Your battery doesn't seem to be giving you as much life as you think it should, so you figure that you'll measure the voltage when it's charged. That should tell you if it's good, right? That's open-circuit (no load) testing - an almost dead battery will read full voltage that way.
As a battery is used, rechargeable or not, the internal resistance (think of a battery as really a battery in series with a resistor) goes up, so the current being drawn causes a voltage drop across the resistance (basic Ohm's Law). The more current, and the higher the resistance (because of having been used), the less the terminal voltage - the voltage you measure at the terminals. (The rest appears across the resistor.)
Lithium batteries have a nominal terminal voltage of 3.60 volts (even if the manufacturer labels the battery 3.75 volts - that represents an overcharged condition, it's not what the battery should be charged to). Since there are 2 materials in a lithium battery, lithium combined with another material, the situation isn't that clear - using manganese (lower internal resistance) results in a battery with a nominal voltage of about 3.65 volts. Using pure spinel results in a battery with a nominal voltage of around 3.75 volts (but don't expect to see one in a cellphone). The normal cellphone battery is lithium-cobalt.
The phone "knows" the amount of current being drawn (the circuits in the phone can measure it), so it knows about what the terminal voltage (the voltage after the drop across the internal resistance) should be. Comparing that to the actual terminal voltage tells it about how high the internal resistance is, which doesn't indicate the amount of charge, but it's about the best reference we have to it aside from a battery analyzer, which is about the size and weight of a car battery or more (and costs a LOT more), or a chemical analysis inside the battery.
If your battery measures 3 volts, is that 3.00? Or somewhere between 3 and 4? If it's 3.00, find a place that accepts rechargeable batteries for disposal (lithium is more toxic than a petroleum spill) - the battery's been so badly mistreated that it has one foot in the grave and someone amputated the other leg. Otherwise, open-circuit testing is pretty useless for determining battery health. A fully charged lithium-cobalt battery should measure about 3.6 volts about 5 minutes after being fully charged and outside the phone. After enough use that the phone says it's 50% discharged, it may read 3.74 volts open-circuit. Since most digital voltmeters these days are 2 digits after the decimal point (not cheap junk either, good quality meters - only a few have 3 digits after the decimal point), and (due to the way digital voltmeters all work) the fact that the last digit is +/- 0.5 of that digit, the difference between a fully charged and half-discharged battery, measured open-circuit on a digital voltmeter is less than can be measured. Basically, a reading of 3.60 volts means that the battery is somewhere between 3.595 and 3.604 volts - a larger range than the open circuit voltage difference between a fully charged battery and one with about 10% charge left.
An analog meter? Even on a 0-5 volt scale and a large meter, you're not going to be able to read it closer than about .02 volts (and that's going to be an estimate) and, again, the difference between a new battery and one that's about to die is going to be about that or less open-circuit.
As far as starting to fail? That has nothing to do with the voltage at all. A battery that's throwing dendrites is one you should replace, even if it's a week old. (There are professors of chemistry and physics all over the world working on why this happens and ways to prevent it. The biggest problem is in early failures of lithium batteries in hybrid and electric cars - 2 grand down the tubes for the manufacturer when that happens to a single cell.) That's why you should look at the second page of the battery stats for a "fall off the cliff" voltage just before the phone shut off or rebooted. A dendrite causes a short. If it's thin and the short burns out almost immediately (microseconds), the phone will reboot. If the short lasts tenths of a second or more the phone shuts off. Either one shows the typical drop to zero in zero time of a dendrite. (Why do batteries grow dendrites? They've figures out where and sort of how, but why? We'll have to wait a while for a definitive answer to that.)
A cheaply made battery might have been assembled in a "not-so-clean" clean room, and fail young - it'll still show 3.6 volts open circuit until it's so bad that the phone won't turn on even long enough to make the screen flicker. And then it'll show 3.58 volts open-circuit, or maybe more.
The two tests are the spin test (lay the battery down on a flat table and spin it - if it spins, there's a bulge so it's either on its way out or gone) and if the battery can't hold a charge as long as it did when it was new - running about the same apps for about the same time. (If you've started spending hours on the phone every day, of course the battery won't last as long as 6 months ago when you were making 1 or 2 calls a day.) When it gets down to about 85% of capacity it's time to think about getting a new one. It's still usable, but if you can just get through the day with a new battery (down to 40% charge), one with 85% capacity will need a recharge or swap before the day is done - it gets annoying.
If the battery can't get you through the day when it's new without dropping it down to less than 40%, buy a spare battery if your phone has a battery that can be replaced by popping the back off (I wouldn't buy one that didn't). Most replaceable cellphone batteries run in the $8-$15 range - they're not expensive. And if you look on Amazon, you can usually find them sold as 2 batteries and a charger that will charge the one not in the phone. So go to work, use the phone, and if the battery gets down to 40% before your day is done, swap batteries. At home, put the phone on the charger and pop the spare battery into its charger. (I also swap batteries every month if I haven't swapped them in the past month.) If you keep using the battery until it's down to 10%, you might get close to a year out of it. If you're lucky.
If you're going to put a battery away for a while (maybe you got a new phone, but you aren't sure yet if you want to sell the old one), use it until the battery is down to 40% (more charge and there's more chemical activity, causing the battery to age faster), then take it out of the phone and store it away. Check it every 6 months and if it's down to less than 30%, charge it back up to 40%. (Lithium batteries - almost all batteries - suffer from what's called self-discharge. Just sitting on a shelf causes them to slowly discharge. [Primary batteries - non-rechargeables - self-discharge much slower than rechargeables, which is why the date on a new AA cell is so far into the future. But by 2 or 3 years after that date, if you haven't used the battery, it'll probably be useless.])
When you get a new battery, or a new phone, you should condition the battery. That means fully charging it before turning the phone on. The store normally won't let you walk out without turning the phone on and setting it up, so I always tell them that it's their choice, to use one of their batteries or to use the one that came with the phone but give me a new one, still sealed, instead of the one they used to set the phone up. If they say no I walk. They may disagree with conditioning - there are differing opinions in the industry - but if they don't respect my opinion about the device I'm paying for, they aren't getting my money. (You'll hear that you don't really have to condition lithium batteries - you don't if they're new. But if the battery was sitting on the battery factory's shelf for 2 months, then on the phone manufacturer's shelf for a few weeks, then in the store for a few weeks - you do. Since you don't know, and conditioning it can't hurt, condition any battery you get, or any one you've stored unused for more than 3 months before putting it back into regular service.) Fully charge the battery with the phone off. Then use the phone normally until the phone tells you to plug in the charger. (If you can't charge it then, turn it off.) Plug the charger in (the phone can be on or off) and let it charge until it's fully charged. Do this for a total of 3 cycles (3 charges, 3 uses), then try to NEVER let the battery get below 40%. (50% seems to be about the ideal spot, the "sweet spot", for maximum battery life, but 40% won't reduce the lifetime by that much.) With more and more phones coming with non-replaceable batteries, maximizing the life is important. (Non-replaceable batteries are more expensive, probably because of the wire and connector, and you have to pay a shop for labor to have them replaced.) Why don't the manufacturers tell us that letting the battery drop below 40% is harmful to them? Because replacement batteries, especially today, when most phones don't have user-removable batteries, are a high-profit item.
You may think that the measure of a good phone is how long you can keep using it until it shuts off because the battery discharged too far, but that's only a measure of how fast you can kill a battery. (I've seen completely killed batteries - batteries that won't power a phone for more than a couple of hours on a full charge - after 6 months. And I still use the batteries that came with my Motorola V551 in late 2004 - they're down to about 95% capacity now. Conditioned, never discharged too far, never used when they're too hot or too cold.)
But don't say that you've measured the battery and it's 3.60 volts, so it should still be good. It can be a few charges away from being totally shot and still measure 3.60 volts with no load. (If you're into electronics, put a 25% load on it when measuring it - 25% of the rated capacity of the battery - and you'll get an approximate idea of its condition.)
One final note: NEVER throw a lithium battery in the trash. If they burn solid waste where you are, people are going to be breathing in lithium gas - and that's toxic. It could also be illegal where you are. Find some place that accepts batteries for disposal, like your cellphone carrier. (In the US, Lowes, the home improvement chain, has a battery disposal bin by customer service. Probably other chains do too.)
As a battery is used, rechargeable or not, the internal resistance (think of a battery as really a battery in series with a resistor) goes up, so the current being drawn causes a voltage drop across the resistance (basic Ohm's Law). The more current, and the higher the resistance (because of having been used), the less the terminal voltage - the voltage you measure at the terminals. (The rest appears across the resistor.)
Lithium batteries have a nominal terminal voltage of 3.60 volts (even if the manufacturer labels the battery 3.75 volts - that represents an overcharged condition, it's not what the battery should be charged to). Since there are 2 materials in a lithium battery, lithium combined with another material, the situation isn't that clear - using manganese (lower internal resistance) results in a battery with a nominal voltage of about 3.65 volts. Using pure spinel results in a battery with a nominal voltage of around 3.75 volts (but don't expect to see one in a cellphone). The normal cellphone battery is lithium-cobalt.
The phone "knows" the amount of current being drawn (the circuits in the phone can measure it), so it knows about what the terminal voltage (the voltage after the drop across the internal resistance) should be. Comparing that to the actual terminal voltage tells it about how high the internal resistance is, which doesn't indicate the amount of charge, but it's about the best reference we have to it aside from a battery analyzer, which is about the size and weight of a car battery or more (and costs a LOT more), or a chemical analysis inside the battery.
If your battery measures 3 volts, is that 3.00? Or somewhere between 3 and 4? If it's 3.00, find a place that accepts rechargeable batteries for disposal (lithium is more toxic than a petroleum spill) - the battery's been so badly mistreated that it has one foot in the grave and someone amputated the other leg. Otherwise, open-circuit testing is pretty useless for determining battery health. A fully charged lithium-cobalt battery should measure about 3.6 volts about 5 minutes after being fully charged and outside the phone. After enough use that the phone says it's 50% discharged, it may read 3.74 volts open-circuit. Since most digital voltmeters these days are 2 digits after the decimal point (not cheap junk either, good quality meters - only a few have 3 digits after the decimal point), and (due to the way digital voltmeters all work) the fact that the last digit is +/- 0.5 of that digit, the difference between a fully charged and half-discharged battery, measured open-circuit on a digital voltmeter is less than can be measured. Basically, a reading of 3.60 volts means that the battery is somewhere between 3.595 and 3.604 volts - a larger range than the open circuit voltage difference between a fully charged battery and one with about 10% charge left.
An analog meter? Even on a 0-5 volt scale and a large meter, you're not going to be able to read it closer than about .02 volts (and that's going to be an estimate) and, again, the difference between a new battery and one that's about to die is going to be about that or less open-circuit.
As far as starting to fail? That has nothing to do with the voltage at all. A battery that's throwing dendrites is one you should replace, even if it's a week old. (There are professors of chemistry and physics all over the world working on why this happens and ways to prevent it. The biggest problem is in early failures of lithium batteries in hybrid and electric cars - 2 grand down the tubes for the manufacturer when that happens to a single cell.) That's why you should look at the second page of the battery stats for a "fall off the cliff" voltage just before the phone shut off or rebooted. A dendrite causes a short. If it's thin and the short burns out almost immediately (microseconds), the phone will reboot. If the short lasts tenths of a second or more the phone shuts off. Either one shows the typical drop to zero in zero time of a dendrite. (Why do batteries grow dendrites? They've figures out where and sort of how, but why? We'll have to wait a while for a definitive answer to that.)
A cheaply made battery might have been assembled in a "not-so-clean" clean room, and fail young - it'll still show 3.6 volts open circuit until it's so bad that the phone won't turn on even long enough to make the screen flicker. And then it'll show 3.58 volts open-circuit, or maybe more.
The two tests are the spin test (lay the battery down on a flat table and spin it - if it spins, there's a bulge so it's either on its way out or gone) and if the battery can't hold a charge as long as it did when it was new - running about the same apps for about the same time. (If you've started spending hours on the phone every day, of course the battery won't last as long as 6 months ago when you were making 1 or 2 calls a day.) When it gets down to about 85% of capacity it's time to think about getting a new one. It's still usable, but if you can just get through the day with a new battery (down to 40% charge), one with 85% capacity will need a recharge or swap before the day is done - it gets annoying.
If the battery can't get you through the day when it's new without dropping it down to less than 40%, buy a spare battery if your phone has a battery that can be replaced by popping the back off (I wouldn't buy one that didn't). Most replaceable cellphone batteries run in the $8-$15 range - they're not expensive. And if you look on Amazon, you can usually find them sold as 2 batteries and a charger that will charge the one not in the phone. So go to work, use the phone, and if the battery gets down to 40% before your day is done, swap batteries. At home, put the phone on the charger and pop the spare battery into its charger. (I also swap batteries every month if I haven't swapped them in the past month.) If you keep using the battery until it's down to 10%, you might get close to a year out of it. If you're lucky.
If you're going to put a battery away for a while (maybe you got a new phone, but you aren't sure yet if you want to sell the old one), use it until the battery is down to 40% (more charge and there's more chemical activity, causing the battery to age faster), then take it out of the phone and store it away. Check it every 6 months and if it's down to less than 30%, charge it back up to 40%. (Lithium batteries - almost all batteries - suffer from what's called self-discharge. Just sitting on a shelf causes them to slowly discharge. [Primary batteries - non-rechargeables - self-discharge much slower than rechargeables, which is why the date on a new AA cell is so far into the future. But by 2 or 3 years after that date, if you haven't used the battery, it'll probably be useless.])
When you get a new battery, or a new phone, you should condition the battery. That means fully charging it before turning the phone on. The store normally won't let you walk out without turning the phone on and setting it up, so I always tell them that it's their choice, to use one of their batteries or to use the one that came with the phone but give me a new one, still sealed, instead of the one they used to set the phone up. If they say no I walk. They may disagree with conditioning - there are differing opinions in the industry - but if they don't respect my opinion about the device I'm paying for, they aren't getting my money. (You'll hear that you don't really have to condition lithium batteries - you don't if they're new. But if the battery was sitting on the battery factory's shelf for 2 months, then on the phone manufacturer's shelf for a few weeks, then in the store for a few weeks - you do. Since you don't know, and conditioning it can't hurt, condition any battery you get, or any one you've stored unused for more than 3 months before putting it back into regular service.) Fully charge the battery with the phone off. Then use the phone normally until the phone tells you to plug in the charger. (If you can't charge it then, turn it off.) Plug the charger in (the phone can be on or off) and let it charge until it's fully charged. Do this for a total of 3 cycles (3 charges, 3 uses), then try to NEVER let the battery get below 40%. (50% seems to be about the ideal spot, the "sweet spot", for maximum battery life, but 40% won't reduce the lifetime by that much.) With more and more phones coming with non-replaceable batteries, maximizing the life is important. (Non-replaceable batteries are more expensive, probably because of the wire and connector, and you have to pay a shop for labor to have them replaced.) Why don't the manufacturers tell us that letting the battery drop below 40% is harmful to them? Because replacement batteries, especially today, when most phones don't have user-removable batteries, are a high-profit item.
You may think that the measure of a good phone is how long you can keep using it until it shuts off because the battery discharged too far, but that's only a measure of how fast you can kill a battery. (I've seen completely killed batteries - batteries that won't power a phone for more than a couple of hours on a full charge - after 6 months. And I still use the batteries that came with my Motorola V551 in late 2004 - they're down to about 95% capacity now. Conditioned, never discharged too far, never used when they're too hot or too cold.)
But don't say that you've measured the battery and it's 3.60 volts, so it should still be good. It can be a few charges away from being totally shot and still measure 3.60 volts with no load. (If you're into electronics, put a 25% load on it when measuring it - 25% of the rated capacity of the battery - and you'll get an approximate idea of its condition.)
One final note: NEVER throw a lithium battery in the trash. If they burn solid waste where you are, people are going to be breathing in lithium gas - and that's toxic. It could also be illegal where you are. Find some place that accepts batteries for disposal, like your cellphone carrier. (In the US, Lowes, the home improvement chain, has a battery disposal bin by customer service. Probably other chains do too.)
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