Question

One ampere $(1A)$ current is is drawn by a filament of an electric bulb. Number of electrons passing through a cross-section of the filament in $16$ seconds would be roughly

• A. ${10}^{20}$
• B. ${10}^{16}$
• C. ${10}^{18}$
• D. ${10}^{23}$

Answer 1

The correct option is A

${10}^{20}$

Step 1. Given data

1. Current $\mathrm{I}=1\mathrm{A}$
2. Time period $\mathrm{t}=16\mathrm{s}$
3. Charge of electron $\mathrm{e}=1.6\times {10}^{-19}\mathrm{C}$

Step 2. Formula used

$\mathrm{I}=\frac{\mathrm{Q}}{\mathrm{t}}=\frac{\mathrm{Ne}}{\mathrm{t}}$ [Since, $\mathrm{Q}=\mathrm{Ne},$ where $\mathrm{N}$ is the number of electrons crossing in time $\mathrm{t}$]

$\Rightarrow \mathrm{N}=\frac{\mathrm{It}}{\mathrm{e}}$

Step 3. Find the number of electrons passing through a cross-section of the filament

The number of electrons is passing through a cross-section of the filament is

$\mathrm{N}=\frac{\mathrm{It}}{\mathrm{e}}=\frac{1\times 16}{1.6\times {10}^{-19}}={10}^{20}$

Hence, option A is correct.