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In physics, the capacitance of a conductor is (roughly) the net charge accumulated when it is grounded relative to a unit voltage at infinity. The same quantity comes up in mathematics, but we call it capacity instead.

Why don't both communities call this capacity? I can't help but think engineers accustomed to "resistance is what a resistor has" and the word "capacitor" came along and invented "capacitance" by analogy...

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  • $\begingroup$ Actually, engineers used to call them condensers. The invention of the first one is described here: sparkmuseum.com/BOOK_LEYDEN.HTM $\endgroup$ – Peter Diehr Jan 2 '18 at 1:09
  • $\begingroup$ Aside from hopelessness of enforcing terminological uniformity, "capacity" is already used for a different purpose, for the maximal output electrical generator can produce. $\endgroup$ – Conifold Jan 3 '18 at 1:30
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    $\begingroup$ @Conifold, I'm not interested in enforcing anything. I'm actually curious about the history of the word "capacitance." $\endgroup$ – fourierwho Jan 3 '18 at 16:11
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Because the word "capacity" has a very general meaning, whereas capacitance is a very specific property in the theory.

For example, resistance could be reformulated as "the capacity to resist", and capacitance could be reformulated as "the capacity to hold (charge)". We could also talk about "current-carrying capacity", or "battery capacity". But in each case the type or nature of the capacity being referred to is different.

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