Question

The number of free electrons per 10 mm of an ordinary copper wire is about $2 \times {10^{21}}$. The average drift speed of the electrons is 0.25 mm/sec. The current flowing is
(A) 0.8 A
(B) 8 A
(C) 80 A
(D) 5 A

Answer 1

To answer this question we have to first derive the expression of Q or charge from the number of electrons and the charge present in one electron. Once done we have to find the value of time from the speed and distance relation. At the end we have to find the value of current from the values of charge and time.

Complete step by step answer
From the question we can see that,
The number of electrons is denoted by n which is $2 \times {10^{21}}$.
The average drift speed is given as 0.25 mm/s
Now,
We know that the formula to calculate the charge Q is given as: $Q = n \times e$
The value of e is given as $1.6 \times {10^{ - 19}}$.
So, after we put the values in the expression, we get the value of Q as:
$Q = 2 \times {10^{21}} \times 1.6 \times {10^{ - 19}}$
Hence the value of Q is 320 C.
Now the formula of speed is given as Distance / Time. So, the value of Time is defined to be
Distance / Speed.
Therefore,
$T = \dfrac{D}{s}$
Now we have to put the values in the above expression to get:
$T = \dfrac{{10}}{{0.25}} = 40$
The value of current is given as I = Q /T.
Now we have to put the values in the above expression to get:
$I = \dfrac{{320}}{{40}}$
So, the value of I is 8 A. So, the current flowing is 8 A.

Hence the correct answer is option B.

Note: It should be known to us that electron charge is a fundamental concept of Physics that is expressed in the form of a naturally occurring unit of electric charge. The value of unit electron charge is specifically given as $1.602176634 \times {10^{ - 19}}C$.
We should know that in addition to all the electrons that are existing in the free state by the charged subatomic particles which are discovered to have an electric charge being equal to the value of some whole numbers multiplied to it.