How does a DC motor's voltage influence battery Life

[SenSeS]

I've created a PCB that controls a DC motor. However, I would like to use batteries so it becomes more portable. My question is, I have multiple motors both 3V and 6V that fulfill my requirements.  Which one will give me longer battery life? I will use 4x AA and place them in series/parallel, depending your answers, in order to get 3V or 6V.

I thought I read somewhere that a battery contains a certain number of mAh. If this is the case, the 6V would last longer because the motor would need less current for the same amount of power (P=U.I). On the other hand, if the batteries contain a certain amount of energy (J), then battery life in both cases will be equal since the motor will require the same amount of power (W=J/s) in both cases. However, for some reason I would intuitively expect 3V to yield the longest battery life, though I have no way of backing this up mathematically.

An added benefit of the 3V is that it eliminates the need for voltage regulators. Now I have a voltage regulator for the MCU which works at 5V and an IC which uses 3.3V.  I think both should be fine at 3V. Thanks!

[rollatorwieltje]

As a rule of thumb higher voltages are usually better as the current is lower (for the same amount of energy of course). Energy is lost in resistance according to P=i²R, so given the same resistance in a circuit a lower current will be better.

Batteries contain energy of course, but they generally aren't specified like that because of the voltage curve. The mAh number is usually the amount of current you can draw over 10 hours at whatever the cell voltage will be. Considering you're using AA batteries, realize that an AA cell isn't really 1.5V, it's nominally 1.2V. 2 in series is not enough for 3V operation.

[SenSeS]

Thanks for the info! Does this mean that a 9V would be even better? But I'm assuming that 6V with 4xAA or 2x CR123 would last longer than a single 9V battery.

Also, don't voltage regulators dissipate energy or is this loss negligible compared to the dissipation caused by the extra current needed for the motor? (Motor will only rotate for max 1min/day probably.)

[Zero999]

The standard PP6 9V battery contains less energy than a couple of AA batteries.

You're better off using six AAA cells in series.

[rollatorwieltje]

Thanks for the info! Does this mean that a 9V would be even better? But I'm assuming that 6V with 4xAA or 2x CR123 would last longer than a single 9V battery.

Also, don't voltage regulators dissipate energy or is this loss negligible compared to the dissipation caused by the extra current needed for the motor? (Motor will only rotate for max 1min/day probably.)

The rule of thumb is only valid if the amount of work that has to be delivered is identical. I.e. using a motor to move an object a certain distance, you generally want the one drawing a lower current at higher voltages (while staying reasonable of course). For stuff like processors you generally want the lowest voltage possible, as all power they consume is waste and it's generally less at lower voltages.

What battery configuration is better is difficult to say without actually measuring and calculating the use. If the motor is pretty much never used I would rather try to get rid of as much idle consumption as possible, like avoiding regulators and running the processor at a lower voltage.

9V batteries are not really great, they don't deliver that much energy. A single 9V battery contains maybe half the amount of energy of a single AA cell. Also the difference between the battery voltage and your processor is big, so your regulator is going to piss away lots of energy.