Question

How many electrons flow through a wire, when 1A current passes for a millisecond?

Answer 1

Hint: Current flowing through a wire is the charge flowing through it per unit time. The total charge is defined as the product of total number of charge carriers with the basic unit of charge e.
Formula used:
Current flowing through a wire is given as

$I={\displaystyle \frac{q}{t}}$
where $q=ne$ and $e=1.6\times {10}^{-19}C$. Here n = no. of charge carriers or electrons.

Step by step solution:
The flow of electric charge constitutes an electric current which is defined as the rate of flow of charge.

$I={\displaystyle \frac{q}{t}}$

The smallest amount of charge that can exist is defined as

$e=1.6\times {10}^{-19}C$ and total charge on a body is equal to the no. of charge carriers times the basic unit of charge.

Using this information, we can calculate the number of electrons flowing through a wire. We are given

$$\begin{gathered} I=1A \\ t=1ms={10}^{-3}s \end{gathered}$$


Now, $I={\displaystyle \frac{ne}{t}}\Rightarrow n={\displaystyle \frac{It}{e}}$


Putting various values, we get

$$\begin{gathered} n={\displaystyle \frac{1\times {10}^{-3}}{1.6\times {10}^{-19}}}=0.625\times {10}^{16} \\ \Rightarrow n=6.25\times {10}^{15} \end{gathered}$$

This is the number of electrons which flow through a wire when 1A current passes through it for 1ms which is the required answer.

Additional Information:
The current flowing through a wire is directly proportional to the potential difference across the wire. This is called the Ohm’s law and can be represented as follows:

$$\begin{gathered} I\propto V \\ I={\displaystyle \frac{V}{R}} \end{gathered}$$

Where 1/R is the constant of proportionality, R is called resistance across the wire and 1/R is called the conductance of the wire.

Note: The basic unit of charge e is defined as the charge on an electron. It is always fixed and charges less than it doesn’t exist. All the charge found in nature is integral multiple of this basic unit of charge