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I understand the relation that Ohm's Law sets up: $$R=V/I$$

What I am confused about is what happens to maintain that relationship if the resistance suddenly changes.

If I have a circuit that starts off at a very high resistance but then suddenly decreases, the voltage would have to change for the current to stay the same. Conversely, in order for the voltage to stay the same, the current would have to change.

Which is it?

PS: Please do not use the hydraulic analogy in explaining this. It's both a severely limited approximate and does not describe the actual physics happening.

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    $\begingroup$ The actual physics is way more complicated than resistances, voltages and current. The hydraulic analogy is good because with the simplifications we make when modelling both, the models can actually be analogous (along with some other physical systems). That said; the only real reason to use hydraulic analogies is if you are more comfortable with simple fluids than simple circuits. It seems odd to specify "no hydraulic analogies", especially since a good answer on this site would require more detail than that. That analogy might help someone else, I wouldn't exclude it. $\endgroup$ – JMac Jun 2 '17 at 12:15
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Which of the two changes depends on what sort of source your circuit has.

Commonly, you will have a constant voltage source such as a battery or socket, so current will change if you change the resistance, but it is perfectly possible to have a constant current source so the voltage will change.

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