# Rate of battery life varies with charge?

1. Jul 17, 2015

### tom aaron

Batteries and rate of charge?

It 'seems' that when he battery if fully or mostly charged it lasts proportionately longer than when less charged.

For instance, all things equal, the battery takes a shorter time to drain from 30% charged to 10% than it does from 90% to 70%.

Is this physics of some sort? Or, Is it just a quirk of the display, sensor, etc.

Thanks

2. Jul 17, 2015

### Dr. Courtney

Sensor quirk. It is very hard to make a good, linear sensor for battery charge that is cheap.

3. Jul 17, 2015

### tom aaron

Thanks.
That's good to know for this and other devices in future.

4. Jul 17, 2015

### fzero

I think it's a bit more than just the sensor sensitivity. If you search around for "discharge curve" for batteries, you'll typically find a plot of voltage vs capacity or time. You'll see that the voltage tends to drop steeply when the battery is fully-charged, levels out over most of the discharge and then starts to drop steeply again towards the end of the capacity. I think there are various reasons for this behavior related to the efficiency of the various reactions that can occur in the battery under the varying capacity and voltage conditions. First is the efficiency of the reactions at the positive and negative electrodes. Second are the side-reactions, which involve the substances that make up the electrolytic solution between the electrodes that carries the ions. Basically there are competing process where the solution "steals" some ions from the primary reaction. I would expect that the batteries are designed so that the discharge curve is as flat as possible which will be when the primary reaction is optimally efficient compared to any possible side reactions.

You can also search for charging curves which are not the mirror of the discharge curve but have analogous features due to the same processes. Anyway, I don't really know the specifics of the electrochemistry involved, but you might be able to turn up some sources to piece a better picture together.

5. Jul 17, 2015

### tom aaron

Thanks.

One thing that seems odd is the IPad will stay charged at 100% if I use it for 10 minutes. I wonder if it is like gas in a car...you can add more after it reaches the 'full' marker. Otherwise...it says 100% but that's really 97% ( or whatever) and the battery will charge a bit more after the battery reads 100%.

Anyways, good to be reminded that something that appears simple can have multiple variables.

6. Jul 17, 2015

### Dr. Courtney

Right, the sensor is not measuring the "charge" on the battery at all. It is measuring a proxy for charge such as voltage. The voltage changes as a battery discharges are not a linear representation of the remaining charge, and the measurement is subject to a variety of other factors that cause it to deviate from a linear representation.

7. Jul 17, 2015

### fzero

Reading at 100% for awhile is probably totally sensor/software related. The voltage output from the battery is probably changing a relatively large amount during that time, but the software driver for the sensor is probably coded not to show any change in capacity because it wouldn't be as reliable as the measurements during the flat part of the discharge curve. It could also be that it just isn't worth coding in that part of the discharge curve because it is probably sensitive to the cycle age of the battery. An older battery might have a significantly different discharge curve, at least at the edges, because the same side reactions and electrode deterioration are the factors that drive battery cycle life. I won't speculate that battery life can be a huge issue driving sales so you wouldn't want buyers to see a (possibly unreliable) quick change over short usage on a ostensibly fully charged battery.

The fuel level sensor in a car is a totally different beast because it has a very mechanical component that is usually some version of a float on a rod that acts as a variable resistor. Depending on the application, the gauge may even be inserted diagonally in the tank. In any case, the float has a limited range of movement and at full, there will be room in the tank above it to put more gas and similarly at "empty" there is fuel below.

8. Jul 17, 2015

### mgkii

Hope it's ok to share a link here. The OP asked if this is a physics effect. Yes in so far as chemistry is just a sub branch of physics (oops! Did I say that out loud?) But no in that in this case your answer is all chemistry. Enjoy the vid.

9. Jul 18, 2015

### CWatters

Its not always safe to use voltage as a proxy. Battery voltage can change with temperature and the age of the cells. Some systems monitor the current going in and out of the battery and use that to estimate the capacity of the cells and the charge state.

10. Jul 19, 2015

### derek10

I don't know about ipads but I get just the opposite in my Samsung laptop and Sony phone, when partially charged, they take longer to "discharge" from the same range than from 100, so they charged more than the indicator shows. Maybe a software calibration.