When a current flows in an aluminum wire of diameter 4.41 mm. the drift speed of the conduction electrons is 1.01 x 10 -4 m/s. What is the electron current in the wire? The conduction electron density in aluminum is 6.00 x 1028 m-3

14.5A

Explanation:

The following data are given

Diameter,D=4.41mm=0.00441m,Hence the area can be calculated as

also the speed of the electron which we refer to as the drift speed is given as

1.01*10^-4m/s

and lastly the conduction electron density, n =6.00*10^28

From the formula connecting the drift velocity to the current which is

if we insert values we arrive at

Hence the electron current in the wire is 14.5A

The electron current in the wire is 14.976A in the direction opposite the motion of the charges.

The current (I) flowing through a wire of cross-sectional area (A), made of a material with free charge density (n), is related to the carriers of the current each of charge Q, and the drift velocity v at which the carriers move, as follows;

I = n x Q x A x v       -------------------------(i)

From the question;

The wire is made of aluminium and has

diameter d, = 4.41mm = 0.00441m

A =

Take = 3.142

=> A =

=> A = 1.5 x 10⁻⁵m²

drift speed, v = 1.01 x 10⁻⁴m/s

electron charge density, n = 6.00 x 10²⁸ m⁻³

Q = charge on an electron = -1.6 x 10⁻¹⁹C

Substitute these values into equation (i) to get the current through the wire as follows;

I = 6.00 x 10²⁸ x (-1.6 x 10⁻¹⁹) x 1.5 x 10⁻⁵ x 1.01 x 10⁻⁴

Solve for I;

I = -14.976A

The negative sign indicates that the direction of conventional current is opposite that of the motion of the negative charges.

Therefore, the electron current in the wire is 14.976A in the direction opposite the motion of the charges.

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