Question

Ram knows that relation between current and drift velocity is $I=neA{V}_d$_.He is trying to solve a question where the current in a cylindrical conductor is to be calculated. The total number of electrons In the conductor is given as ${10}^{26}$, their drift speed is ${10}^{-2}cm/s$ and the cross- sectional area is $1m^2$ uniform throughout the conductor and its length is given as 2m
He writes this equation $I=neA{V}_d$
$={10}^{26}\times 1.6\times {10}^{-19}\times 1\times \frac{{10}^{-2}}{100}$
He gets a terribly wrong answer.
This is because

• A. Ram is not using the correct value of the charge of an electron
• B. Ram converted the units of speed into SI units wrongly
• C. Ram doesn’t know that n stands for number of electrons per unit volume and not total number of electrons.
• D. None of the above! Ram must have done some calculation mistake.

Answer 1

The correct option is C Ram doesn’t know that n stands for number of electrons per unit volume and not total number of electrons.

So what’s given in the question as number of electrons is the total number of electrons in the material. Not the number of electrons per unit volume. So Ram should have divided this number by the volume before plugging it in the equation. So, $n=\frac{{10}^{26}}{\left(2x1\right)}$