# In batteries, does stored energy vary with battery voltage?

• B
Hi
For a 1200 watt tool, there are 20, 40 and 60 volt batteries, and in the case of a 2 amp hour (7200 Coulomb) battery, using energy = charge x voltage gives different values of stored energy for each of the three batteries, which are 144000, 288000 and 432000 Joules.
Is this correct?
Thanks

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sophiecentaur
Gold Member
Hi
For a 1200 watt tool, there are 20, 40 and 60 volt batteries, and in the case of a 2 amp hour (7200 Coulomb) battery, using energy = charge x voltage gives different values of stored energy for each of the three batteries, which are 144000, 288000 and 432000 Joules.
Is this correct?
Thanks
I am not sure exactly what you mean when you imply that the same tool can use different voltage batteries. That would be an unusual situation for a cordless appliance and could add needless complexity to the power management inside the tool (internal voltage changers needed). I'll assume that you are comparing different tools with equal powers.
If the same technology is used for the individual cells in each battery then the same energy will be stored for batteries with equal values of Volts times Ah. SO your sums are right, basically. There could be other factors at work here, though. The losses due to resistance would be higher for a given power with a lower voltage battery so the higher voltage system could be more efficient. That would depend on the different motor designs etc. Higher power (and better quality) tools tend to use higher voltages, in my experience of reading (drooling over) many catalogues..

russ_watters and techniker
Merlin3189
Homework Helper
Gold Member
Yes.
You could make the 40 V, 2 AHr battery from two 20 V, 2 AHr ones, or the 60 V from 3 of them, (in series.)

The 20 V 2 AHr battery is supplying (1200W / 20V) = 6A , so will run for (2AHr / 6A) = 1/3 Hr
The 40 V 2 AHr battery is supplying (1200W / 40V) = 3A , so will run for (2AHr / 3A) = 2/3 Hr
The 60 V 2 AHr battery is supplying (1200W / 60V) = 2A , so will run for (2AHr / 2A) = 1 Hr

In theory! In practice I don't know how the nominal capacity relates to actual capacity in use.
Presumably the 1200W rating is a maximum and the actual power usage will vary with the task, so I'd think you'd get more hours actual use.

Edit: I missed SC's post. Agree with his comments.
But other thoughts it provokes about the relative merits of different battery packs:

When rechargeables are in series, they are as durable as the weakest link. When one fails (or heads in that direction), the others tend to get overcharged and deteriorate faster.
Since Li cells came along, more sophisticated equalising chargers have become more common. I expect, as SC says, that the higher voltage machines, being more the expensive ones, are likely to have better charging circuits. Even so I wonder how easy it is to keep 18 cells balanced, especially if the user regularly fast charges.
When you do have to replace them, the step cost is greater.

On the plus side, for the same useage the higher voltage battery is supplying lower current and generally that is less stressful (damaging) to the battery. So all the cells should have an easier and longer life.

As CS implies, it would be nice to be able to comment on this from experience rather than theory!

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sophiecentaur and techniker
CWatters
Homework Helper
Gold Member
Hi
For a 1200 watt tool, there are 20, 40 and 60 volt batteries, and in the case of a 2 amp hour (7200 Coulomb) battery, using energy = charge x voltage gives different values of stored energy for each of the three batteries, which are 144000, 288000 and 432000 Joules.
Is this correct?
Thanks
As others have said - You are correct.

If you think about it you can make an 40V 2AH battery by connecting two 20V 2AH batteries together in series.

When designing a battery pack to have a certain energy capacity (say 80WH = 288,000 Joules) the designer can choose either a 40V 2AH arrangement or a 20V 4AH arrangement. Both store the same energy.

However there might be an advantage to making it 40V 2AH instead of 20V 4AH... When running at 1200W the currents would be..

40V Pack : 1200/40 = 30A
20V Pack : 1200/20 = 60A

The I2R losses in things like the motor brushes or wiring would be higher with the 20V pack than with the 40V pack. This is basically the reason why the National Grid uses very high voltages (because it reduces the current).

techniker
I am not sure exactly what you mean when you imply that the same tool can use different voltage batteries. That would be an unusual situation for a cordless appliance and could add needless complexity to the power management inside the tool (internal voltage changers needed). I'll assume that you are comparing different tools with equal powers.
Yes you are right. I did not know a single tool can have multiple voltages.

If the same technology is used for the individual cells in each battery then the same energy will be stored for batteries with equal values of Volts times Ah. SO your sums are right, basically. There could be other factors at work here, though. The losses due to resistance would be higher for a given power with a lower voltage battery so the higher voltage system could be more efficient. That would depend on the different motor designs etc. Higher power (and better quality) tools tend to use higher voltages, in my experience of reading (drooling over) many catalogues..
OK, thanks a lot for the info. This saved me a lot of of reading.

As others have said - You are correct.

If you think about it you can make an 40V 2AH battery by connecting two 20V 2AH batteries together in series.

When designing a battery pack to have a certain energy capacity (say 80WH = 288,000 Joules) the designer can choose either a 40V 2AH arrangement or a 20V 4AH arrangement. Both store the same energy.

However there might be an advantage to making it 40V 2AH instead of 20V 4AH... When running at 1200W the currents would be..

40V Pack : 1200/40 = 30A
20V Pack : 1200/20 = 60A

The I2R losses in things like the motor brushes or wiring would be higher with the 20V pack than with the 40V pack. This is basically the reason why the National Grid uses very high voltages (because it reduces the current).

Yes.
You could make the 40 V, 2 AHr battery from two 20 V, 2 AHr ones, or the 60 V from 3 of them, (in series.)

The 20 V 2 AHr battery is supplying (1200W / 20V) = 6A , so will run for (2AHr / 6A) = 1/3 Hr
The 40 V 2 AHr battery is supplying (1200W / 40V) = 3A , so will run for (2AHr / 3A) = 2/3 Hr
The 60 V 2 AHr battery is supplying (1200W / 60V) = 2A , so will run for (2AHr / 2A) = 1 Hr

In theory! In practice I don't know how the nominal capacity relates to actual capacity in use.
Presumably the 1200W rating is a maximum and the actual power usage will vary with the task, so I'd think you'd get more hours actual use.
OK, this answers my question, thanks.

Edit: I missed SC's post. Agree with his comments.
But other thoughts it provokes about the relative merits of different battery packs:

When rechargeables are in series, they are as durable as the weakest link. When one fails (or heads in that direction), the others tend to get overcharged and deteriorate faster.
Since Li cells came along, more sophisticated equalising chargers have become more common. I expect, as SC says, that the higher voltage machines, being more the expensive ones, are likely to have better charging circuits. Even so I wonder how easy it is to keep 18 cells balanced, especially if the user regularly fast charges.
When you do have to replace them, the step cost is greater.

On the plus side, for the same useage the higher voltage battery is supplying lower current and generally that is less stressful (damaging) to the battery. So all the cells should have an easier and longer life.

As CS implies, it would be nice to be able to comment on this from experience rather than theory!

Thanks a lot for the valuable info. This also saved me from a lot of reading.

60 volt tools are more expensive than 20 volt tools. However, when adding the price of batteries and the revenue of the additional runtime of 60 volt tools (assuming 1380 watts because that is the average wattage of their corded saws [1200-1560 watts] ), the less expensive option becomes the 60 volt tool, at day one after purchase.

The example I used to calculate this is Dewalt reciprocating saws.

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To address the original question, as a practical matter, except kinda backwards.....
or maybe sideways...
For, say, a car battery specced at 12V, you typically have a higher available voltage when the battery is charged up than when it is mostly drained. If you give a car battery a full charge, you can usually get a read of 13.something volts with the engine off, but when the battery is pretty low, you can get only maybe 8 to 10 Volts reading on the meter. So, in real world terms, this is not a totally even progression. I am sure if there is a suitably knowledgeable engineer here, they can describe the applicable curves.

Note that this is backyard automechanics on my part and not scientific research.

diogenesNY

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CWatters
Homework Helper
Gold Member

sophiecentaur
Gold Member
Different Voltage batteries will have the same cell Voltage (say 2V nominal) so the only relevant difference would probably be Ah and peak Amps.

gleem
As previously noted batteries have a total energy capacity given in amp-hours but the actual energy that can be extracted from a battery often depends on how fast the energy is extracted. The discharge behavior of a battery is described by a graph of the terminal voltage versus capacity used for different discharge rates called C-rate. 1C discharge rate discharges the total capacity of the battery in one hours. 0.5C is discharging (using) half the capacity in one hour. The amount of capacity available for some batteries depends on how fast you discharge the battery which in turn depends on the minimum voltage that can be useful for the application. Most batteries have a relatively strong dependence of terminal voltage with the state of charge. These characteristics depend on the chemistry and physical construction of the batteries.

The graphs below show two Li -ion batteries with significantly different discharge characteristics. Other batteries like Lead Acid batteries are different.

Panasonic NCR18650B

Panasonic UR18650RX