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## Capacitors in Series – Capacitors in Parallel

The capacitor is a device made up of two metal plates separated by an insulator called a dielectric. A dielectric or insulator is a material that prevents the passage of direct current between the plates, but allows the passage of alternating current signals to a degree that depends on their frequency.

There are two typical connection types between capacitors, and they are **capacitors in series** and **capacitors in parallel**.

## Capacitors in series

**Capacitors in series** are capacitors connected one after the other. These capacitors can be replaced by a single equivalent capacitor that has a value that is the equivalent of those that are connected in series.

To obtain the value (capacitance) of this single equivalent capacitor, the following formula is used (for 4 capacitors):

1/Ceq = 1/C1+1/C2+1/C3+1/C4 or Ceq = (C1 x C2 x C3 x C4) / (C1 + C2 + C3 + C4)

It is easy to make this calculation for any number of capacitors using the most general formula:

1/Ceq = 1/C1+1/C2+………+1/CN or Ceq = (C1 x C2 x …. x CN) / (C1 + C2 + ….. + CN)

Where N is the number of capacitors that are connected in series. See the diagram.

**For example:**

If I have 2 capacitors connected in series, C1 = 470uF, C2 = 100uF. What is the capacitance of the equivalent capacitor?

Using the formula: Ceq = (C1 x C2) / (C1 + C2).

Ceq = (470uF x 100uF) / (470uF + 100uF) = 47000/570 = 82.456uF

## Capacitors in parallel

**Capacitors in parallel** are capacitors connected one beside the other. The terminals on either side of the capacitors are connected together (connected to the same point).

These capacitors can be replaced with a single equivalent capacitor with a value (capacitance) equivalent of those that are connected in parallel.

The following picture shows how to connect 4 capacitors in parallel. To find the equivalent capacitor value (CT) we use the formula : CT = C1 + C2 + C3 + C4.

It is easy to make a calculation for any number of capacitors with the most general formula:

CT = C1 + C2 + ………+ CN, where N is the number of capacitors.

As we already notice, to get the equivalent capacitor value (capacitance) of a set of capacitors in parallel we only have to add the capacitors values (capacitance) of the original circuit.

**For example:**

If I have 3 capacitors connected in parallel, C1 = 470uF, C2 = 1000uF and C3 = 100uF. What is the capacitance of the equivalent capacitor?

Using the formula: Ceq = C1 + C2 + C3.

Ceq = 470uF + 1000uF + 100uF = 1570uF.