# Why can the Ampere not be defined as the flow of $n$ Coulomb in $n$ seconds?

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.

• 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. Commented Sep 9, 2023 at 6:34
• 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. Commented Sep 10, 2023 at 11:39

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.

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.