I get that, for a house/solar battery, it sort of makes sense as your typical energy usage would be measured in kWh on your bills. For the smaller devices, though, the chargers are usually rated in watts (especially if it’s USB-C), so why are the batteries specified in amp hours by the manufacturers?
In: 7
Let’s start with some definitions, a logic approach, and then a math approach.
**Definitions/Laws**
Ohm’s Law: V = I R
V = voltage
I = current
R = resistance
Power = I^2 * R = energy (Joules) / second
**Logic approach**
Watts are a unit of power, so kWhr (kilowatt hours, or hours of kilowatts) is saying “I can provide with this much power for this many hours.” Makes perfect sense, right? You want to know how long a 10kWhr battery can power your 1 kW device? 10 hours.
Now, how long can the 10mAh battery power that same device? I have no idea. A (amps) is a unit of electrons per second… but it’s very misleading. Think of current as being the current of a stream and resistance as the resistance provided by a water mill. How big of a water mill is it? Telling me that the current can move at 1m/s is useless information if I don’t know how big of a water mill it’s turning at that speed. I can’t tell if it’s a 5th grader’s science project capable of powering a toy robot or the Mississippi River and capable of powering NYC, so I cannot compare power to current.
**Math approach**
kWh is telling you hours of X power, but how do you convert mAh into that? For this comparison, we can remove the hours from both of them to simplify things.
Now we have … current (the m is just milli as in millimeter, and the A is for amps, the unit current is measured in). I^2 * R = power, so we have no idea how much power that represents without the voltage of the battery or the resistance. In fact, since V = I R and we don’t know for sure the resistance (R) of the device that will be plugged into the battery, that current figure is absolutely meaningless. With no V and no R and V =I R, you can arbitrarily assign any value to I knowing that no matter what V is, there will be a mathematical solution to V = I R that will make “I” (current” correct. It’s a relic of back before conventions had really been set up to standardize things in a logical manner (just like us using gallons of gas and F in the US). It’s a little bit like asking “How strong are you?” and the guy responding, “I can hold something up for 5 seconds!” Hold what up? A feather? A glass of water? A car? 5 minutes is a unit of time, not strength.
**So why do marketers use it?**
Let’s say my battery sucks. It’s 10 kWh and my competitors is 30 kWh. Do you think I’m advertising my kWh? Heck no! But I can truthfully say it’s 45 mAh. A customer that has no idea what either of those means will see one is 30 and the other is 45 and hopefully conclude that my product is better.
**Isn’t that dishonest?**
Phineas says yes, yes it is.
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