Capacitors in Series
Connecting capacitors in series is less common than in parallel, but it is a vital technique for specific engineering needs. In a series configuration, the total equivalent capacitance ($C_{eq}$) is always lower than the smallest individual capacitor in the string.
Why use Series Capacitance?
- Increased Voltage Rating: This is the primary reason to use series capacitors. While the total capacitance drops, the total voltage the string can handle is the sum of the individual voltage ratings. Two $100 , \text{V}$ capacitors in series can safely handle $200 , \text{V}$.
- Specific Tuning: Used in radio frequency (RF) circuits to achieve very precise, small capacitance values that aren't available as standard components.
The Formula
Where:
=
Equivalent Capacitance=
Individual CapacitancesExample Calculation
You connect a $10 , \mu\text{F}$ and a $20 , \mu\text{F}$ capacitor in series.
- Calculate Reciprocals: $1/10 = 0.1$ and $1/20 = 0.05$.
- Sum them: $0.1 + 0.05 = 0.15$.
- Take the Reciprocal: $1 / 0.15 = 6.67 , \mu\text{F}$.