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I am a little confused. I have been told that electrons carry a charge of $-1.6 \cdot 10^{-19}$ coulombs, and that 1 coulomb is $6.25 \cdot 10^{18}$ electrons, and $1 \,\mathrm{A}$ is the current from when $1$ coulomb of charge flows in $1$ second.

However, when we are asked questions such as 'How many electrons pass a point when a current of $0.4\,\mathrm A$ flows for $900$ seconds?'

I understand $Q = I \cdot t = 0.4 \cdot 900 = 360\,\mathrm C$ and

$$\text{no. of electrons} = \dfrac{\text{total charge}}{\text{charge of one electron}}$$

so

$$\text{no. of electrons} = \frac{360}{-1.6 \cdot 10^{-19}} = -2.25 \cdot 1021 $$

So do I just give my answer as a negative number of electrons? Or do I just totally ignore the negative sign?

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    $\begingroup$ It is a sign convention. Note also that the question did not ask which way the electrons went. $\endgroup$ – Jon Custer Sep 12 '16 at 13:48
  • $\begingroup$ conventionnal sense of the current ... $\endgroup$ – user46925 Sep 12 '16 at 13:49
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    $\begingroup$ Related: physics.stackexchange.com/q/17109/2451 and links therein. $\endgroup$ – Qmechanic Sep 12 '16 at 14:35
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For questions like these, you can get away with just ignoring the minus sign.

A more rigorous version would be to recognize that what's actually happening is that you have $2.25\cdot 10^{21}$ electrons traveling in the opposite direction of the current. It's that opposite direction that accounts for the minus sign.

Unfortunately for electrical engineers and physics undergrads everywhere, when Ben Franklin first hypothesized that electricity might be a flow of particles, there was no way of knowing which charge the electron had. So he picked a direction. Sadly, he did not pick the right one. Many years later we identified that the primary charge carrier was, in fact, the electron and had a negative charge. Thus, everything we do with current is backwards!

XKCD comic

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The total number of electrons is the answer, which is a natural number (positive or 0). You obtain it by counting the electrons.

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