Sure! Let's solve this step-by-step.
1. Identify the given values:
- Current ([tex]\( I \)[/tex]) = 5.0 amperes (A)
- Time ([tex]\( t \)[/tex]) = 10 seconds (s)
2. Understand the relationship:
The total charge ([tex]\( Q \)[/tex]) that flows through a device is given by the formula:
[tex]\[
Q = I \times t
\][/tex]
where [tex]\( I \)[/tex] is the current and [tex]\( t \)[/tex] is the time.
3. Calculate the total charge [tex]\( Q \)[/tex]:
[tex]\[
Q = 5.0 \, \text{A} \times 10 \, \text{s} = 50.0 \, \text{coulombs (C)}
\][/tex]
So, the total charge flowing through the device is 50.0 coulombs.
4. Know the charge of a single electron:
The charge of a single electron ([tex]\( e \)[/tex]) is [tex]\( 1.60219 \times 10^{-19} \, \text{coulombs} \)[/tex].
5. Calculate the number of electrons:
The number of electrons can be found using the formula:
[tex]\[
\text{Number of electrons} = \frac{\text{Total charge}}{\text{Charge of one electron}}
\][/tex]
Substituting the values, we get:
[tex]\[
\text{Number of electrons} = \frac{50.0 \, \text{C}}{1.60219 \times 10^{-19} \, \text{C/electron}}
\][/tex]
6. Perform the division:
[tex]\[
\text{Number of electrons} \approx 3.120728502861708 \times 10^{20}
\][/tex]
Therefore, the number of electrons that flow through the device in 10 seconds is approximately [tex]\( 3.120728502861708 \times 10^{20} \)[/tex].
