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I have simple project composed of an Arduino Nano, a HC-05 module, and a small toy DC motor controlled using a L293D driver, I want to be able to power this circuit entirely using a battery, here is what I tried:

-The motor/L293D combo works when the Arduino Nano is powered through it's USB jack, except the L293D is drawing power from the Nano, which I know is very bad practice, but I only did it for testing purposes.

-The HC-05 module also works fine when the Nano is powered through it's USB jack, as expected.

-However, the power received through the USB jack is not enough power for both the HC-05 and the L293D & motor simultaneously, if I want to change the PWM through the HC-05, I have to disconnect the motor, send the instruction, then disconnect the HC-05 and re-connect the motor.

-I have tried 3, pretty much new 9V batteries, none of them were enough to power anything, not the Nano board through the Vin pin, not an Uno board through barrel plug, not the motor, nothing, except a LED diode, I've read somewhere that most brands of these kinds of batteries don't actually provide nearly as much power as they claim, so that might explain it. (In case it's relevant, the brands I tried are VARTA, Uniross and Goldmen.)

-Someone gave me the idea of using an old mouse cable to power the Arduino, by taking the VCC and GND wires from the mouse cable and using those to power the Nano board through it's Vin and GND ports, it works, but not any components connected to it, not even the HC-05 module, which I even tried powering directly from the mouse cable, which lit up it's LED, but did not get it to work.

Honestly this isn't that relevant, I just wanted to make sure the Vin pin worked.

-Also, few side notes:

My multimeter mysteriously stopped working when I actually needed it, which is why I couldn't take any measurements.

The L293D datasheet and other pinouts suggest no less than 12V supply voltage, so maybe a 9V battery wasn't the right answer to begin with.

The power coming from the mouse cable is enough to power the DC motor independently, but not through the L293D, it says online the average output for these cables is around 5V, but without measurements I can't be sure.

The battery holder for the toy train that has DC motor inside accepts 1.5V batteries wired in series, and considering there's not much else there aside from the motor itself, it's safe to say that 3V is the minimum required voltage for the motor.

So, what battery do you think would be most suitable for my project?

And if it's not against the rules, what brand would you recommend?

The Riser
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The L293D has about a 2.6V drop on the output pins. That means for a 3V motor you need to provide about 5.6v for it to run at full speed. 5V will work, but it will run slightly slow and underpowered.

9V batteries are useless. Only any good for very low power applications like smoke alarms. They just can't provide the current you need.

Instead you need to be looking at model aircraft / drone suppliers for a "2S" battery (7.4V Li Poly / Li Ion) and a suitable 5V (or 5.6V if you can get it) UBEC (switching regulator).

Majenko
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You could also use a 4 channel relay for making the motors work and they can be independent of using power from arduino and is really effective, I sometimes use it for high voltage optocoupling and can be used for small ones too all you need to do is build logic and everything would work fine I assume you know how to reverse polarity on a dc motor. Relays are not power hungry and can be powered from arduino but if you could give it an external 5 volts that would be better. Which in case of L293d driver is not the case you would require at least 12 volt to power the driver itself.