What Are Capacitors in Series?

Capacitors are connected in series when they are connected one after another in a single path between two points of a circuit.

        C1          C2          C3
+ ──────||──────────||──────────||───── -

Unlike capacitors connected in parallel, series capacitors do not add their capacitance directly. The equivalent capacitance is always lower than the smallest individual capacitor.

Series Capacitor Formula

For capacitors connected in series:

1
─── = 1/C1 + 1/C2 + 1/C3 + ...
Ce

Therefore:

Ce = 1 / (1/C1 + 1/C2 + 1/C3 + ...)

For two capacitors, the formula can be simplified to:

C1 × C2
Ce = ─────────
     C1 + C2

Series Capacitor Calculator

Example — Two 100 µF Capacitors in Series

Suppose two 100 µF capacitors are connected in series.

C1 = 100 µF

C2 = 100 µF

The equivalent capacitance is:

Ce = (100 × 100) / (100 + 100)

Ce = 10000 / 200

Ce = 50 µF

Therefore, two identical 100 µF capacitors in series produce an equivalent capacitance of 50 µF.

Equal Capacitors in Series

When identical capacitors are connected in series, the equivalent capacitance is:

Ce = C / N

where C is the capacitance of one capacitor and N is the number of capacitors.

For example, four 100 µF capacitors in series produce:

Ce = 100 / 4

Ce = 25 µF

Voltage Across Series Capacitors

When capacitors are connected in series, the magnitude of charge on each capacitor is the same in the ideal case.

Q1 = Q2 = Q3

The voltage across each capacitor is determined by:

V = Q / C

Therefore, a smaller capacitor receives a larger voltage for the same charge.

Series Capacitor Voltage Calculator

Example — Voltage Distribution

Consider two capacitors connected in series:

C1 = 100 µF

C2 = 50 µF

Supply = 30 V

The equivalent capacitance is:

Ce = (100 × 50) / (100 + 50)

Ce = 33.33 µF

The same charge appears on both capacitors. Since C2 is smaller, it receives the larger voltage.

The voltage ratio is inversely proportional to capacitance:

V1 / V2 = C2 / C1

Charge in a Series Capacitor Network

The charge stored by the equivalent capacitance is:

Q = Ce × Vtotal

For an ideal series network, this same magnitude of charge appears on each capacitor.

Charge Calculator

Why Capacitors Are Connected in Series

There are several reasons for connecting capacitors in series.

• To obtain a lower equivalent capacitance.
• To increase the overall voltage capability of a capacitor bank.
• To obtain a capacitance value not available as a single component.
• To distribute voltage across multiple capacitors.

Voltage Rating of Series Capacitors

Connecting capacitors in series can increase the overall voltage capability of the network, but the voltage does not necessarily divide equally between real capacitors.

Differences in leakage current can cause unequal voltage distribution, particularly with electrolytic capacitors.

For high-voltage capacitor banks, balancing resistors may be required to control the voltage distribution.

Series Electrolytic Capacitors

Electrolytic capacitors require special attention when connected in series because their leakage currents can differ significantly.

For a high-voltage capacitor bank, equalizing resistors are often placed across individual capacitors to help establish a predictable DC voltage distribution.

       C1
+ ─────||─────+
|            |
|           R1
|            |
+ ─────||─────+
       C2

The resistor values should be selected according to the capacitor voltage rating, leakage characteristics and application requirements.

Series Capacitors and AC Circuits

The capacitive reactance of a capacitor is:

1
XC = ───────
     2πfC

where:

• XC is capacitive reactance in ohms.
• f is frequency in hertz.
• C is capacitance in farads.

For capacitors connected in series, their equivalent capacitance can be used to determine the combined capacitive reactance.

Series Capacitors in Power Supplies

Series capacitors are sometimes encountered in AC circuits, coupling networks and specialized power circuits.

In high-voltage applications, capacitor voltage ratings, leakage current, surge current and safety requirements must all be considered.

Series Capacitors vs Parallel Capacitors

Common Applications

• High-voltage capacitor banks
• Voltage balancing networks
• AC coupling circuits
• Signal coupling
• Capacitance matching
• Specialized power circuits
• Creating non-standard capacitance values

Common Mistakes

• Adding series capacitances directly.
• Assuming voltage divides equally between unequal capacitors.
• Ignoring capacitor leakage current.
• Ignoring individual capacitor voltage ratings.
• Using electrolytic capacitors without considering polarity.
• Ignoring balancing resistors in high-voltage capacitor banks.
• Forgetting that the equivalent capacitance is lower than the smallest capacitor.

Key Points

• Series capacitors have an equivalent capacitance lower than the smallest capacitor.
• The reciprocal capacitances add together.
• The same charge magnitude appears on ideal series capacitors.
• Voltage divides inversely according to capacitance.
• Smaller capacitors receive a larger voltage.
• Series capacitors can be used to increase the overall voltage capability.
• Real capacitors may require voltage-balancing resistors.
• Electrolytic capacitor polarity must be considered carefully.