To determine how many electrons flow through the device delivering a current of 5.0 amperes for 10 seconds, we can follow these steps:
1. Understand the Relationship Between Current, Charge, and Time:
- Current ([tex]\( I \)[/tex]) is defined as the rate of flow of electric charge. Mathematically, this is given by [tex]\( I = \frac{Q}{t} \)[/tex], where [tex]\( Q \)[/tex] is the charge in coulombs, and [tex]\( t \)[/tex] is the time in seconds.
- Rearranging the formula, we get [tex]\( Q = I \times t \)[/tex].
2. Calculate the Total Charge ([tex]\( Q \)[/tex]) that Passed Through:
- Given the current [tex]\( I = 5.0 \)[/tex] amperes and the time [tex]\( t = 10 \)[/tex] seconds, we can calculate the total charge.
[tex]\[
Q = 5.0 \, \text{A} \times 10 \, \text{s} = 50.0 \, \text{C}
\][/tex]
- So, the total charge that flowed through the device is 50.0 coulombs.
3. Determine the Number of Electrons:
- The elementary charge ([tex]\( e \)[/tex]), which is the charge of a single electron, is approximately [tex]\( 1.602176634 \times 10^{-19} \)[/tex] coulombs.
- To find the number of electrons ([tex]\( n \)[/tex]) that corresponds to the total charge, we use the formula [tex]\( n = \frac{Q}{e} \)[/tex].
[tex]\[
n = \frac{50.0 \, \text{C}}{1.602176634 \times 10^{-19} \, \text{C/electron}}
\][/tex]
- Solving this, we get:
[tex]\[
n \approx 3.120754537230381 \times 10^{20} \, \text{electrons}
\][/tex]
Therefore, the number of electrons that flow through this device in 10 seconds is approximately [tex]\( 3.121 \times 10^{20} \)[/tex] electrons.
