge copper wire has a diameter of 1.676 mm. What magnitude current flows in amperes when the drift velocity is 0.500 mm/s? (The density of free electrons in copper is 8.34 ✕ 1028 e−/m3.).)

14.7 A

Explanation:

The magnitude current flowing in a conductor is given by

where

Q is the total charge

t is the time interval

The total charge passing through a point in the conductor can be written as

where

n is the density of free electrons

A is the cross-sectional area of the conductor

is the electron charge

d is the length of the conductor

The time interval can be written as

where

d is the length of the conductor

is the drift velocity of the electrons

Re-arranging the three equations, we get:

For the copper wire here we have:

The diameter is 1.676 mm, so the area is

So, the current in the wire is

it's c (engineer's do their work with mechanical stuff not on any living being)