To determine how much level the battery been charged, why do we use voltage, but not capacity?

The reason we use voltage, and not capacity to determine how much charged a battery is stems from our difficulty in measuring capacity. Voltage is simple to measure — if you’ve ever used s voltmeter to measure a AA battery, you understand how trivial it is to measure voltage.

Capacity, however, is nearly impossible to measure accurately. We can measure how much energy is going into a battery (at least somewhat accurately), but we can’t measure how much is actually in the battery.

Think of it like beakers of water. For voltage, the beaker is transparent, and we can easily see the amount of water in the beaker in the same way we can measure voltage whenever we like. On the other hand, we have the beaker representing capacity, and it’s opaque — we can’t see through it, and so the only way to know how much is inside is to empty it and measure the water (energy) as it’s leaving the beaker (battery).

Because amperage and voltage are intertwined, as we will discuss later in detail, the voltage of a battery does correlate, approximately, to the capacity left in the battery, and while there are times when the voltage can deceive you, in general, it’s okay to rely on voltage as our primary measure of how full a battery is.