Capacitor Series Connection

Calculator and formula for a capacitor series connection with two capacitors

Capacitance Calculator

Two Capacitors in Series

This function calculates the total capacitance or one of the capacitors in a series connection of two capacitors. Select what to calculate and enter the known values.

Result
Total Capacitance:
Capacitance C₂:

Circuit Diagram & Formulas

Capacitor Series Connection with 2 Capacitors
Calculate Total Capacitance
\[C_{total}=\frac{C_1 \cdot C_2}{C_1 + C_2}\]

Formula for the total capacitance of two capacitors connected in series.

Calculate Capacitor C₂
\[C_2=\frac{C_1 \cdot C_{total}}{C_1 - C_{total}}\]

To calculate C₂ given the total capacitance and C₁.

More Capacitors?

For series connections with more than 2 capacitors, use the general function.

Theory - Two Capacitors in Series

Basics of Two-Capacitor Series Connection

In a series connection of two capacitors, the calculation of the total capacitance is particularly simple because a direct formula can be used. This circuit is often used in practice.

Calculation Formulas

Total Capacitance
\[C_{total}=\frac{C_1 \cdot C_2}{C_1 + C_2}\]

The total capacitance is the product of the two capacitances divided by their sum.

Capacitor C₂
\[C_2=\frac{C_1 \cdot C_{total}}{C_1 - C_{total}}\]

Calculation of C₂ when C₁ and the total capacitance are known.

Calculation Examples

Example 1: Total Capacitance

Given: C₁ = 100μF, C₂ = 220μF

\[C_{total}=\frac{100 \cdot 220}{100 + 220}=\frac{22000}{320}=68.75μF\]

Result: The total capacitance is 68.75μF.

Example 2: Capacitor C₂

Given: C₁ = 100μF, Ctotal = 60μF

\[C_2=\frac{100 \cdot 60}{100 - 60}=\frac{6000}{40}=150μF\]

Result: Capacitor C₂ has 150μF.

Practical Applications

Capacitance Adjustment:
• Combine standard values
• Fine-tuning
• Tolerance compensation
• Prototyping
Voltage Divider:
• DC voltage divider
• High voltage applications
• Measurement circuits
• Calibration
Filter Design:
• Crossovers
• Noise filters
• Audio crossover
• Signal conditioning
Important Notes
  • The total capacitance is always smaller than the smallest individual capacitance
  • For equal capacitance values: Ctotal = C/2
  • Voltages are distributed inversely proportional to the capacitances
  • To calculate C₂, Ctotal must be less than C₁
  • All capacitors carry the same charging current
  • The total voltage rating is the sum of the individual voltages
Special Case: Equal Capacitances
Two Identical Capacitors
\[C_{total}=\frac{C \cdot C}{C + C}=\frac{C^2}{2C}=\frac{C}{2}\]

For two identical capacitors with capacitance C, the total capacitance is exactly half.

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