Two students calculate the charge flowing through a circuit. The first student concludes that 300 C of charge flows in 1 minute. The second student concludes that $3.125\times 10^{19}$ electrons flow per second. If the current measured in the circuit is 5 A, which of the two students (if any) have performed the calculations correctly?

Video Transcript

This is College Physics Answers with Shaun Dychko. Two students are calculating the amount of charge that flows through a circuit and they are all measuring the same thing; it turns out that both students are correct they are just expressing their answers in different ways. So the first student talks about the amount of charge that passes through the circuit in a minute. So current is the amount of charge that passes through a circuit divided by time and we can multiply both sides by t to solve for Q and we get the amount of charge then it's going to be 5 amps times 1 minute, which we have to express in seconds because we always want mks units in our formulas— meters, kilograms and seconds— and so we have 5 amps times 60 seconds and that is 300 coulombs so the first student is correct. The second student says that there are 3.125 times 10 to the 19 electrons flowing per second through the circuit. So we can express this 5 amps—which the two students agree on— in terms of electrons per second by multiplying the coulombs by 1 electron for every 1.602 times 10 to the minus 19 coulombs— this is the elementary charge the number of coulombs on a single electron— the coulombs cancel and we will be left with electrons per second and that works out to 3.12 times 10 to the 19 electrons per second— just as the second student said— so both students are correct.