59.1k views
7 votes
A copper wire has a diameter of 1.947 mm. What magnitude current flows when the drift velocity is 1.79 mm/s

User HolKann
by
5.3k points

1 Answer

8 votes

Answer:

72.5 A

Step-by-step explanation:

There are about 13.6 coulombs of free electron charges in each cubic mm of copper. So, the rate of movement of charge is that quantity multiplied by the volume in the flow.

V = πr²h . . . . . volume of a cylinder

V = π(1.947 mm/2)²(1.79 mm/s) = 5.329 mm³/s

Then the charge flow rate is ...

(13.6 C/mm³)(5.329 mm³/s) = 72.5 C/s

The magnitude of the current is about 72.5 amperes.

______

Additional comment

The volume of free charge in copper can be computed from the density, molar mass, number of atoms in a mole, number of charges in a coulomb, and the number of free charges per atom. Some of the combinations of necessary calculations can be found with a web search, so it is not unreasonable to presume that the charge density is known.

User John Grant
by
5.2k points