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I know that equivalent capacitance of multiple capacitors in series is $$ C = \left(\frac{1}{C_1} + \cdots + \frac{1}{C_n}\right)^{-1} $$ and in parallel is $$ C = C_1 + \cdots + C_n. $$ But there are circuits that are neither in parallel nor series.

So what is the canonical definition of equivalent capacitance?

This question sprung to mind when I tried to find equivalent capacitance in this circuit:

enter image description here

Apparently, there are some techniques known as Y-Delta transforms. But I wouldn't understand it without a clear definition of equivalent capacitance.

This is not a question about calculating capacitance/resistance in parallel or series, but the very definition of "equivalent capacitance."

For example, the definition of equivalent resistance goes something like this. If we replace all the individual resistors with one of equivalent resistance, we get the same current/power (provided constant voltage). In effect, the equivalent resistance is really defined by the ratio $$\Delta V / I$$.

So what is the analog for capacitance? For only one capacitor, its capacitance can be defined as $$\Delta V/Q.$$ But for a network of multiple capacitors (not necessarily in parallel or series), what is the quantity Q here?

Thank you!

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  • \$\begingroup\$ It's not a duplicate. My question is about capacitors, not resistors. And this is not a question about calculations of resistance in parallel or series. The question is what "equivalent capacitance" really means. \$\endgroup\$
    – Myath
    Feb 16, 2016 at 9:00
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    \$\begingroup\$ How are capacitors different from resistors? \$\endgroup\$ Feb 16, 2016 at 9:09
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    \$\begingroup\$ You say "This is not a question about calculating capacitance/resistance in parallel or series, but the very definition of "equivalent capacitance." " - and I disagree. \$\endgroup\$
    – Andy aka
    Feb 16, 2016 at 9:10
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    \$\begingroup\$ calculating series/parallel capacitance/resistance is essentially the same. The same principles of calculation apply to both, so the questions are similar enough for a duplicate vote \$\endgroup\$ Feb 16, 2016 at 14:31
  • \$\begingroup\$ @RobhercKV5ROB No, the equations for series/parallel capacitors are the inverse of those for resistors; they aren't the same. \$\endgroup\$
    – endolith
    Feb 17, 2016 at 15:57

3 Answers 3

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In a more general way, when you connected something between A and B, this something sees an equivalent impedance, which in your case would be an equivalent capacitance because there's only ideal capacitors. The equivalent impedance would be the one viewed between A and B from any circuit connected between these points. Regardless if the capacitors are in series/parallel/star/whatever...

All of this comes from the superposition principle.

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The canonical definition for capacitance between two nodes, whether total, equivalent or other, is the charge in coulombs required to change the potential difference by one volt. This is true whether there is a single capacitor between the nodes, a simple network like series or parallel, or an arbitraliy complicated network.

I'm not sure your term 'equivalent capacitance' is used by the rest of the community the way you are using it.

Generally, that term is used for the capacitance of a diode junction, or a FET input, where the fact that current flows into a component raising its voltage, and can flow out again, means you can define a capacitance. However, the primary purpose is not to be a capacitor, and that capacitance is likely to change under different operating conditions.

Most people would call the formulae you have quoted the 'total capacitance'.

Having said that, the Y-Delta transformation works for any type of impedance, not just capacitors. It works for resistors, inductors, and when you can handle the maths, a mix of all those.

For the moment, the Y-Delta transform, followed mathematically, will let you transform a Y of capacitors in to a Delta of capacitors, only needing a definition of impedance, to make sure you get the component description the 'right way up'. Be aware that the impedance of a capacitor is of the form 1/C. So when, as you know, you adds caps in series, you add impedances, when in parallel, you admittances.

With the Y-Delta, you can transform the inner Y in your diagram to a Delta, which will then line up with your outer Delta nicely, to allow you to do the series and parallel thang.

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Equivalent Capacitance in the context that you use it can simply be called capacitance. Capacitance can be defined as ΔV/Q. This is true for any capacitor or network of capacitors. If a circuit behaves in a purely capacitive way then it HAS that capacitance, rather then being equivalent to that capacitance. Of course the situation gets a whole lot more complex when a network does not behave of a pure capacitance (or resistance or inductance).

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