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Capacitors in Series

Connecting capacitors in series is no more difficult than connecting resistors in series. After all, as an electronic component a capacitor has two leads, so capacitors can be connected to each other or to other types of components very easily. But what is the effect of such a connection?

We have already seen resistors connected in series and in parallel. Clearly, capacitors can be connected in series and in parallel as well, or they can be interconnected with resistors. We'll look at the latter possibilities elsewhere in this series of pages. For the moment, we'll concentrate on capacitors in series.

Two capacitors connected in series.

The figure to the right shows two capacitor symbols connected in series. As a starting point, let's assume that these are two identical capacitors. The connection between them is assumed to have no resistance, and therefore no effect on the behavior of these two capacitors or any circuit in which they may be connected. Therefore, this connection may be any length, covering any distance, without having any noticeable effect.

Series capacitors with no separation between them.

This being the case, let's shorten the distance between capacitors to zero. This means that the connected plates of the two capacitors will actually touch, as shown in the second image to the right.

Next, we recognize that the thickness of that center plate is unimportant; it's simply a broad conductor between the two capacitors. Therefore we can make this center plate as thin as we want. Therefore, at least in theory, we can reduce it to atomic thickness without any effect on the capacitance of the series combination.

Series capacitors with the center plate removed.

But that center plate is nothing more than an equipotential plane in the middle of an electric field. Since the outer plates are still parallel to each other, removing the center plate won't change the total electric field. This leaves us with a single capacitor, but with the plates spaced twice as far apart as for either of the original capacitors. As a result of this, the combined capacitance of the two identical capacitors in series is just half the capacitance of either one.

Capacitors of differing values may also be connected in series. In such cases, we can note that such capacitors may all be constructed with the same plate size and shape, with only the plate spacing determining the capacitance value. Connecting them in series, we note that the effective spacing between the end plates is equal to the sum of the spacings of the individual capacitors. This applies to any number of such capacitors in series.

Since the capacitance of any capacitor is inversely proportional to the distance between the plates, we can express the total capacitance, CT, of any number of capacitors connected in series as:

1  =  1  +  1  +  1  + ···

CT C1 C2 C3

For two capacitors in series, this can be written as:

CT C1 × C2

C1 + C2

You probably noticed that this formula looks just like the formula for resistors in parallel. This is correct, and it is no accident. Remember that resistance is a property that reduces current flow, while capacitance is a property that enables current flow, at least briefly. Since these are inverse properties, it is only reasonable that they would behave in opposite ways when connected in series or parallel. This is in fact the case.

Prev: Reading Capacitance Values Next: Capacitors in Parallel

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