Question

The diameter of a 12-gauge copper wire is 0.081 in. The maximum safe current it can carry (in order to prevent fire danger in building construction) is 20 A. At this current, what is the drift velocity of the electrons? The number of electron carriers in 1.0 cm3 of copper is 8.5 × 1022 and e = 1.60 × 10-19 C.

Answer 1

To calculate the drift velocity in the copper wire, use the formula Id = (nqAd)/J, where Id is the drift current, n is the number of electron carriers per unit volume, q is the charge of an electron, Ad is the cross-sectional area of the wire, and J is the current density.

Step-by-step explanation:

To calculate the drift velocity of electrons in the copper wire, we can use the equation Id = (nqAd)/J, where Id is the drift current, n is the number of electron carriers per unit volume, q is the charge of an electron, Ad is the cross-sectional area of the wire, and J is the current density. In this case, the current density J is equal to the maximum safe current (20 A) divided by the cross-sectional area of the wire.

Using the given diameter of the wire, we can calculate the cross-sectional area using the formula Ad = πrd2, where rd is the radius of the wire. Once we have the cross-sectional area, we can substitute all the values into the drift current equation to find the drift velocity.