Question

For a wire has a circular cross section with a radius of 1.23mm.

a. If the wire carries a current of 3.70A, find the drift speed ofthe electrons in the wire.
b. All other things being equal, whathappens to the drift speed in wires made of metal having a largenumber of conduction electrons per atom than copper?

Answer 1

`5.731* 10^(-5)\ m/s`

Decrease

Step-by-step explanation:

I = Current = 3.7 A

e = Charge of electron =
`1.6* 10^(-19)\ C`

n = Conduction electron density in copper =
`8.49* 10^(28)\ electrons/m^3`

`v_d` = Drift velocity of electrons

r = Radius = 1.23 mm

Current is given by

`I=neAv_d\\\Rightarrow v_d=(I)/(neA)\\\Rightarrow v_d=(3.7)/(8.49* 10^(28)* 1.6* 10^(-19)* \pi (1.23* 10^(-3))^2)\\\Rightarrow v_d=5.731* 10^(-5)\ m/s`

The drift speed of the electrons is
`5.731* 10^(-5)\ m/s`

`v_d=(I)/(neA)`

From the equation we can see the following

`v_d\propto (1)/(n)`

So, if the number of conduction electrons per atom is higher than that of copper the drift velocity will decrease.