Question

In a parallel circuit, the electric potential drop of two different path is identical. What is the explanation of this phenomenon?

Answer 1

The basic reason for the identical potential drop across two parallel non-identical paths is that electric charge cannot accumulate at a point in a closed circuit.

Answer 2

All by itself, that doesn't imply equal potential drops -- you could build a circuit that doesn't have charge piling up anywhere but also has uneven potential drops if you wanted to.

In this context, since I assume nobody is talking about magnetic fields right now, I think the proper explanation is that the potential drop around any closed loop must be zero -- which means that if you split the loop in half, going around one side must be exactly the same as going around the other.

Answer 3

@Jemurray3 ".........you could build a circuit that doesn't have charge piling up anywhere but also has uneven potential drops if you wanted to." No so in the case in question which has dissimilar parallel branches.
Having said that, your explanation is correct.

Answer 4

Perhaps I'm misunderstanding the question. In this circuit, there is no charge buildup, but the potential difference between points A and B certainly depends on whether you take the top route or the bottom route.

Answer 5

@Jemurray3 Can you please explain your diagram in detail. I understand that resistors R1 and R2 are connected in parallel. However what do the central symbol of a circle with a dot and the equation B = B(t) mean?

Answer 6

That denotes that there is a changing magnetic field in this region. The circle with the dot means its pointing out of the screen, but that doesn't really matter. The point is, if there is a changing magnetic field in that region, then the potential drop will depend on whether you go around the top or around the bottom.

Answer 7

@Jemurray3 So you are pointing out that an external changing magnetic field can induce a current into the loop formed by the resistors in parallel. However this is doing more than "...build a circuit.....".

Answer 8

Why? My circuit has a magnetic field, that's all. The whole point of this is that MY circuit has no charge buildup AND the potential difference between the branches is not the same. That means that the lack of charge buildup is not the answer to that question, at least not all by itself.

Answer 9

The reason my sides are different is because the total voltage drop around the square loop is not zero, as a result of my magnetic field. If my field didn't exist, then the voltage drop WOULD be zero, and the branches WOULD be the same. That is the cause.