# Prove to me how capacitors in parallel can have the same V across plates

• mhrob24
In summary: I'm not sure how this works, but it makes sense to me. In summary, when looking at a capacitor connected in parallel, you can't assume that the charge on the plates is the same as the charge on another capacitor within the parallel connection. However, the electric field between each capacitor in the parallel connection can't be the same if the charge on one capacitor can be different from another.
mhrob24
*If at any point I say something incorrect or its clear I don't have the right understanding of something, please point it out and correct me. I need to be sure I'm understanding it all correctly. So please don't answer unless you're willing to read this entire post*

So I know capacitors in series have same the charge (Q) stored on each of their plates because of conservation of charge (the magnitude of the charge moved through the circuit across the battery terminals must be conserved so as the charge travels, each conducting capacitor plate with have the same magnitude charge Q). I also know that its possible that the potential between each capacitor is different. My book doesn't directly explain why after stating this, but I can see how that's possible :

V = Q/C

When doing the calculation for capacitance between 2 parallel plates, we get: C = ε0*A/D. Thus, for parallel plate capacitors (or any other type of capacitor for that matter), the capacitance only depends on the geometry (area) of the conducting plates and the distance between them. So, you can effectively change the voltage of a capacitor without messing with the magnitude of charge on the plates because capacitance is independent of Q (and also of V). So that makes sense to me. So not all the capacitor plates in a series will have the same area or distance between them, but they will all have the same magnitude Q stored.

What DOESN'T make sense to me is the fact that each capacitor connected in parallel will have the same V across their plates, but at the same time, its also possible that each capacitor stores a different charge.

So the voltage in our case is basically the work done in moving a charge in an electric field divided by the charge's magnitude. So, the voltage depends on the electric field, not the charge moving in it. So when we look at a capacitor connected in parallel, we know that the charge Q stored on its set of plates could possibly be different from the charge stored on another capacitor within the parallel connection. With that said, the electric field DOES depend on the charge stored on the capacitor (that's what causes the uniform field between the plates in the first place). So, this means that the electric field between each capacitor in the parallel connection can't be the same if we know that its possible for the charge on one capacitor can be different from another capacitor. Thus, if the electric field on one capacitor can be different from another, and the voltage depends on the electric field, how can each capacitor have the same V?

The only way I can kind of see how it makes sense is if you use V = Q/C and plug in Q*d/ε0*a for V. Then you get:

Q*D/ε0*a = Q/C. Then, the charge Q cancels so V won't depend on the electric field or the charge Q on the capacitor plates...but this just goes against everything I learned previously about potential difference between a uniform electric field (V = E*D, where E depends on magnitude of charge Q stored on each plate)...

mhrob24 said:
Thus, if the electric field on one capacitor can be different from another, and the voltage depends on the electric field, how can each capacitor have the same V?
You are looking at that backwards. The field depends on the voltage.

Looking at it another way, how could you possibly have parallel caps (or anything else) with different voltages? That would imply that there was a zero-resistance wire with different voltages at different point. Not possible.

Asymptotic, berkeman, vanhees71 and 1 other person
mhrob24 said:
Summary: n/a

So, this means that the electric field between each capacitor in the parallel connection can't be the same if we know that its possible for the charge on one capacitor can be different from another capacitor.
This part is where you are going wrong (I think).

For each capacitor you have a relationship between V and Q. In a series circuit all of the capacities have the same Q, so we solve for each V. In a parallel circuit all of the capacitors have the same V, so we solve for each Q.

Either way there is a unique solution.

mhrob24
Ok, let me see if I've got this correct.

So, E ∝ Q. However, Q doesn't reach the plates without the V from the battery moving it. So I can see how the poster before you is correct by saying that the E field depends on the V, not the other way around. So, basically, this is saying E ∝ V. If you rearrange C = Q/V to solve for Q, you get:

Q = C * V.

Thus, this proves that each capacitor in a parallel circuit CAN store a different charge on its plates while still having the same V as the other capacitors in the circuit because you can simply change the capacitance (which only depends on geometry of the plates and distance between them) without changing the V (Since C doesn't depend on Q or V)...right?

Also, the poster before you stated that its impossible to have a different voltages for each capacitor in a circuit. However, my understanding is that it is possible in a series circuit, because V = Q/C, so by changing the capacitance on one capacitor in a series circuit, you are changing the potential difference between the plates of that capacitor. Thus, you add up the potential drops between each capacitor to get your total supply voltage (Unless he meant that its impossible to change the SUPPLY voltage of the circuit, which is correct. You can't do that.)

mhrob24 said:
Also, the poster before you stated that its impossible to have a different voltages for each capacitor in a circuit. However, my understanding is that it is possible in a series circuit,
Yes, of course it's possible in a series circuit. I specifically, and clearly, spoke about a parallel circuit. They are not even remotely the same thing.

In parallel all components must have the same potential difference across their terminals because each terminal is interconnected by "perfect" conductors. That is what @phinds said. Please don't misrepresent a comment and then disagree!

davenn and phinds
Temporarily closed for moderation.

Edit: No, I changed my mind. Closed permanently. The OP question has been answered. I'm going to clean up the off topic stuff about interpretation of words.

weirdoguy, jbriggs444 and phinds

## 1. How do capacitors in parallel have the same voltage across their plates?

When capacitors are connected in parallel, they share the same voltage across their plates. This is because the voltage across each capacitor is equal to the total voltage of the circuit. Since the capacitors are connected in parallel, they are connected to the same two points in the circuit and therefore have the same voltage across them.

## 2. Can you prove mathematically that capacitors in parallel have the same voltage?

Yes, the voltage across capacitors in parallel can be proven mathematically using Kirchhoff's Voltage Law (KVL). KVL states that the sum of the voltage drops in a closed loop circuit is equal to the sum of the voltage sources in the same loop. In this case, the voltage drop across each capacitor is equal to the total voltage of the circuit, so the voltage across each capacitor must be the same.

## 3. What happens to the total capacitance when capacitors are connected in parallel?

When capacitors are connected in parallel, the total capacitance increases. This is because the total capacitance of a parallel circuit is equal to the sum of the individual capacitances. So, when capacitors are added in parallel, the total capacitance increases due to the addition of the individual capacitances.

## 4. Is there a limit to the number of capacitors that can be connected in parallel?

Technically, there is no limit to the number of capacitors that can be connected in parallel. However, it is important to consider the practical limitations of the circuit, such as the available space and the desired capacitance value. Additionally, too many capacitors in parallel can lead to a higher risk of failure and can also affect the overall performance of the circuit.

## 5. Can capacitors in parallel store more charge than a single capacitor?

Yes, capacitors in parallel can store more charge than a single capacitor. This is because the total charge stored in a parallel circuit is equal to the sum of the individual charges stored in each capacitor. So, when capacitors are connected in parallel, the total charge stored increases due to the addition of the individual charges stored in each capacitor.

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