Question

A copper wire has a diameter of 4.00mm. If the drift speed of the electrons in the wire is 0.0002 m/s, calculate the current flowing in the wire. Assume each copper atom contributes two free electrons to the current. The density of copper is 8.93 g/cm^3 and it's molar mass is 63.5 g/mol.

Answer 1

number density of electron(n)-

n = $\frac{\rho N_a}{M}$

Here, $\rho$ is the density of material in g/m³, N_a is Avagadro Number, M is the molecular mass in g/mol.

n = $\frac{8930000 \times 6.022 \times 10^{23}}{63.5}$

= 8.5 $\times$ 10²⁸ atoms per m³

Current in the conductor (I)-

I = neAv_D

Here, e is the electronic charge in C, A is the cross-section area of wire in m², v_D is the drift velocity of electron in m/s

I = (2 $\times$ 8.5 $\times$ 10²⁸)(1.6 $\times$ 10^-19)($\pi \times$ 4 $\times 10^{-6}$ )(0.0002)

= 68.36 A