Capacitors in Series
When capacitors are connected in series, they are connected end-to-end so that the same electric charge flows through each capacitor. Series connections are commonly used to increase the maximum working voltage of a capacitor bank or to obtain a capacitance value that is not readily available. Unlike resistors, connecting capacitors in series decreases the total capacitance.
What Is a Series Connection?
In a series connection, the positive terminal of one capacitor is connected to the negative terminal of the next capacitor, forming a single current path.
+ ──||────||────||── -
The same charge is stored on every capacitor in the series chain, while the total applied voltage is divided across the individual capacitors.
Equivalent Capacitance
The total capacitance is calculated using the reciprocal formula:
1 / CT = 1 / C1 + 1 / C2 + 1 / C3 + ...
For only two capacitors:
CT = (C1 × C2) / (C1 + C2)
Series Capacitance Examples
| Capacitors | Total Capacitance |
|---|---|
| 10 µF + 10 µF | 5 µF |
| 100 µF + 100 µF | 50 µF |
| 220 µF + 220 µF | 110 µF |
| 100 µF + 220 µF | 68.75 µF |
| 470 µF + 1000 µF | 319.7 µF |
Voltage Distribution
The total voltage applied across a series capacitor network is divided among the individual capacitors.
If all capacitors have the same capacitance, the voltage is shared equally.
| Configuration | Total Voltage | Voltage on Each Capacitor |
|---|---|---|
| 2 × 100 V capacitors | 200 V | 100 V each |
| 3 × 100 V capacitors | 300 V | 100 V each |
Voltage Balancing Resistors
Electrolytic capacitors connected in series may not share voltage equally due to manufacturing tolerances and leakage-current differences.
To improve voltage sharing, high-value balancing resistors are often connected in parallel with each capacitor.
R
/\/\
+ ---||---+
R
/\/\
+ ---||---+
Balancing resistors are commonly used in high-voltage power supplies and industrial equipment.
Why Connect Capacitors in Series?
- Increase the overall voltage rating.
- Obtain uncommon capacitance values.
- Create high-voltage capacitor banks.
- Design pulse power circuits.
- Build high-voltage DC supplies.
Advantages
- Higher voltage capability.
- Simple construction.
- Useful in high-voltage applications.
- Allows use of standard capacitor values.
Disadvantages
- Total capacitance decreases.
- Voltage may not divide equally.
- Balancing resistors may be required.
- Failure of one capacitor can affect the entire network.
Typical Applications
- High-voltage DC power supplies.
- Tube amplifiers.
- Pulse generators.
- Laser power supplies.
- X-ray equipment.
- Industrial inverters.
- Capacitor banks.
- Energy storage systems.
Common Mistakes
| Mistake | Result |
|---|---|
| Assuming capacitance increases. | Series connection reduces capacitance. |
| Ignoring voltage imbalance. | One capacitor may be overstressed. |
| Using different capacitor values. | Unequal voltage distribution. |
| Omitting balancing resistors. | Reduced reliability in high-voltage circuits. |
Real-World Examples
| Equipment | Typical Application |
|---|---|
| Valve (Tube) Amplifier | High-voltage filter capacitors. |
| CRT Television | High-voltage power supply. |
| Industrial Inverter | DC-link capacitor bank. |
| Tesla Coil | High-voltage pulse capacitor bank. |
| Laboratory Power Supply | High-voltage filtering. |
Key Points
- Connecting capacitors in series decreases the total capacitance.
- The total voltage rating increases.
- The same charge exists on every capacitor in the series chain.
- Voltage balancing is important when electrolytic capacitors are connected in series.
- Series connections are widely used in high-voltage electronic equipment.