Question

A current of $1A$is drawn by a filament of an electric bulb. Number of electrons passing through a cross-section of the filament in $16s$ would be roughly
A. ${10^{20}}$
B. ${10^{16}}$
C. ${10^{18}}$
D. ${10^{23}}$

Answer 1

Substitute the given values in the current equation to obtain the number of electrons. Keep in mind that even though the charge of an electron is negative, we need to use the absolute value here.

Formula used
$i = \dfrac{{nq}}{t}$ where $i$ is the current flowing through the conductor, $q$ is the charge, $t$ is the time taken and $n$is the number of electrons.

Complete step by step answer
Electric current is defined as the flow of electric charge (electrons) per unit time through a conducting medium. Its SI unit is Ampere and is symbolized by $A$. It is measured using a device called the ammeter.
The flow of electric current is due to the stream of charged particles such as electrons from a region of higher potential to a region of lower potential. This means that current can only flow through a medium when there is a potential difference present.
Now, we can solve the question given by using the definition of current which gives us the relation,
$i = \dfrac{{nq}}{t}$ where $i$ is the current flowing through the conductor, $q$ is the charge, $t$ is the time taken and $n$is the number of electrons.
Using this formula, we have $i = 1A$, $q = 1.6 \times {10^{ - 19}}C$and $t = 16s$
$\begin{gathered} n = \dfrac{{i \times t}}{q} \\\ \Rightarrow n = \dfrac{{1 \times 16}}{{1.6 \times {{10}^{ - 19}}}} = {10^{20}} \\\ \end{gathered}$
Therefore, the number of electrons passing through the cross-section of the filament is ${10^{20}}$

Thus, the correct option is A.

Note: In a conductor, the total current is due to the flow of electrons which are negative charge carriers. However, in case of semiconductors, the flow of current is due to both positive and negative carriers. Unlike conductors, semiconductors can only conduct electricity at very high temperatures. This is due to the fact that semiconductors have a negative coefficient of resistance with temperature. Which means that their resistance decreases with increase in temperature.