Calculate Capacitor Series Connection

Calculator and formulas for calculating a capacitor series connection

Calculation

Capacitor Series Connection

In a series connection of capacitors, the capacitors are connected one after another. The total current flows through all capacitors.

Capacitor Series Connection
Input Instructions
  • Exponents are not allowed
  • Enter values in a suitable unit
  • Enter values separated by semicolons (e.g. 3.3; 12; 22)
  • The result will be displayed in the same unit
Example: 3.3; 12; 22
Result
Total Capacitance:

Formulas

Basic Formula for Series Connection
\[\frac{1}{C_{total}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}\]

The total capacitance is calculated using the reciprocal of the individual capacitors.

Formula for 2 Capacitors
\[C_{total}=\frac{C_1 \cdot C_2}{C_1 + C_2}\]

Simplified formula for two capacitors connected in series.

Calculation Example

Given: C₁ = 4μF, C₂ = 6μF

\[\frac{1}{C_{total}}=\frac{1}{4μF}+\frac{1}{6μF}=\frac{5}{12}\]
\[C_{total}=\frac{12}{5}=2.4μF\]

Result: The total capacitance is 2.4μF.

Capacitor Series Connection - Theory and Formulas

Fundamentals of Series Connection

In a series connection of capacitors, the capacitors are connected one after another. The total current flows through all capacitors. The total capacitance of a series connection is calculated using the reciprocal of the individual capacitors.

Properties of Series Connection

Current Behavior
  • The current is the same everywhere
  • I = I₁ = I₂ = I₃
  • All capacitors are charged with the same current
Voltage Behavior
  • The total voltage is divided
  • U = U₁ + U₂ + U₃
  • Smaller capacitances receive higher voltages

Calculation Formulas

General Formula:
\[\frac{1}{C_{total}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+...\]

For any number of capacitors in series.

Two Capacitors:
\[C_{total}=\frac{C_1 \cdot C_2}{C_1 + C_2}\]

Simplified formula for exactly two capacitors.

Equal Capacitances:
\[C_{total}=\frac{C}{n}\]

For n equal capacitors with capacitance C.

Calculation Examples

Example 1: Two Different Capacitors

C₁ = 100μF, C₂ = 220μF

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

The total capacitance is smaller than the smallest individual capacitor.

Example 2: Three Equal Capacitors

C₁ = C₂ = C₃ = 90μF

\[C_{total}=\frac{90μF}{3}=30μF\]

For equal capacitors: capacitance divided by number.

Practical Applications

Voltage Dividers:
• Voltage division
• High voltage applications
• Measurement circuits
• DC voltage dividers
Capacitance Adjustment:
• Smaller capacitance values
• Precise tuning
• Fine adjustment
• Compensation
Voltage Rating:
• Higher total voltage
• Voltage distribution
• Safety margin
• High-voltage applications
Important Rules
  • The total capacitance is always smaller than the smallest individual capacitance
  • The more capacitors in series, the smaller the total capacitance becomes
  • The voltage is distributed inversely proportional to the capacitance
  • Smaller capacitors receive higher partial voltages
  • All capacitors carry the same current
  • The charge is the same on all capacitors: Q = Q₁ = Q₂ = Q₃
Voltage Distribution
Voltage Division in Series Connection
\[U_1 = U_{total} \times \frac{C_{total}}{C_1}\]

The voltage across a capacitor is inversely proportional to its capacitance. Capacitors with smaller capacitance receive a higher voltage.

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Capacitor functions

Series connection with capacitors  •  Series connection with 2 capacitors  •  Reactance Xc of a capacitor  •  Time constant of an R/C circuit  •  Capacitor charging voltage  •  Capacitor discharge voltage  •  R/C for the charging voltage  •  Series circuit R/C  •  Parallel circuit R/C  •  Low pass-filter R/C  •  High pass-filter R/C  •  Integrator R/C  •  Differentiator R/C  •  Cutoff-frequency R,C  •  R and C for a given impedance  •