Capacitors in Series

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.

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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 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:

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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,

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 Formula

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