Ampère-hour

An ampere-hour or amp-hour (symbol: A⋅h or A h; often simplified as Ah) is a unit of electric charge, having dimensions of electric current multiplied by time, equal to the charge transferred by a steady current of one ampere flowing for one hour (3,600 seconds), thus equal to 3600 A⋅s or Coulomb.

The commonly seen milliampere-hour (symbol: mA⋅h, mA h, often simplified as mAh) is one-thousandth of an ampere-hour (3.6 coulombs).

Use

The ampere-hour is frequently used in measurements of electrochemical systems such as electroplating and for battery capacity where the commonly known nominal voltage is understood.

A ''milliampere second'' (mA⋅s) is a unit of measurement used in X-ray imaging, diagnostic imaging, and radiation therapy. It is equivalent to a ''millicoulomb''. This quantity is proportional to the total X-ray energy produced by a given X-ray tube operated at a particular voltage. The same total dose can be delivered in different time periods depending on the X-ray tube current.

To help express energy, computation over charge values in ampere-hour requires precise data of voltage: in a battery system, for example, accurate calculation of the energy delivered requires integration of the power delivered (product of instantaneous voltage and instantaneous current) over the discharge interval. Generally, the battery voltage varies during discharge; an average value or nominal value may be used to approximate the integration of power.

When comparing the energy capacities of battery-based products that might have different internal cell chemistries or cell configurations, a simple ampere-hour rating is often insufficient.

In other units of electric charge

One ampere-hour is equal to (up to 4 significant figures):
* 3,600 coulombs
* 2.247 × 10²² elementary charges
* 0.03731 faradays
* 1.079 × 10¹³ statcoulombs ( CGS-ESU equivalent)
* 360 abcoulombs ( CGS-EMU equivalent)

Examples

*An AA size dry cell has a capacity of about 2,000 to 3,000 milliampere-hours.
*An average smartphone battery usually has between 2,500 and 6,000 milliampere-hours of rechargeable electric capacity.
*Automotive car starter batteries vary in capacity but a large automobile propelled by an internal combustion gasoline engine would have about a 50-ampere-hour 12 V battery capacity.
*Battery electric vehicle capacities are usually given in kWh, but in 2013, the BMW i3 60 Ah was named after the capacity of one of its 96 cells, for a total of 96x3.6Vx60Ah=20,736Wh with about 18 kWh usable energy, to match the number of the entry level Tesla Model S60 which had 60 kWh. Later BMW i3 had 94 Ah and 120 Ah batteries, each topping Tesla's S85, S90 and S100 designations.
*Since one ampere-hour can produce 0.336 grams of aluminium from molten aluminium chloride, producing a kg of aluminium required transfer of at least 2980 ampere-hours.T. L. Brown, H. E. Lemay Jr, "Chemistry the Central Science", Prentice-Hall, 1977 page 562 One kilogram of aluminium commonly requires 15.37 kWh, thus electric power represents about 20 to 40% of the cost of producing aluminium.

See also

* Electrochemical equivalent
*Kilowatt-hour (kW⋅h)

References

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Units of electrical charge
Non-SI metric units