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1 Ampere is defined as the flow of 1 Coulomb of charge in one second. However, I do not understand why it cannot be defined as the flow of n Coulomb of charge in n seconds.

This definition is fundamentally the same as the earlier one and seems to be more precise, since it takes away the ambiguity of the flow of 1 electron per second.

Why then, can it not be defined this way?

There may be some flaws in my logic, since I am a beginner, but I am not able to find any sources which tackle this particular issue. I am familiar with the basics of electricity.

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    $\begingroup$ Do you mean to ask about different letters perhaps 'n' and 'm' where they don't have common factors? Because otherwise they would just cancel and leave unity as before. $\endgroup$
    – Triatticus
    Commented Sep 9, 2023 at 6:34
  • $\begingroup$ No, I had meant n Coulomb in n seconds, because I was confused why it couldn't be defined the way I have written it. $\endgroup$ Commented Sep 10, 2023 at 11:39

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Mathematically, both are equivalent. Practically, we might have difficulties.

There at least 3 issues or flaws with your proposition.

  1. When we say $n$, we are leaving it unknown.
    When I report my research numbers with $n = 3$ coulomb in $n = 3$ seconds, somebody else may reject it saying that only $n = 45$ coulomb in $n = 45$ seconds is valid. Which definition should I use to claim equivalence? Definitions must be totally unambiguous & repeatable.

  2. Theoretically, how can I "a priori" know that it is linear? Hypothetically, 2 coulomb in 2 seconds may be $2 \times 2 = 4$ ampere. In a non-linear case, the increase in one quantity may not give an exactly proportional increase in another quantity.

  3. Matter is discrete & quantized. Electrons in particular are discrete & quantized as well.

According to Wikipedia:

1 ampere is equal to 1 coulomb, or $6.241509074×10^{18}$ electrons moving past a point in 1 second.

1 ampere is defined by fixing the elementary charge $e$ to be exactly $1.602176634×10^{−19}$ coulomb, which means 1 ampere is the electric current equivalent to $10^{19}$ elementary charges moving every $1.602176634$ seconds or $6.241509074×10^{18}$ elementary charges moving in 1 second.

In such a case, the decrease or increase of a few electrons will not change the overall value by much.

When we go with $n$ seconds & make it very small, a few electrons increasing or decreasing will change the calculations quite a lot.

We can make $n$ so small (around $10^{-19}$ seconds) that exactly 1 electron has to move across the point.

Then we can make $n$ even smaller (around $10^{-20}$ seconds), that a "half" electron or "fractional" electron has to move which may not occur due to the discrete nature of electrons. 1 ampere will be zero!

When 1 electron randomly moves in that tiny time interval, 1 ampere will be too large!

For preventing all these complications, a definition which is precise & unambiguous & repeatable, with no chance for reinterpretation & confusion.

Out of all equivalent definitions, usually the most intuitive, useable, unambiguous, useful & repeatable definition is the best choice.

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That’s how it is defined, using the 1’s rather than the n’s.

You’re not really missing anything about the math/physics of the situation. Yes your definition would indeed give the same result. It’s just not the definition of an ampere. If your name was André-Marie Ampère, maybe we’d have a different definition.

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