Question

If the charge on an electron is \[1.6\times {{10}^{-19}}\]coulombs, how many electrons should pass through a conductor in one second to constitute 1 ampere current?

Answer 1

Hint: We want here to determine how many electrons should be needed to move so that the current constituted is one ampere. We can use the Coulomb relationship between the charge and current to determine the value.

Complete step by step answer:
Given charge on one electron is q= \[1.6\times {{10}^{-19}}\] C.
The current is 1 A and time t= 1 s
We know q=It and from the quantization of charge q = one, where n is the number of electrons and e is the charge on one electron.
In both the equations LHS are the same, so RHS must also be the same.
It=ne
\[\begin{align}
&\Rightarrow n=\dfrac{I\times t}{e} \\
&\Rightarrow n=\dfrac{1\times 1}{1.6\times {{10}^{-19}}} \\
&\Rightarrow n=6\times {{10}^{18}} \\
\end{align}\]
So, the number of electrons needed to be passed in one second to constitute a current of one ampere is \[6\times {{10}^{18}}\].

So, \[6\times {{10}^{18}}\]electrons are the answer.

Additional Information:
Quantization of charge means that charge can assume only certain discrete values. And not any general value. The observed value of the electric charge of a particle will be integral multiples of (e), charge is also a conserved quantity, that is it cannot be created and nor be destroyed but it can be transferred from one body to another

Note: We had just used the relationship between quantization of charge and Ampere formula to arrive at our answer. . It is the negative charge which moves because the positive charge sits inside the nucleus and is not free to move.