Question

A current of 1.6mA flows through a conductor. If charge on an electron is\[ - 1.6 \times {10^{( - 19)}}\]Coulomb, then find the number of electrons that will pass each second across the cross section of the conductor.
\[
A. {10^5} \\
B. {10^4} \\
C. {10^{(16)}} \\
D. {10^9} \\
\]

Answer 1

Hint:We will use the relationship between electric charge and electric current to obtain the number of electrons passing through the cross section. Electric current is directly proportional to electric charge and inversely proportional to the time passed. The SI unit of charge is coulomb and SI unit of time is seconds.

Complete step by step answer:
The flow of electric charges produces an electric current. If there is a net amount of charge Q which is flowing across a cross sectional area in time t, then the electric current is given by the formula below:
\[I = \dfrac{{nQ}}{t}\] ,
Where \[I\] is the electric current through the cross sectional area, t is the time taken and n is the number of electrons.

Thus the amount of charge flowing per unit time across any cross sectional area of a conductor held perpendicular to the direction of the flow of charge is defined as an electric current \[I\]. In metallic conductors, current is due to the motion of negatively charged particles, that is the electrons. Since the charge is measured in coulombs and time in seconds, so the unit of electric current is coulomb/Sec or ampere (A). The ampere is the SI unit of the conductor. Thus, a wire is said to carry a current of one ampere when a charge at the rate of one coulomb per second is flowing through it.

Thus the number of electrons per second would be:
\[ n = \dfrac{I}{Q} \\
\Rightarrow n = \dfrac{{1.6 \times {{10}^{( - 3)}}}}{{1.6 \times {{10}^{( - 19)}}}} \\
\therefore n = {10^{(16)}} \\
 \]
Thus option C is the correct answer.

Note: Here, if instead of electrons, there were positrons in the system, even then, the current in the system would have been the same. But if instead of the whole cross section having only electrons or positrons, there were some amount of positrons along with electrons, as they have opposite charges, the total current in the system would be lesser.