Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.
Sign up to join this community
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.
Why then, is it not defined this way?
There may be some flaws in my logic, as 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.
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.
Mathematically , both are Equivalent. Practically , we might have Difficulties.
There at least 3 Issues or flaws with your way.
(1) When we say "n" , we are leaving it unknown.
When I report my research numbers with n=3 Coulombs in n=3 Seconds , somebody else may reject it saying , only n=45 Coulombs in n=45 Seconds is valid.
Which Definition should I use to claim Equivalence ?
Definition 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 $2 \times 2 = 4$ Amperes.
In non-linear Case , Increase in 1 Items may not give Exact Proportional Increase in other Item.
(3) Matter is Discrete & Quantized. Electron in Particular is Discrete & Quantized.
According to https://en.wikipedia.org/wiki/Ampere :
... 1 Ampere is equal to 1 Coulomb, or $6.241509074×10^18$ Electrons moving past a point in 1 Second ...
... 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 that Case , a few Electrons more or less will not change the over-all value too much.
When we go with "n" Seconds & make it very small , few electrons more or less will change the calculations too much.
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 ) , then "half" Electron or "fractional" Electron has to move which may not occur due to Discrete Nature of Electron. 1 Ampere will be 0 !
When 1 Election randomly moves in that tiny time Interval , 1 Ampere will be too large !
Preventing all those Complications , Definition given is Precise & unambiguous & repeatable , with no Chance for Interpretation & confusion.
Out of all Equivalent Definitions , usually the most Intuitive , useable , unambiguous , useful & repeatable Definition is the Best Choice.
