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I'm wondering if something similar could be created by simply attaching a fan to a cheap engine air filter...
500 sheets of paper is called a ream.
IC7805 voltage Regulator is used for providing 5V power supply to Arduino. However, using this IC is not necessary and battery can be directly plugged to Arduino. This is just used for Safety PurposesNot only is it "not necessary", it's a bloody stupid thing to do. By using that you are starving the Arduino of power by under-powering it. The minimum voltage for the barrel jack input is 6V with a recommended minimum of 7V. Providing it with 5V means the internal regulator would then not be regulating and just dropping the voltage by its drop-out voltage of around a volt, so the Arduino will only be getting 4V. At 4V you are right on the lower voltage limit for running at 16MHz. Any slight variation (which there may well be since you don't precisely know the dropout of the 1117 is 1V, in fact it's nearer 1.2V) will put the Arduino into an unguaranteed state where you are running at too low a voltage for the frequency, and stability issues may well occur, making you self-balancing robot run over your pet hamster.You only need the external regulator if you want to bypass the on-board regulator and feed the power direct into the 5V pin, which you aren't doing, and since the 1117 is marginally more modern (by about 30 years) than the ancient 7805 (which few designers actively use in current designs unless they started using it back in the dark ages), why would you want to do that? If it's for increasing current availability then you don't want a linear LDO in any case - you need a buck regulator.Also your choice of battery tells me you don't have much practical knowledge. 9V PP3 batteries aren't suitable for powering much more than a smoke detector or small transistor radio. They lack the current and power capacity to do anything useful. Whoever first publicised using them with an Arduino needs shooting. They are the worst choice ever for doing anything that isn't highly optimized for low current consumption. At little more than 150mAh you can expect maybe an hour of use out of it - if it can even provide enough current to drive the motors under load, especially with the current hungry Bluetooth module in the mix. You really need at least 7.2V worth of AA batteries (6S NiMh are good) or a 2S Lithium-Ion battery pack.
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