One key concept that might help in clarifying any misunderstandings is this:
- A voltage is the potential difference between two points in a circuit, it is not an absolute value of any physical characteristic at a single point in a circuit. Thus, there is no absolute potential involved, it is relative value, a difference.
How this applies:
The "ground" of the Arduino is the point (or PCB trace, to simplify the concept) relative to which, the potential on the "Vcc" trace of the Arduino is measured. Thus, when powered by the USB cable, the Arduino's "ground" is the measurement basis, and is incidentally at the same potential as the "ground" of the computer whose USB port is being used.
The "negative" of the battery is merely one of two points across the battery, between which the potential difference i.e. the voltage of the battery is measured. Relative to the rest of the (electrical) universe, the "negative" terminal of the battery is floating, i.e. has no specific relative value until this so-called negative terminal of the battery is connected to a circuit.
When you connect the negative terminal of your battery to the ground of the Arduino, you are providing a reference value for the battery, relative to the Arduino. Thus, only while such a connection is made, the "positive" terminal of the battery is at a potential of "battery voltage" compared to the Arduino's zero level or ground.
If, instead, you connected the battery "positive" to the Arduino ground line, then the other terminal of the battery would be at a negative value compared to the Arduino's zero level or ground.
The battery, or for that matter any arbitrary voltage, is relative to the reference you provide. It is a difference, from your defined base point in the circuit, not an absolute value, to reiterate the basic principle mentioned at the start here.
Voltage = current / resistance.
No, voltage is the product of current and resistance: voltage = current \$\times\$ resistance. Ohm's law:
$$v = i \cdot R $$
If a circuit has no resistors, does that imply that the current is
equivalent to the voltage(no resistance)?
If there is no resistance in the (DC) circuit , \$R = 0 \Omega\$, and thus, \$v = 0V\$
$$v = i \cdot 0 = 0V $$
Someone tells me voltage is current divided by resistance,
Don't listen to them, they're wrong.
Best Answer
You most certainly can.
But, be sure to take care to shift all your datasheet values correctly. This especially includes absolute maximum ratings. Also have a look at the protection diodes often found around IC pins.
What makes this often very useless (or sometimes very useful) is that the logic levels are also shifted.
This is in particular done with operational amplifiers. There the manufacturer may even be nice enough to specify typical shifted supplies for you.