Question

The current in a 1.10 mm × 1.10 mm square aluminum wire is 2.80 A .

Part A

Part complete

What is the current density?

2.31×106

A/m2

Part B

What is the electron drift speed?

______  μm/s  

Answer 1

(a) To find current density (J), the equation is just J = I / A, where I = the current and A is the area of the surface.

In this case

I = 2.8 Amp

and the cross sectional area A isn't given, but you can find it using 1.1mm x 1.1mm.

Don't forget though to convert mm into m before dividing the current by area, to get m^2. (1000mm = 1m -> 1.1mm = 0.0011m)

A = 0.0011m(0.0011m) = 1.21E-6

Thus, you have J = (2.8A) / (1.21E-6) = 2.31*10^6 A/m^2.

(b) The electron drift speed can be found using this equation:

v = J/nq, where v is the drift speed you are trying to find, J is the density you just found, q = the charge of an electron, and n = the number of charges carried per unit volume (the electron density).

For aluminum n = 6.02E28 electrons/m^3

So

v = (2.31*10^6) / ((6.02E28)(1.6E-19) in m/s

v = 2.4E-4 m/s

= 240 um/s