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I've been teaching myself DC electronics as a hobby and, although I have a feeling i'm "missing something obvious", I was wondering if someone could help me out. If two components of differing resistance are wired in series, they likewise drop different voltages; yet when they are wired in parallel they apparently share a single magnitude of voltage drop. I would like to better understand why a common drop is exhibited across components of differing internal resistance wired in parallel?

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    $\begingroup$ If they are in parallel, the positive ends of all the resistors are connected together, and the negative ends of all the resistors are connected together, by definition. How could there be a different voltage drop between the same two points $\endgroup$
    – DJohnM
    Jul 8, 2013 at 21:38

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Consider a voltage source, e.g. an ideal 5V cell phone power supply. There is a 5V drop between Source and Ground.

Now put in a resistor of let's say 10kOhm between Source and Ground. The voltage drop across this resistor is 5V.

Now wire in another resistor of 10kOhm - parallel or serial does not matter for this part.

What is the voltage drop across the system of resistors? It is 5V - because that is what the source supplies.

If they are in series, it is 2.5V over the first, and then 2.5V over the second, for a total drop of 5V.

If they are in parallel, it is 5V over the both of them because the source creates a 5V voltage across the both of them. Wire in any number of resistors in parallel and the voltage across them will stay 5V because "The voltage across them" is the voltage of the source, which is 5V.

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Please look at the potential difference (voltage drop) definition. Potential difference between two points A and B is the energy required to move a unit charge between those points. Now consider the resistors in parallel. From basic physics the energy in moving a unit charge from A to B should be the same irrespective of the path. Hence, their voltage drop should be the same

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The key to the answer is Ohm's law V=RI

If your resistors are in series, then the same current must flow through both, which fixes the voltage for each at differing values if they have different resistance.

If the resistors are in parallel, then you impose the same voltage on both, but no constraint on the currents, and the currents will differ if the resistors differ.

The resistors only adapt current to voltage or voltage to current, according to Ohm's law.


More intuitively:

The resistor is only a path for the current. The voltage is only a potential applied to its end (like a height difference for water) so that the current will flow. So , if the resistor is alone, it will just ajust the current permitted by Ohms law. If they are 2 identical resistors in parallel, they can both let a current flow as before, and you get twice as much current in the system

Now if you put two identical resistors in series, they both have to let the same current through, like two connected pipes for water. Also the total voltage is the one you fixed, no other. The flow of current will be resisted twice, because it has to go through both resistors. So the curent will be half the current you had before with one resistor (Ohm'slaw). For half the current you need only half the voltage for a given resistor. So both your resistors in series will have half the voltage, which totals to the full voltage you are applying.

Resistors do not fix the voltage drop in the absolute, only proportionally to the current they let through.

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The other point is that different currents flow through each resistor, so that V=IR holds for each.

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