Series Capacitor Calculator
Calculate the equivalent capacitance of capacitors connected in series. Enter multiple capacitor values to calculate the total capacitance, common charge, voltage across each capacitor and stored energy.
Series Capacitor Inputs
Capacitor Voltage Distribution
| Capacitor | Capacitance | Charge | Voltage | Energy | Voltage Share |
|---|---|---|---|---|---|
| Enter capacitor values and calculate. | |||||
Series Capacitor Formula
When capacitors are connected in series, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitances.
Ctotal = 1 / (1/C1 + 1/C2 + ... + 1/Cn)
Two-Capacitor Formula
For exactly two capacitors, the equation simplifies to:
How Series Capacitors Work
Capacitors connected in series form a chain between two circuit nodes. In the ideal steady-state model, the magnitude of charge on each capacitor is the same.
The total applied voltage is divided among the capacitors. Because voltage is given by V = Q/C, a smaller capacitance receives a larger voltage for the same charge.
Same Charge
The ideal series model has the same charge magnitude on each capacitor.
Divided Voltage
The supply voltage is distributed among the individual capacitors.
Lower Equivalent C
The equivalent capacitance is always lower than the smallest individual capacitor.
Two Capacitors in Series
For two capacitors, the product-over-sum formula provides a convenient shortcut.
Example: 100 nF and 100 nF
Two equal 100 nF capacitors produce:
Ctotal = 10000 / 200
Ctotal = 50 nF
Two equal capacitors in series therefore produce an equivalent capacitance equal to half the value of either capacitor.
Voltage Distribution Across Series Capacitors
Since the charge is the same on each capacitor, the voltage across an individual capacitor is:
Using the equivalent capacitance:
Vᵢ = Q / Cᵢ
Example: 100 nF + 200 nF at 12 V
First calculate the equivalent capacitance:
Ctotal = 66.67 nF
Q = 66.67 nF × 12 V
Q ≈ 800 nC
The voltage across the 100 nF capacitor is:
V1 = 8 V
The voltage across the 200 nF capacitor is:
V2 = 4 V
The voltages add to the 12 V applied voltage.
Energy Stored in Series Capacitors
The energy stored in an individual capacitor is:
The total energy stored in the network is the sum of the energy stored in each capacitor:
For an ideal equivalent capacitor, the same total energy can also be represented by:
Worked Series Capacitor Examples
Example 1: Two 1 µF Capacitors
Two 1 µF capacitors are connected in series across a 12 V supply.
Ctotal = 0.5 µF
Q = 0.5 µF × 12 V
Q = 6 µC
Because the capacitors are equal, each capacitor has 6 V across it.
Example 2: 100 nF + 220 nF
A 100 nF capacitor and a 220 nF capacitor are connected in series across 12 V.
Ctotal = 68.75 nF
Q = 68.75 nF × 12
Q = 825 nC
The 100 nF capacitor receives approximately 8.25 V, while the 220 nF capacitor receives approximately 3.75 V.
Common Series Capacitor Examples
| Capacitors | Equivalent Capacitance | Applied Voltage | Total Charge |
|---|---|---|---|
| 100 nF + 100 nF | 50 nF | 12 V | 600 nC |
| 1 µF + 1 µF | 500 nF | 12 V | 6 µC |
| 100 nF + 220 nF | 68.75 nF | 12 V | 825 nC |
| 100 nF + 220 nF + 330 nF | ≈53.78 nF | 12 V | ≈645.4 nC |
| 10 nF + 100 nF + 1 µF | ≈9.01 nF | 24 V | ≈216.2 nC |
Applications of Series Capacitors
Series Capacitor Voltage Ratings
Connecting capacitors in series can allow a capacitor network to withstand a higher total voltage than an individual capacitor, but the voltage does not necessarily divide equally.
The voltage division depends on capacitance, leakage current, tolerance, dielectric properties and operating conditions. A smaller capacitance can experience a larger voltage.
Practical Design Notes
- The equivalent capacitance of positive capacitors in series is lower than the smallest individual capacitor.
- Capacitors in series carry the same charge magnitude in the ideal steady-state model.
- Voltage divides inversely with capacitance.
- Capacitor tolerance affects the actual capacitance and therefore the voltage distribution.
- Leakage current can affect voltage sharing in real capacitor networks.
- Electrolytic capacitors require correct polarity and should not be treated like ideal polarity-independent capacitors.
- For high-voltage series capacitor arrangements, verify individual voltage ratings under worst-case tolerance and leakage conditions.
- Capacitor ESR, ESL and dielectric behavior can become important at higher frequencies.
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Frequently Asked Questions
How do you calculate capacitors in series?
For capacitors connected in series, calculate the reciprocal of the equivalent capacitance by adding the reciprocals of each capacitor: 1/Ctotal = 1/C1 + 1/C2 + ... + 1/Cn.
What is the formula for two capacitors in series?
For two capacitors in series, the equivalent capacitance is Ctotal = (C1 × C2) / (C1 + C2).
Is series capacitance lower than the smallest capacitor?
Yes. For positive capacitance values connected in series, the equivalent capacitance is lower than the smallest individual capacitor.
What happens to voltage across capacitors in series?
In a series capacitor network, the same charge magnitude appears on each capacitor in the ideal steady-state model. The voltage across each capacitor depends on its capacitance: V = Q/C.
Do capacitors in series have the same charge?
In the ideal series-capacitor model, each capacitor carries the same magnitude of charge.
How is voltage divided between series capacitors?
Because the charge is the same, the voltage across each capacitor is inversely proportional to its capacitance. A smaller capacitor receives a larger voltage.
Why are capacitors connected in series?
Series capacitors can be used to obtain a lower equivalent capacitance and, in some configurations, to increase the effective voltage rating of a capacitor network when voltage sharing is properly controlled.
What is the equivalent capacitance of two equal capacitors in series?
Two equal capacitors connected in series have an equivalent capacitance equal to half the value of either capacitor. For example, two 100 nF capacitors produce 50 nF.
How do you calculate energy stored in a capacitor?
The energy stored in a capacitor is E = 1/2 × C × V², where C is capacitance in farads and V is voltage across the capacitor.