Capacitors in Series

By Mohit Uniyal|Updated : August 25th, 2022

Capacitors in series are done to improve the stability of the system. In an electric circuit, a capacitor is a passive component designed to store energy in its electric field. A capacitor can be modeled as electrical capacitance in an electric circuit. Tuning circuits, Dynamic memory elements, etc. are some of the applications of capacitors and connections of capacitors in series.

A capacitor can be formed by separating two conductors, and between the separation, insulators or dielectrics can be filled. The equivalent capacitance depends on individual capacitance as well as the way they have connected, either capacitor in series or capacitors in parallel. The article elaborates on the equivalent capacitance of capacitors in series, formula, etc.

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Capacitors in Series

A capacitor is a two-terminal passive component that can store energy electrostatically in an electric field. There exist different types of capacitors, but all contain two electrical conductors separated by a dielectric between the conductors. The purpose of the dielectric is to increase the storage charge capacity of the capacitor.

Multiple connections of capacitors in series can be modeled as a single equivalent capacitor in series. The total equivalent capacitance of the capacitors in series is always less than the smallest capacitor present in the circuit.

Equivalent Capacitance of Capacitors in Series

Consider a series connection of N capacitors having equivalent circuits, also as shown below. The same current is flowing through all the capacitors as they are in series.

If a current I is flowing through a capacitor having capacitance C, the voltage V across the capacitor at any interval of time is equal to,

 

Capacitors in Series 1

Capacitors in series are similar to that of resistors in parallel. The equivalent capacitance of capacitors in series is always less than the value of the smallest capacitance present in the circuit. For two capacitors, C1 and C2 connected in series, the equivalent capacitance will be:
Capacitors in Series 2

 

Voltage and Current Across Capacitors in Series

For simplification, assume two capacitors C1 and C2 connected in series and voltage across capacitor are V1 and V2, respectively, as shown below:

Since the capacitors are in series, the current through both the capacitors will be the same. The total equivalent capacitance will be,

 

Capacitors in Series 3

Since the capacitor is in series, the charge will not get distributed between capacitors. If Q1 and Q2 are the charges across capacitors C1 and C2, respectively, then

 Capacitors in Series 4

Capacitors in Series Formula

When N number of capacitors are connected in series, then the overall equivalent capacitance is calculated by the given Capacitors in series formula:

 

Capacitors in Series Formula

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FAQ on Capacitors in Series

  • On connecting the capacitors in series, the current flow across all the capacitors will be the same, and the voltage drops across individual capacitors. The overall capacitance also decreases and is always less than the value of the smallest capacitance present in the circuit.

  • The overall equivalent capacitance in series decreases, and hence from the relation Q=CV, to maintain a charge, the net voltage increases. Capacitors in series provide a high total voltage rating.

  • When N number of capacitors are connected in series, the overall equivalent capacitance is given by:

    1/C_eq=1/C_1+1/C_2+1/C_3+ . . . .1/C_N

  • Capacitors in series increase the total voltage rating of the circuit, thus improving the voltage handling capability.

  • Yes, capacitors can be added in a series combination same as the resistors. The properties of capacitors in series are different than that of resistors in series. 

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