How many electrons flow through a point in a wire in 3.00 of seconds, if there is a constant current of 4.00 amps?
We can call the time value given of 3.00 seconds 𝑡. And the current of 4.00 amps, we’ll call 𝐼. We want to know the number of electrons flowing through a point in a wire. We’ll call that number capital 𝑁. We can start by recalling the definition of electrical current. Current 𝐼 is equal to the amount of charge 𝑄 flowing past a point in sometime 𝑡 in seconds.
In our case, both 𝐼 and 𝑡 are quantities given in the exercise statement. If we rearrange this equation to solve for 𝑄, seeing that it’s 𝐼 times 𝑡, we know it’s not exactly 𝑄 we want to solve for but 𝑁 the number of charged particles, particularly electrons, flowing through a point in the wire. The total charge 𝑄 represented in this current is equal to the charge on an individual electron times the number of electrons in the current. In other words, 𝑄 equals the charge on an electron times 𝑁 which equals 𝐼 times 𝑡.
We can now rearrange this equation to solve for 𝑁. When we do, we see that 𝑁 is 𝐼 times 𝑡 divided by the charge on an electron. If we assume positive charge carriers as is assumed in conventional current, then we’ll take the magnitude of that charge of an electron in our equation. We can recall that the charge on a single electron is negative 1.6 times 10 to the negative 19th coulombs. Knowing that, we know all three values to plug in and solve for 𝑁.
When we do and enter these values on our calculator, we find that 𝑁 is 7.50 times 10 to the 19th. This is the number of electrons passing through a point in the wire under these conditions.