Question

A \[1.6\,mA\] current flowing in conducting wire then the number of electrons flowing per second is
A. \[{10^{11}}\]
B. \[{10^{16}}\]
C. \[{10^{19}}\]
D. \[{10^{15}}\]

Answer 1

Hint:The relationship between the physical quantities current and charge needs to be established in order to resolve the problem. After finding the relationship, we must divide the obtained charge by the electron's fundamental charge to determine the number of electrons. This is done because the total charge can be written as the product of the charge on each electron and the number of charges (that is, number of electrons).

Formula used:
Current, $I = \dfrac{Q}{t}$
where $Q$ is the total charge and $t$ is the time for which the charge flows.
Also, the total charge, $Q = ne$ where $n$ is the number of electrons and $e$ is the charge on each electron.

Complete step by step solution:
Given: Amount of current flowing, $I = 1.6\,mA$
Converting this in SI unit, we get $I = 1.6 \times {10^{ - 3}}\,A$
Time for which the charges flow, $t = 1\sec $
The rate at which charges move through a unit cross-sectional area in a predetermined amount of time is known as the current. Ampere is the SI unit for current.

When we refer to the movement of charges in a conductor, we actually mean the conductor's free electrons. We know that,
$I = \dfrac{Q}{t}$ ...(1)
Also, $Q = ne$ ...(2)
Where the quantity $n$ should always be positive since the charge is quantized in this case, or exists in integral multiples of the fundamental charge, $e$. The fundamental charge that the electron carries is known as e having the value of $1.6 \times {10^{ - 19}}C$ .

Now we substitute equation (2) in equation (1), we get,
$I = \dfrac{{ne}}{t} \\ $ ...(3)
From equation (3), we get,
$n = \dfrac{{I\,t}}{e} \\ $ ...(4)
Substituting the known values in equation (4), we get,
$n = \dfrac{{1.6 \times {{10}^{ - 3}} \times 1}}{{1.6 \times {{10}^{ - 19}}}} \\ $
Solving this, we get,
$\therefore n = {10^{16}}$
Thus, ${10^{16}}$ electrons flow through the wire per second.

Hence, option B is the correct answer.

Note: An important point to keep in mind is to convert all the physical quantities into SI systems of units. Also, while solving this question one can first find the value of $Q$ , the total charge, and then divide it by the charge on a single electron to obtain the number of electrons flowing through the wire per second.