Question

An unknown wire in a circuit has a circular cross-section with diameter 2.6 mm. It carries a current of 2.9 mA. 33% Part (b) If you assume the drift velocity in this wire is 1×10⁻² cm/s, what is the density of charge carriers per cubic ceritimeter n=cm⁻³

Answer 1

The density of charge carriers per cubic centimeter in the wire can be calculated using the given diameter, current, and drift velocity. We can use the equation I = nqAvd to find the drift velocity and then solve for n. Substituting the known values will give us the desired density.

Step-by-step explanation:

To calculate the density of charge carriers per cubic centimeter (n=cm⁻³), we need to determine the number of free electrons per cubic meter (n) in the wire. We can use the density of copper, the atomic mass of copper, and Avogadro's number to calculate n. The given diameter of the wire is 2.6 mm, so the radius (r) is half of that. We can then calculate the area of the cross-section of the wire using the formula A = πr².

Next, we can use the equation I = nqAvd to find the drift velocity (vd) of the electrons. The current (I) is given as 2.9 mA, and we assume the drift velocity is 1×10⁻² cm/s. Rearranging the equation, we can solve for n:

n = I / (qA vd)

Substituting the known values, we can calculate the density of charge carriers per cubic centimeter.