# Voltage of Capacitors in Series, a widely held assumption

• Hirams_bro
In summary, the conversation discusses the relationship between the voltage of each capacitor in a series circuit and the total voltage of the battery. The participants question how this relationship is proven using the laws of electrostatics, rather than Kirchoff's Laws. They also examine different attempts at explaining this relationship and consider the use of Maxwell's equations to derive it. Finally, they discuss the concept of using an electric potential in electrostatics to understand this relationship.
Hirams_bro
Say we have a simple circuit with just a battery and two capacitors. Why must the voltage of each capacitor in series add up to the total voltage of the battery? It seems intuitively plausible, I admit. But can someone show how to go about proving this using the laws of electrostatics ( please, not Kirchoff's Laws )?
I've already consulted 3 physics texts and none of them shed any light on this question. In one book, it says "clearly the voltage Vac = Vab + Vbc." That's it. Just because they wrote it in the form of an equation and said its clear, I guess they think they proved it. But that doesn't really prove much.
In Jewett's Physics for Scientists, their attempt at explaining this is to simply refer to a diagram and say "as can be seen, the diagram shows that these voltages add up..." Well drawing a diagram and labeling it doesn't it make it so. And this fact is used to prove the Law of Series Capacitance.

It seems to be a widely held assumption that individual voltages add up to the circuit voltage for series capacitors, but how can we assume this? I'm not aware of any conservation of voltage. Can someone please explain it?

Thank you. I'm sure after this semester, when I finish Calc 3, I'll be able to make sense of Maxwell's Equations, gradient and curl, etc., and derive it from those. Until then is there any other way of showing this relationship, one that might be more familiar for a Physics 2 student?

OK, maybe try this. In electrostatics, we can use an electric potential instead of an electric field. Work done by a force usually depends on the path taken, but if the force can be represented by a potential, the work done only depends on the start and end points of the path. In a circuit, the charge starts out and ends up at the same place, so the total work done (charge times potential difference) in a loop is zero.

## 1. What is the equation for calculating the voltage of capacitors in series?

The equation for calculating the voltage of capacitors in series is V = V1 + V2 + V3 + ... + Vn, where V is the total voltage and V1, V2, V3, etc. are the individual voltages of each capacitor.

## 2. Is it true that the voltage across each capacitor in a series is the same?

No, it is a widely held assumption but it is not always true. In theory, the voltage across each capacitor in a series should be the same, but in reality, there may be slight differences due to factors such as internal resistance and leakage currents.

## 3. Can the voltage of capacitors in series be greater than the voltage of the power supply?

Yes, the voltage of capacitors in series can be greater than the voltage of the power supply. This is because the voltage across each capacitor adds up, resulting in a total voltage that is higher than the power supply voltage.

## 4. How does the voltage of capacitors in series affect the total capacitance?

The voltage of capacitors in series does not affect the total capacitance. However, the total voltage applied to the circuit will be divided among the capacitors based on their individual capacitance values.

## 5. Can capacitors in series be replaced by a single capacitor with the same total capacitance?

Yes, capacitors in series can be replaced by a single capacitor with the same total capacitance. This is because capacitors in series have a cumulative effect on the total capacitance, so a single capacitor with the same total capacitance will have the same effect on the circuit.

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