Question

If \[62.5 \times {10^{18}}\] electrons per second are flowing through a wire of area of cross-section \[0.1{m^2}\] , the value of current flowing will be:
A. $1A$
B. $0.1A$
C. $10A$
D. $0.11A$

Answer 1

Hint:By the definition of current, we know that it is the rate of flow of charges through an area of cross section. The definition suggests that current is total charge divided by the time taken for the flow of charge through a given area of cross section. We will use this to find the required value of current.

Formula used:
$I = \dfrac{Q}{t}$ and $Q = ne$
where $I$ is the current, $Q$ is the total charge, $t$ is the time taken by the charges to flow, $n$ is the number of electrons and $e$ is the charge on each electron.

Complete step by step solution:
Given: Number of electrons flowing per second, \[n = 62.5 \times {10^{18}}\]
We know that a stream of charged particles, such as electrons or ions, travelling through an electrical conductor or a vacuum is known as an electric current. The net rate of electric charge flowing through a surface or volume is how it is calculated. From the definition of current we have,
$I = \dfrac{Q}{t}$
But we are not given the value of the total charge so we will calculate it using the formula,
$Q = ne$
The value of $n$ is given in the question and we know that the value of $e$ is $1.6 \times {10^{ - 19}}C$.

Thus we get,
$Q = \left( {62.5 \times {{10}^{18}}} \right)\left( {1.6 \times {{10}^{ - 19}}} \right)$
Multiplying them we get,
$Q = 100 \times {10^{ - 1}}$
Thus, $Q = 10C$
Since, we are given the number of flow of charges per second, this implies that, $t = 1\operatorname{s} $
Substituting this value in the formula to find current we get,
$I = \dfrac{{10\,C}}{{1\,s}}$
$\therefore I = 10\,A$

Hence, option C is the correct answer.

Note: One must not confuse between the values of $e$ and $Q$ because $e$ is the charge on a single electron and has a fixed value whereas $Q$ is the total value of charge on the given number of electrons and so it does not have any fixed value. Also, time is taken to be $1s$ because flow of charges per second has been given in the question.