# Partial capacitances of a system of conductors

• Granger
In summary, the conversation discusses a problem involving a three-conductor system and determining the partial capacitance scheme of the system. The equations for determining the capacitance between conductor 2 and 0, and between conductor 1 and 2 are provided. There is a question about why the partial capacitance C10 is zero, and it is determined that the conducting shell acts as a shield and there are no field lines between conductor 1 and 0. The conversation also discusses the concept of partial capacitances and their relation to actual capacitances.
Granger

## Homework Statement

I have a small question about the following problem. The figure represents the cross-section of a three-conductor system comprising a communications coaxial cable of length l running parallel to a conducting wall (reference conductor). Determine the partial capacitance scheme of the conductor system.

[![enter image description here][1]][1] [1]: https://i.stack.imgur.com/G0l6u.png

## Homework Equations

3. The Attempt at a Solution [/B]

So, I had zero troubles finding out the capacitance between conductor 2 and zero and between conductor 1 and 2.

$$C_{20} = \frac{2 \pi \epsilon_0 l}{\ln (\frac{d}{r_2} + \sqrt{(\frac{d}{r_2})^2 -1})}$$

$$C_{12} = \frac{2 \pi \epsilon l}{\ln (\frac{r_2}{r_1})}$$

However I'm having trouble understanding why $$C_{10} = 0$$. My guess is that somehow conductor 2 acts as an electric shield between conductor 1 and conductor zero, so that the electric field due to conductor 1 is not "felt" by conductor zero. However I'm not sure if this is correct and would like some more insight about this. Can someone help me?

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Hmm, that doesn't look right to me either. From an EE perspective, C12 and C20 are in series to form C10... I'm not familiar with the term "partial capacitance" though -- maybe it has some other meaning?

berkeman said:
Hmm, that doesn't look right to me either. From an EE perspective, C12 and C20 are in series to form C10... I'm not familiar with the term "partial capacitance" though -- maybe it has some other meaning?

Hey berkeman! Thank you for trying to help.
Yes partial capacitances are a little bit different than "regular capacitances" (i.e. the capacitances that figure out on a capacitance matrix). What my book says is

" An alternative method – the so-called partial capacitance scheme – consists of modeling theelectric interactions among conductors through a network of n(n+1)/2 fictitious capacitors. Physically speaking, each capacitor connecting any two conductors is intended somehow to represent the electric field lines existing between those conductors. The electric energy stored in the multiple conductor system is the sum of the electric energies pertaining to the capacitors of the scheme."

I'll provide an example if you need one.
That's why I think they're right when they say the partial capacitance C10 is zero because there are no field lines that go from conductor 1 through conductor 0 (only between conductors 1 and 2 and conductors 2 and zero) because the conducting shell acts as a shield. What do you think?

EDIT: Because in the next question we are supposed to relate the partial capacitances to the actual capacitances and C10 is indeed different than zero

Granger said:
That's why I think they're right when they say the partial capacitance C10 is zero because there are no field lines that go from conductor 1 through conductor 0 (only between conductors 1 and 2 and conductors 2 and zero) because the conducting shell acts as a shield. What do you think?
Yes, okay, that all makes sense now. You are correct that there are no field lines starting on 1 and ending on 0.

Granger

## 1. What are partial capacitances?

Partial capacitances refer to the individual capacitances of each conductor in a system of conductors. They represent the amount of charge that can be stored on each conductor for a given voltage.

## 2. How are partial capacitances calculated?

Partial capacitances can be calculated using the formula C = Q/V, where C is the capacitance, Q is the charge and V is the voltage. The charge and voltage values used in this formula should correspond to the specific conductor being analyzed.

## 3. Why are partial capacitances important?

Partial capacitances are important because they determine the overall capacitance of a system of conductors. This information is crucial in understanding the behavior of the system and designing circuits or devices that utilize capacitors.

## 4. How are partial capacitances affected by the distance between conductors?

The partial capacitances of a system of conductors are inversely proportional to the distance between conductors. This means that as the distance between conductors increases, the partial capacitances decrease.

## 5. Can partial capacitances be added together?

Yes, partial capacitances can be added together to determine the total capacitance of a system of conductors. This is known as the principle of superposition and is a fundamental concept in the analysis of circuits and systems.

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