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If I use 10mA for 40 milliseconds. How much current have I used in mAh (milliamperes per hour)?

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    \$\begingroup\$ None because mAh is a measurement of charge not current. - 3600 Coulombs = 1 AHr \$\endgroup\$ – JIm Dearden May 30 '13 at 9:15
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    \$\begingroup\$ And mAh is milliamp-hours, not milliamps per hour. \$\endgroup\$ – Olin Lathrop May 30 '13 at 13:02
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40 milliseconds is 0.04/3600 hours = 1.1111e-5 hours therefore you have used 1.1111e-4 mAh.

= 0.0001111 mAh

Please note that you haven't used x amount of milli-amps per hour. You have used 10mA for 1.1111e-5 hours - the two numbers multiply

An ampere-hour is a unit of charge

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Try using dimensional analysis:

$$ \require{cancel} \dfrac{10mA \cdot 40\cancel{m}\cancel{s}}{1} \dfrac{1\cancel{min}}{60\cancel{s}} \dfrac{1hr}{60\cancel{min}} \dfrac{1}{1000\cancel{m}} = 0.000\overline{111}mA\cdot hr $$

The fractions represent things we know to be true:

  1. there are 60 seconds in a minute
  2. there are 60 minutes in an hour
  3. there are 1000 mili- in 1

For each of these fractions, the thing in the numerator is equal to the thing in the denominator. Anything divided by the same thing is equal to 1. So really, we are just multiplying your original quantity by 1, but changing the units.

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