Power (watts) = voltage (v) * current (amps)
Multiple both sides by hours to get power over time.
Phone batteries are fixed voltage and refers to how many amps-hours it can deliver in total. Multiply by 3.8 (typical voltage of phone battery) or the voltage of the battery to get kWh.
Where as cars batteries can support various voltages. So you just rate the total capacity as kwh since some of the car might use 12v, some might use 5v, some might use 120v. Theres no way to know the total capacity if you used amp-hours.
kWh is more useful if your device uses more current at lower voltage to make up the same power usage. mAh is more useful if your device uses the same current regardless of voltage, and is easier to measure. Modern phones do often use switching regulators, but many battery operated products just use linear regulators(or no regulators), and the extra voltage just gets wasted as heat. This isn’t necessarily less efficient either, as switching regulators have their own losses.
Conventions based on two separate industries that suddenly got thrown together via EVs.
Most battery users prefer amp-hours (and all it’s variations) as it allows them to more directly calculate the total state of charge on a given pack; all you need is the voltage. Plus, for most applications, the voltage is fixed, so there’s no need to convert to watts when amps will do fine.
However, automotive prefers watt-hours (and all its variations) because the ratings for engines are either in terms of power (i.e. kilowatts or horsepower), or in brake-specific terms (i.e. fuel consumption per kilowatt-hour).
Because of how they are used–although it should be noted that LiPo batteries are also frequently specified using a Wh rating.
When dealing with small electronics we generally aren’t trying to pump out a lot of power. We are more concerned with a steady state usage and trying to minimize power usage. IC’s can use different voltages (sometimes multiple different voltages) so calculating the power usage of components can be a bit tricky–we tend to just consider typical current draw. This value is almost always provided by the manufacturer. Because we know current draw, it is more direct for us to calculate the length of time our device will run based upon amps instead of power (it is an extra step to get to power).
With EVs, most of what you are doing is trying to output a lot of energy quickly–this is power. The motors which use the majority of the energy are rated in power (kW or HP). Since your major power consumers are rated in power, it makes sense to specify the battery capacity in a power*hour unit (kWh).
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