A current of 1.0 A exists in a copper wire of cross-section 1.0 mm2. Assuming one free electron per atom calculate the drift speed of the free electrons in the wire. The density of copper is 9000 kg m–3.
0.074mm/s
Given,
Current in the wire, I= 1A
Cross section of the wire, A= 1mm2=10-6m2
Density of Copper, d=9000 kg m–3
Formula Used
The current due to ‘n’ freely bounded electrons per unit volume with a drift speed ‘Vd’ can be expressed as,
Where ‘A’ is the cross-sectional area of the material through which electrons are passing; and ‘e’ is the charge of the electron, which is
1.6×10-19C.
In the given problem, n is not directly given. But we know that 63.5 grams of Copper have Avogadro number (6.022×1023) of atoms. So ‘m’ Kilograms have,
Also, in terms of density, d, the mass m can be replaced in the above expression as,
And for Unit volume, the number of atoms are,
So, the number of free electrons/ atoms are,
From eqn.1, the expression for Drift Velocity, Vd
Substituting the known values, it becomes,
Hence the drift speed of free electrons is 0.074mm/s