Question

A current of $ 4.8\;A $ is flowing in a conductor. The number of electrons passing per second through the conductor will be:
(A) $ 3\times {{10}^{20}} $
(B) $ 76.8\times {{10}^{20}} $
(C) $ 7.68\times {{10}^{-19}} $
(D) $ 3\times {{10}^{19}} $

Answer 1

Hint: Here, the current flowing through can be defined as the charge passing through a cross section per unit time. And the total charge can be defined as the product of the charge of the electrons and the number of electrons, from which the number of electrons can be found.

Complete answer:
Here, we are given that $ 4.8\;A $ current is passing through the conductor.
Now, we know that the current (in amperes) flowing through a cross section can be defined as the amount of charge (in coulomb) passing through the considered cross section per unit time (in seconds).
From this definition of current, we can say that $ 4.8\;C $ current is flowing through the cross section in one second.
Now, we know that the charge of an electron is $ e=1.6\times {{10}^{-19}}C $
So if one electron passes through a cross section, we say that $ e $ amount of charge has passed through the cross section.
Hence, if $ n $ number of electrons pass through a cross section, we can say that $ n\times e $ amount of charge has passed through the cross section.
Hence, the equation can be expressed as,
 $ Q=n\times e $
From the given data, substituting the values,
 $ \therefore 4.8C=n\times (1.6\times 10^{-19}C) $
 $ \therefore n=\dfrac{4.8}{1.6\times {{10}^{-19}}} $
Shifting the power to the numerator,
 $ \therefore n=3\times {{10}^{19}} $
Hence, the correct answer is Option $ (D) $ .

Note:
We know that the charge carried by a single electron is very small i.e. in the negative powers of $ \;10 $ . Hence if we need a current passing through a cross section to be in amperes, we need a huge amount of electrons i.e. in the high positive power of $ \;10 $ . Hence, we can verify if we calculated the correct answer by checking if the power of $ \;10 $ is very high and positive.