# Does current fundamentally determine the speed or the quantity of electrons in a curcit?

I am very much a beginner so I apologize for my ignorance. But this has been bothering me for a long time and I found little to no answers.

I know that the definition of Current is charge passing through a point per second measured in A.

My confusion is how the increase in charge passing through a point achieved when we increase the current.

My belief is by increasing the current we increase the speed of charge, thus allowing us to register charges passing through a point more frequently since they are moving in a circle. Would that be true?

I've done lots of googling but this is the only related thread that in a way confirms what i said: https://physics.stackexchange.com/questions/183482/does-a-resistor-slow-down-the-flow-of-electrons-or-just-let-less-electrons-throu ( i apologize the link I provided the first time was wrong)

The answer does not have upvotes and I found no other proof so I am very not confident that this is true.

Could it be that increasing the current releases more particles from the terminal, thus increasing the quantity, instead of speed?

• Current (Ampere) is charge (Coulomb) per second. One Coulomb is a certain fixed number of electrons (because each electron has a certain charge). So more current means more charge per second. It is unrelated to speed of the electrons. It is the number of electrons passing by, not how fast they are going. To know the speed of an electron you need to know how much there are in the medium (wire) they're flowing through. The current flow does not say anything about this. Commented Dec 1, 2016 at 18:38
• Could it be that increasing the current releases more particles from the terminal, thus increasing the quantity Watch out that as increasing the number of electrons increases the charge. In a current loop the number of electrons remains the same, the value of the current only tells you how many electrons pass a certain point in the loop per second. Commented Dec 1, 2016 at 18:44
• Exactly - consider what happens if you have a loop of wire which you pass a magnet through. Current flows, but there is no "terminal". Commented Dec 1, 2016 at 19:23

Assume you have a conductor of volume $A l$ (cross-sectional area = $A$ and length = $l$)

Let $n$ be the number of free electrons per unit volume of the conductor, then the total number of free electrons in the conductor is given by $Aln$.

If $e$ is the charge, then net charge $Q$ is, $Q = A l n e$

Let $v$ be the velocity of electrons due to this potential difference. This is called as drift velocity of the electrons.

Let $t$ be the time taken by an electron to cross the length of the conductor. Then, $t = l/v$.

As current, $i = q/t$, we get $i = A l n e/t$. On substituting $t$ from above equation, we get $i = A n e v$.

So current is directly proportional to drift velocity of the electrons

But this drift velocity is in terms of few millimeters per second. It is because of the large value of $n$ (no. of electrons per unit volume) that effect of velocity gets magnified.

• Thank you for the reply. So since current and velocity are proportional, this confirms that current does not release the number of electrons, but just modifies their speed( drift velocity) Right? Because the B. Hosler's answer seems to say the opposite.
– Sam
Commented Dec 1, 2016 at 19:17
• The number of electrons in any circuit remains the same considering the fact that charge is conserved. One case, where the number of electrons can increase is, under too high voltage, the electrons could get knocked out from the outer shell of the atoms, thereby increasing their count. But fundamental reason is drift velocity Commented Dec 1, 2016 at 19:24
• BTW what is B. Hosler's answer? Are you referring to an author of any book? Commented Dec 1, 2016 at 19:27
• It was a user who answered in parallel with you, but he deleted his comment it appears
– Sam
Commented Dec 1, 2016 at 19:36
• @user3219492 When I increase the voltage accross a fixed load does drift velocity increase or the number electrons flowing increase or both increases ?? Commented Feb 23, 2017 at 9:23

Wikipedia has a good relevant article: "Drift Velocity." The speed of electrons in a medium is directly proportional to current and inversely proportional to cross sectional area. There's a constant of proportionality that depends on the medium. In the example in the article, a 2 mm copper wire carries 1 ampere, and the drift velocity is 2.3 X 10^-5 meters/sec.