Question

The number of electrons flowing per second through any cross-section of a wire, if it carries a current of one ampere, is $x\times {10}^{18}$. Find $x$.

Answer 1

Calculation of electric charge
We know current is the amount of charge flowing per second through any cross-section of wire
$i=\frac{\Delta q}{\Delta t}\Rightarrow \Delta q=i.\Delta t$
$\Delta q=$ $\text{charge flowing in time}$ $\Delta t$
Given, $i=1A$
So, charge flowing per second, $\Delta q=1A\times 1S$
$\Delta q=1C$

Calculation of number of electrons
Now, charge of one electron$=-e=-1.6\times {10}^{-19}C$
So, no. of electrons in $1C$ charge $=\Delta qe=\frac{1C}{1.6\times {10}^{-19}C}=6.25\times {10}^{18}$ electrons
Hence, the value of $x$ is $6.25$.