Numeric example of electric current

In order to gain an understanding how moving charges relate to electric current, consider the following case. A copper wire has a cross section of 1 mm. During a time interval of 10 seconds, all electrons move 1 mm towards one end of the wire, resulting in a speed of 0.1 mm/s. What is the value of the electric current?

First, let’s calculate the volume of a small cylinder of length 1mm and a radius of 0.5 mm:

V = π.(0.5 mm)2.(1 mm) = 0.785 mm3

Since there are 8.49 x 1019 copper atoms in a cubic millimeter, the total number of atoms in this cylinder is:

N = (0.785 mm3).(8.49 x 1019 atoms/mm3) = 6.67 x 1019 atoms

Assume now that every atom has one free electron that can be displaced. Given a charge of -1.6 x 10-19 C per electron, the total charge to be moved is:

ΔQ = (6.67 x 1019).(-1.6 x 10 -19 C) = -10.67 C

Now, it takes 10 seconds for this 1 mm long cylinder full of free electrons to move 1 mm in one direction, so it corresponds to a current of:

I = ΔQ/Δt = (-10.67 C) / (10 s) = -1.067 C/s = -1.067 A

Notice the sign of this current. Since the moving charges are negative (the electrons), the electric current is also negative.

Go back to 1.2 Electric current

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