Capacitors in Series

- in some instances capacitors may appear in series and it is necessary to be able to calculate the value.

There are several instances where capacitors may be required to be placed in series. In some circuits, this occurs naturally, for example in some oscillators. In other instances capacitors may be placed in series for a variety of reasons.

Although the most common combination is to see two capacitors in series, it is possible to place three or more in series.

Formula for calculating value of capacitors in series

Unlike capacitors placed in parallel, it is not quite as simple to calculate the overall capacitance of a number of capacitors placed in series, although it is far from difficult.

A diagram showing how capacitors are added in series.
Capacitors in series

In theory there is no limit to the number of capacitors that can be added in series. Obviously there can be practical limits dependent upon the application, space and other physical limitations.

The formula to determine the total capacitance of capacitors in series: 1/Ctot = 1/C1 + 1/C2 + 1/C3 +  . . .

Two capacitors in series

When calculating the general case for the total capacitance value for a series of capacitors in series, the computation can be a little long winded if done manually. As most networks, only two capacitors are placed in series and it is possible to considerably simplify the formula. This makes manual computation very much easier.

A diagram showing two capacitors in a series configuration.
Two capacitors in series


The formula to determine the total capacitance of two capacitors in series: Ctot = C1 x C2 / (C1 + C2)

Capacitors in series calculator

The calculator below provides the total capacitance for two capacitors in series. The capacitance can be entered as Farads, µfarads, nanofarads, or picofarads, provided that the same units are used for both capacitors. The answer is provided in the same units as those entered.


Series Capacitor Calculator

Enter Capacitance Values:

C1:   Farads, F;
C2:   Farads, F;

Results:

Ctotal:   Farads, F


Precautions for using capacitors in series

Although capacitors do appear in series in a number of circuit configurations like oscillators and the like, capacitors may be used in series to increase the working voltage.

When two capacitors are used in series, then the issue is often that the two capacitors do not share the voltage equally. Differences in leakage current occur between capacitors, especially for capacitors like electrolytic versions and this means that the voltages across the two capacitors can differ greatly, and as a result one may be subject to an over-voltage conditions which could result in the destruction of one or both capacitors.

Diagram showing how two capacitors in series can share applied voltage when two resistors are added.

To assist in sharing the voltage equally across the two capacitors, high value resistors are placed around the capacitors as a potential divider. The values of the two resistors should be such that the current flowing through them is at least ten times higher than that of the leakage current. In this way, the voltage will be shared more equally across the capacitors in series. Even so it is best to leave a significant margin in the working voltage.


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