An aluminum wire of diameter 2.6 mm carries a current of 12 A. How long on average does it take

step 1 In this problem we have given diameter as 2 .6 m m so changing it into meter I can write 2 .6 mu

An aluminum wire of diameter 2.6 mm carries a current of 12...

An aluminum wire of diameter $2.6 \mathrm{mm}$ carries a current of 12 A. How long on average does it take an electron to move $12 \mathrm{m}$ along the wire? Assume 3.5 conduction electrons per aluminum atom. The mass density of aluminum is $2.7 \mathrm{g} / \mathrm{cm}^{3},$ and its molar mass is $27 \mathrm{g} / \mathrm{mol}$.

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Key Concepts

Drift Velocity

Drift velocity is the average velocity that electrons attain when moving through a conductor under the influence of an electric field. It is found by dividing the current by the product of the number density of conduction electrons, the elementary charge, and the conductor's cross?sectional area.

Conduction Electron Density

Conduction electron density is the number of free electrons available for conduction per unit volume in a material. It is calculated using the material's mass density and molar mass, along with Avogadro’s number and the number of conduction electrons provided by each atom in the material.

Wire Cross?Sectional Area

The wire cross?sectional area is critical in establishing the relationship between current and drift velocity. It is determined from the diameter of the wire and is used to compute the area through which electrons flow, affecting the overall electron speed for a given current.

Drift Time Calculation

Drift time is the duration required for an electron to travel a specific distance within the conductor. It is computed by dividing the distance by the drift velocity, linking the microscopic movement of electrons with the macroscopic distance traveled.

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