# Why does the current divide through parallel resistors

1. Sep 25, 2015

### kent davidge

why does the current divide through parallel resistors? In parallel both resistors have the same potential difference. So how does the charges know that they must go into the resistor with less resistance than other resistor? (sorry my bad english)

2. Sep 25, 2015

### Staff: Mentor

They don't have to "know" anything, they just go where there is less in their way! Think about how water would flow though a fork in a pipe.

3. Sep 25, 2015

### kent davidge

But what inform they what is the better way to go

4. Sep 25, 2015

### Merlin3189

You said it yourself - they both have the same pd across them.
The current in each resistor is determined by the pd across it.

The current does not 'go into the resistor with less resistance' only. The current goes into both resistors and the current in each resistor is determined by the pd and the resistance of that resistor.

If the resistance of one resistor(R1) changes, the current through that resistor(R1) will change, but the current through the other resistor(R2) may stay the same.
If the current through R2 changes, it will be only because the pd has changed.

When the total current through the two resistors changes, that might change the pd, and that change in pd will change the current in both resistors.

5. Sep 25, 2015

### Staff: Mentor

It bumps its head on the electron in front of it?

6. Sep 25, 2015

### Staff: Mentor

Think about what happens when there's an island in the middle of a river....
The flow divides, some going down one side of the island and the rest going down the other. One channel may be wider than the other so it can accommodate more flow, but somehow each water molecule "knows" to go down one side or the other in a way that keeps the (gravitational) potential difference between top and bottom of both channels the same.

Of course this is an analogy, but if you're comfortable with the analogy you'll be able to apply it to the parallel resistors case.

7. Sep 25, 2015

### kent davidge

Thanks Merlin3189, russ_watters, Nugatory. I understood your explanation. It's how almost all textbooks explain. But I would like to study it in a microscopic view. We know that the charges dont make any choice, it's a simply poetic view. I've read something about surface charges. I know that this surface charges produces the potential difference between the ends of a resistor. What I wish to learn is how the charges are more attracted to the resistor which offers less resistence and why the division of the current occurs by this way. (again sorry my bad english)

8. Sep 25, 2015

### davenn

they are not ... again you are still attributing qualities to the electrons/charges, that they don't and cannot have

and if there is a specific part you don't understand about what he said comment on that

Dave

9. Sep 26, 2015

### Merlin3189

Why do electrons go anywhere? Because there is a potential gradient.
It's like the analogy with water - it flows because it can go downhill.

On the microscopic scale an electron (or water molecule) doesn't "know" it has a choice of two routes. It is just bouncing around and generally "falling" in the direction of the potential gradient. As electrons go one way, the extra charge there reduces the potential gradient in that direction, making it more likely that other electrons will fall in a different direction and end up going the other way. So where macroscopically there are two equal choices, two wires say, half the electrons end up going one way and half the other. If ever there were even a slight random imbalance, the change in potential gradient would change the probabilities of which way they move and correct the imbalance.

Where the two (or more) paths have different resistances, that affects how much the potential gradient changes as electrons flow that way. A high resistance means a bigger change in potential for a given flow of electrons than a low resistance. So to maintain equal potential gradient in both directions in the region where electrons are separating, more electrons must flow through the lower resistance path and fewer must flow through the higher resistance path. If there is any random deviation from the correct proportion, then the potential gradient will shift to correct it.
No single electron ever has to make a choice. It just bounces around falling down the potential gradient.

10. Sep 26, 2015

### robphy

Possibly useful:
http://www.matterandinteractions.org/Content/Articles/circuit.pdf [Broken]

Last edited by a moderator: May 7, 2017
11. Sep 27, 2015

### sophiecentaur

To avoid the 'current takes the easiest route' fallacy, it would be helpful to include, more explicitly, the idea of the split being proportional to the 'ease of passing' through each of the possible routes. What you have written could be taken as 'one way or the other' I think. The 'things in their way' include other electrons in the flow.

12. Sep 27, 2015

### CWatters

Consider what would happen if slightly too much current went down the wrong branch. The voltage drop would increase in that branch and that would reduce the current flow in that branch. In effect there is a feedback process in operation.

13. Sep 27, 2015

### mpresic

Try this one: Consider two resistors in parallel with a voltage source. The potential across both resistors is V. Let the total current flowing out of the battery is i0. The current flowing through resistor 1 is i1 and the current flowing through the second resistor is I0 - i1 . The total power dissipated in the circuit will be P = R1 * i1 squared + R2 * (i1 - i0) squared. Now minimize the power dissipated in the circuit. Taking the derivative of the power with respect to i1 (the variable) leads to a condition on i1 which will minimize the power dissipated in the circuit. dP/di1 = 0 leads to the condition (R1 + R2) * i1 = R2 * i0. so i1 = ( R2 / (R1 + R2) ) * i0, implying the current in resistor 2 is i2 = i0 - i1 = ( R1 / (R1 + R2) ) * i0. The current in resistor 1: i1 = (R2 / R1) * I2. The ratio of the current in resistor 1 to the current in resistor 2 is in inverse proportion to the ratio of resistances (inverse of ratio of R1 to R2, or directly proportional to the ration R2 to R1) .

This longwinded argument shows that for two resistors, the condition that the power dissipated in a circuit should be a minimum leads to the correct distribution of currents in the two resistors. The current goes in the direction which would minimize the power dissipated in the circuit.

Your reflection of this problem brings to mind a question Feynman addresses about least action. Does the particle sniff the correct path in phase space to ffollow. How does it know. The answer is intimately corrected to a minimum principle, just as your question regarding the current distribution in the resistors. Although this is demonstrated for two resistors in parallel, you can generalize is to three resistors in parallel and even more difficult calculations with multiple resistors in series, parallel, and combinations in networks.