# Are the Amp and coulomb equivalent?

1 coulomb is 1 ampere per second and 1 ampere is 1 coulomb per second therefore they are always equivalent. They would only be different if you changed the time but the units themselves are based only on the current/charge in 1 second. So how come their SI definition is not the same?

• 1 Coulomb is 1 Ampere flowing for one second, which is not the same as one Ampere per second. – Javier Aug 19 '17 at 3:06
• @Javier so in my question, should "ampere" be replaced with "ampere-second?" – Sigma Aug 19 '17 at 3:12
• @Sigma, no Coulomb should be replaced by ampere-second – Martin Beckett Aug 19 '17 at 3:17
• This is just wrong. If $1\text{C}$ is $1\text{A/s}$ and $1\text{A}$ is $1\text{C/s}$, then $1\text{C}$ would be the same as $1\text{C/s}^2$ which doesn't make any sense. – alephzero Aug 19 '17 at 17:47

## 2 Answers

You multiply current and time to get charge. So, a coulomb is equal to one amp-second, not one amp per second, which would be division. It's the same as multiplying speed and time to get distance. Speed is km/hr, distance is (km/hr)*(hr), speed times time, which is distance.

• To be sure, the product of current and time has dimension of charge but it isn't the case that it is charge. Similarly, the product of speed and time gives dimension of distance but... – Alfred Centauri Aug 19 '17 at 3:44
• Alright, who let the mathematician in here? – Mark H Aug 19 '17 at 3:46

1 Ampere is the "flow" of 1 Qoulomb of charge per second, or 6.25 x 10^18 electrons per second. Now charge a 1 Farad capacitor to a potential of 1 Volt. The capacitor now holds 6.25 x 10^18 electrons, or 1 Qoulomb of charge. But they are not "flowing" (no per second component = zero amperes).

• Where in the world is charge measured in "Qoulombs"? – The Photon Sep 17 at 17:37
• Arthur, a charged capacitor doesn't hold excess electrons does it? – Hal Hollis Sep 17 at 17:41
• Charge is the ability of a conductive surface to hold electrons. By definition, this is 1 Coulomb per 6.25 trilion-trillion (10^18) electrons. Apply 2 volts to a 1 farad capacitor and current (electrons) will accumulate in the capacitor, until the counter voltage of the capacitor reached 2 volts. Then current (amperes) stops flowing. At this time, there are twicw as many "coulombs" of charge contained in the capacitor or 12.5 x 10^18 electrins. – Arthur Watkins Sep 18 at 19:02