This is a very basic question as I'm just starting to get into things, but I've hit a roadblock with comprehending the definition of voltage as it relates to the relationship defined in Ohm's law.
It might be that I'm misunderstanding the definition of voltage. As it says "voltage is the work needed per unit of charge to move a test charge between two points." My confusion centers around the idea of 'per unit of charge', which suggests to me that amps and volts can vary independently (that is one 'unit' of charge may require different quantities of work to move between two points not related to resistance).
If that's the case, how can I = V/R be a thing? That suggests that current is precisely and deterministically derivable from voltage and does not vary independently. I guess I'm just not really understanding how current actually varies – whether or not it's a property, say, of the conductive medium (copper has 'more available charge' to move, or some such) vs. current actually being directly related to voltage and does not vary independently and I've totally misunderstood the definition of voltage.
I'm hoping I can understand this and move on to more interesting things, but I'm just kept awake at night not really understanding this. My tl;dr question is really summarized in the title.
Best Answer
The short answer is that, if you are varying I and V independently, you must have some means of varying R.
For a fixed R, you understand fine : as you increase V, I will increase dependent on V, at a rate which is exactly the resistance R. Lock in that understanding, it is important.
But that's a special case.
You often want to vary the power level from a fixed voltage - that means varying the current, which generally means varying the resistance. And there are various ways of doing that.
A crude way is to vary the number of loads on a circuit- switch on additional lamps on a lighting circuit, or heating elements in a heater.
Another way is to switch the resistor on or off relatively fast, so its resistance alternates between R, and infinity, to reduce the average current. Examples are thermostatically controlled heaters (or the simmerstat controls in ovens) and PWM "pulse width modulation" used for dimming lights and some motor speed controls. These can only reduce power by increasing the effective "R" - once R is connected all the time ("100% duty cycle") you are at full power.
(Motors are a bit more complicated than that. because motors are also generators. Motor control will keep for another day)
There are also resistances which are variable in themselves - either as a function of temperature (which is a function of the power dissipated in them) or as a function of the voltage across them, or some other effect (like light falling on them). Ohm's Law still applies ( V = I * R ) but R is no longer a constant, and the equation may not be a linear one.
Some of these devices are semiconductors; but consider a simple incandescent lamp bulb first. As its filament wire heats up, its resistance increases, and is more than 10x as high at full power than it is when cold.