Series Combination of Capacitors

A capacitor is a fundamental electronic component that has the ability to store electric charges. A capacitor is made of two metallic plates (also known as conductors) separated by an insulator (dielectric). 

The capacitance of a capacitor C is given by

• Q is the charge on the two metallic plates. 

• V is the potential difference between the two conductors.

The capacitance of a capacitor C is dependent on the size, shape, and distance of the two conductors. Sometimes, the insulating material used in the capacitor can also affect the capacitance.

The SI unit of the capacitance is Farad, named after the eminent scientist Michael Faraday.

1 Farad is equivalent to 1 coulomb volt-1. In other words, 1F = 1 C V-1.

This section will cover the series combination of capacitors and their importance.

Combination of capacitors 

The capacitors are connected in a circuit either in series or in parallel. A circuit containing several connections of capacitors will behave as a single equivalent capacitor. The parallel and series combinations of capacitors can also be used together in a circuit. Such combinations are used in a lot of applications.

If a circuit contains several capacitors arranged in a combination of series and parallel connections, calculate the individual capacitances of the series and parallel connections separately. Combine the value to calculate the equivalent capacitance of the entire network. 

Series combination of capacitors

The capacitors arranged in a single line form the series combination of capacitors. 

The effective capacitance C is calculated by combining several capacitors of capacitance C1, C2, C3…..Cn. However, the way in which the individual capacitors are connected in a circuit determines the effective capacitance C. 

Let us begin by combining two capacitors, C1 and C2, in series. Connect the left plate of the capacitor C1 and the right plate of the capacitor C2 to the two terminals of a charging battery. The charges across the two capacitors will be Q and -Q.

• -Q is the charge on the right plate of the capacitor C1.

• Q is the charge on the left plate of the capacitor C2.

This results in the creation of an electric field in the conductor connecting the two capacitors C1 and C2. The charge would continue to flow until there is no electric field and the net charge on both the capacitors C1 and C2 becomes zero. Thus, the charges are the same on both the capacitors in a series combination.

Let V1 and V2 be the potential drop across the two capacitors, C1 and C2. The total potential drop V is calculated by adding the potential drops V1 and V2 across the capacitors C1 and C2.

V=V1+V2

We know that, C=QV

Combining this in the above equation, we get, 

V=V1+V2=QC1+QC2

Or, VQ=1C1+1C2

Substituting VQ=1C In the above equation, we get the effective capacitance of the series combination.

1C=1C1+1C2

For n number of capacitors arranged in series combination, the total potential drop V would be

V=V1+V2+…..+Vn=QC1+QC2+….+QCn

Similarly, the effective capacitance of n number of capacitors in series combination is given by 

1C=1C1+1C2+…..+1Cn

Importance of series combination of capacitors

Series connection of capacitors is generally preferred when working with higher voltages. When capacitors arranged in series are connected to a voltage source, each capacitor in the arrangement holds an equal amount of charge and the total charge is evenly divided across all the capacitors. A capacitive voltage divider with serially connected capacitors is used in AC circuits.

Conclusion

Capacitors are electronic components that have the ability to store electric charges. The capacitors are connected in a circuit either in series or in parallel. By combining capacitors in a single line, they form a series circuit. The total capacitance C of a circuit containing capacitors in series is the sum of the reciprocals of all of the individual capacitances.