# Potential Difference in Series and Parallel circuit

## Main Question or Discussion Point

Ok I'm new here. I'm only a seconday student, recently exposed to Physics. I have a few doubts and questions on the chapter Electricity.

Why is the potential difference same for all the bulbs in a parallel circuit? My teacher only seems to explain this by rewriting some equations, but what I want to know is that where did the equation derived from, from what concept or theory??

Some one told me a analogy, it goes like this.
Take 3 groups of people as 3 groups of electron. These groups of people are walking in three routes, which means electrons flowing through 3 wires in a parallel circuit. They started walking as a group but split up as they encounter the first, second and third wires leading to the resistors.

As said, the potential difference is potrayed as the energy used by the human to walk. So, when they split up at each branches, the energy[potential difference] is not decreased becasue the energy supports them individually.

I'm not sure have I explained it clearly, im sorry because english is not my first language. If you find any part of my explaination not clear, please feel free to ask. I do appreciate using "lighter" words as I'm still new to physics. Thnk you >.<

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Filip Larsen
Gold Member
Welcome to PF, Kurokari.

Another often used analogy is to compare electrical circuits with fluid circuits like for instance water pipes. Here electrical potential corresponds to the water pressure at some point along the pipes and electrical current corresponds of the flow rate of water. Furthermore, electrical charge corresponds to water mass or volume, and electrical resistance corresponds to the friction in the flowing water. In electrical circuits, if we have a string of wire with a potential difference between the two ends of the string, we have a water pipe with pressure difference between the two ends.

Using this analogy, if you have three parallel water pipes, that is, three pipe segments that all start from the same junction A and all merge again at another junction B, then, since the pressure in junction A and B are single-valued at any given time, the pressure difference between A and B must be the pressure difference over all three pipe segments. Thus, the potential difference over the three segments is equal.

Note that the equal-potential "rule" in parallel branches (both in electrical and fluid systems) does not necessarily mean that the potential is "fixed" for the branches. Each branch will "contribute" to the overall potential difference, for instance forcing it higher or lower than the other branches would do if they were alone. Only in the case where there is an ideal voltage source (or ideal pressure source in a pipe) can we regard the potential difference as fixed, since such a source has limitless capability to provide the necessary electric current (or flow of water) to keep the potential difference fixed.

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Welcome to PF, Kurokari.

Another often used analogy is to compare electrical circuits with fluid circuits like for instance water pipes. Here electrical potential corresponds to the water pressure at some point along the pipes and electrical current corresponds of the flow rate of water. Furthermore, electrical charge corresponds to water mass or volume, and electrical resistance corresponds to the friction in the flowing water. In electrical circuits, if we have a string of wire with a potential difference between the two ends of the string, we have a water pipe with pressure difference between the two ends.

Using this analogy, if you have three parallel water pipes, that is, three pipe segments that all start from the same junction A and all merge again at another junction B, then, since the pressure in junction A and B are single-valued at any given time, the pressure difference between A and B must be the pressure difference over all three pipe segments. Thus, the potential difference over the three segments is equal.

Note that the equal-potential "rule" in parallel branches (both in electrical and fluid systems) does not necessarily mean that the potential is "fixed" for the branches. Each branch will "contribute" to the overall potential difference, for instance forcing it higher or lower than the other branches would do if they were alone. Only in the case where there is an ideal voltage source (or ideal pressure source in a pipe) can we regard the potential difference as fixed, since such a source has limitless capability to provide the necessary electric current (or flow of water) to keep the potential difference fixed.
Thank you for your reply! Ok I get the fluid system analogy. So according to what you have said, this means that the pressure exerted at 3 branches does not decrease, could you elaborate more on it? What do you mean by single valued?

The pressure does not change when branching off into 3 pipes, why? Is there any more mechanical type of explaination?

Im sorry for my slowness, if you will please do elaborate more, I will greatly appreciate it.

Look at the circuit diagram. It shows 3 resistors in parallel. They can have any value.

The connecting wires in all these diagrams are ideal wires and have no resistance. If there is no resistance in the wire there is no pd across or between any two points on the wire, even though there is current flowing. V=IR but R=0 in the wires themselves.

So the potential at the points D, E and F must be the same as at Y
The potential at the points A,B and C must be the same as at X
Therefore
the potential difference between A and D must be equal to the potential difference between X and Y
the potential difference between B and E must be equal to the potential difference between X and Y
the potential difference between C and F must be equal to the potential difference between X and Y
Therefore the potential difference between A and D must be equal to the potential difference between B and E, which must be equal to the potential difference between C and F
So if you connect the 3 resistors to a 2V source, the pd across all 3 must be 2 volts.

Look at the circuit diagram. It shows 3 resistors in parallel. They can have any value.

The connecting wires in all these diagrams are ideal wires and have no resistance. If there is no resistance in the wire there is no pd across or between any two points on the wire, even though there is current flowing. V=IR but R=0 in the wires themselves.

So the potential at the points D, E and F must be the same as at Y
The potential at the points A,B and C must be the same as at X
Therefore
the potential difference between A and D must be equal to the potential difference between X and Y
the potential difference between B and E must be equal to the potential difference between X and Y
the potential difference between C and F must be equal to the potential difference between X and Y
Therefore the potential difference between A and D must be equal to the potential difference between B and E, which must be equal to the potential difference between C and F
So if you connect the 3 resistors to a 2V source, the pd across all 3 must be 2 volts.
I think I got it.

EDIT: sorry i overlooked"in the wires"

Filip Larsen
Gold Member
Thank you for your reply! Ok I get the fluid system analogy. So according to what you have said, this means that the pressure exerted at 3 branches does not decrease, could you elaborate more on it? What do you mean by single valued?
I was just trying to put emphasis on that at any given point in the water pipe there is only "one" pressure value, or rather, if you have three pipes that meet, then even if the pressure down each pipe is different the pressure value must converge to the same value as you move the "measuring point" into the common pipe.

However, I'd rather not elaborate more on this analogy if you think your original question has been answered by Stonebridge's explanation. Even if analogies are useful at times, it is usually always best to try understand a subject in its "own domain".

sophiecentaur
Gold Member
Be careful about using 'pressure' for explaining anything in electricity. We're talking Energy not Forces.
The better analogy for Voltage (Potential Difference) is to talk in terms of gravitational potential. Three people climbing to the top of a hill from the same starting level will gain the same amount of potential energy (per kg) whichever route they take. The maximum work that you can get out of three water turbines is the same (per kg of water) if the potential differences (i.e. distance fallen by the water) are the same.

Of course the Volts must be the same for parallel circuit elements because the PD is set by the supply.
Steer clear of 'pressure'. Once you let your intuition take over, you risk getting the wrong idea about what's going on and your conclusions may not lead to the right prediction for a problem.

Filip Larsen
Gold Member
Steer clear of 'pressure'. Once you let your intuition take over, you risk getting the wrong idea about what's going on and your conclusions may not lead to the right prediction for a problem.
While I fully agree that everyone (and especially newcomers) should be careful about putting too much into an analogy, it is nevertheless remarkable how the modelling of electrical, hydraulic and mechanical system structure and dynamics end up following the same rules, so from a certain abstraction level and up you can certainly can "reuse" knowledge in one domain in another. It is like learning a new language that has a common origin with a language you already know.

In that context it may, in my opinion as a non-instructor, be beneficial to see that the abstraction of potentials and flows (as generalized force and generalized flow for instance) is a fundamental property of many (engineering) systems that, when modelled, captures the underlying energy flow in the system. So, what I think you can walk away with using an analogy to explain something like the OP question (why is voltage over three parallel branches equal) is that such a rule is indeed necessary to properly model the energy flow in systems. It has more to do with "systems" than it has to do with "potential" alone.

I guess it really depends on whether you try to understand it bottom-up as two "isolated" concepts of force and force potential, or top-down as a dual part of systems with energy flow. To me the top-down system view often makes more sense, since it in effect uses "conservation of energy" directly as a common guiding principle, while the bottom-up approach often "drowns" in detailed force considerations. I mean, does it really help explaining the original question by referring to people climbing up the hill or water having pressure. I would say, no, you need the full picture that includes the dual concept of flow for it to really make sense.

(Sorry, for the long reply. I didn't set out to make this much out of it, and to me it sounds like we all mostly agree on the matter anyway).
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