Electrical phenomena are defined by the movement and storage of electric charge. The Coulomb (C) is the standard SI unit used to quantify electrical charge. In practical applications, such as measuring battery capacity, the Ampere-hour (Ah) is the preferred unit. This article clarifies the definitions of these units and explains the mathematical relationship connecting the Ampere-hour back to the Coulomb.
Defining the Fundamental Units of Electricity
The Ampere (A) is the standard unit for measuring electric current, representing the rate at which charge flows. One Ampere is formally defined as the current that moves one Coulomb of charge past a fixed point in a conductor every second. This establishes the Ampere as a flow rate.
The Coulomb (C) measures the actual quantity of electrical charge, independent of time. One Coulomb represents approximately \(6.24 \times 10^{18}\) individual electrons. This unit is the fundamental building block for quantifying the total charge transported in a circuit.
Understanding the Ampere-Hour
The Ampere-hour (Ah) is a unit of charge designed for practicality in energy storage applications, such as consumer electronics and electric vehicle batteries. It measures the total charge a battery can deliver over time. The Ampere-hour is not an SI base unit but is a convenient metric that relates directly to a device’s runtime.
A battery rated at 1 Ampere-hour is capable of supplying a current of one Ampere for one hour. Alternatively, it could supply half an Ampere for two hours, or two Amperes for half an hour. This calculation allows engineers and consumers to easily estimate battery life based on a device’s current draw.
The Step-by-Step Conversion
The conversion from Ampere-hours to Coulombs is a straightforward process based on time conversion, since both units measure the same physical quantity: electric charge. The Ampere is defined as one Coulomb per second (1 A = 1 C/s).
To find the charge in one Ampere-hour, the time component must be converted from hours to the SI unit of seconds. One hour contains 60 minutes, and each minute contains 60 seconds, totaling 3,600 seconds.
The conversion equation multiplies the current (1 Ampere) by the time (1 hour in seconds): \(1 \text{ Ah} = 1 \text{ A} \times 1 \text{ h}\). By substituting the Ampere with Coulombs per second and the hour with 3,600 seconds, the calculation is \(1 \text{ Ah} = (1 \text{ C/s}) \times (3,600 \text{ s})\).
This multiplication results in the final conversion factor: one Ampere-hour is precisely equal to 3,600 Coulombs. For example, a 3 Ampere-hour (3 Ah) battery stores a total charge of 10,800 Coulombs.