Capacitors in Series Calculator
Calculate the equivalent capacitance of capacitors connected in series
Calculate Series Capacitance
Equivalent Capacitance
Formula: 1/C_total = 1/C₁ + 1/C₂ + ... + 1/Cₙ
Note: Series capacitance is always less than the smallest individual capacitor
Series Circuit Diagram
Capacitors connected in series - same charge, voltages add up
Example Calculation
Common Electronics Example
Scenario: Three capacitors in series for filtering
C₁: 100 µF (electrolytic)
C₂: 10 µF (ceramic)
C₃: 1 µF (film)
Step-by-Step Solution
1. Convert to Farads: C₁ = 100×10⁻⁶ F, C₂ = 10×10⁻⁶ F, C₃ = 1×10⁻⁶ F
2. Apply formula: 1/C = 1/(100×10⁻⁶) + 1/(10×10⁻⁶) + 1/(1×10⁻⁶)
3. Calculate: 1/C = 10⁴ + 10⁵ + 10⁶ = 1,110,000 F⁻¹
4. Result: C = 1/1,110,000 = 0.901 µF
Note: Much smaller than any individual capacitor!
Series Capacitors Properties
Same Charge
All capacitors store equal charge Q
Voltages Add
V_total = V₁ + V₂ + ... + Vₙ
Reduced Capacitance
Always less than smallest capacitor
Capacitance Units
Quick Tips
Series capacitance decreases total capacitance
Useful for voltage division in circuits
Common in filter and timing circuits
Consider voltage ratings in real circuits
Understanding Capacitors in Series
What are Series Capacitors?
Capacitors connected in series are arranged end-to-end in a single path, where the positive plate of one capacitor connects to the negative plate of the next. This configuration has unique electrical properties that differ from parallel connections.
Key Characteristics
- •Same charge (Q) flows through all capacitors
- •Voltages across capacitors add up to total voltage
- •Total capacitance is less than any individual capacitor
- •Impedance of capacitors add up
Formula Derivation
V_total = V₁ + V₂ + ... + Vₙ
Q/C_total = Q/C₁ + Q/C₂ + ... + Q/Cₙ
Dividing by Q:
1/C_total = 1/C₁ + 1/C₂ + ... + 1/Cₙ
Practical Applications
- ✓Voltage dividers in AC circuits
- ✓Timing circuits (555 timers)
- ✓High-voltage applications
- ✓Filter networks
Important Considerations
Voltage Ratings
Each capacitor must handle its portion of the total voltage. The voltage divides inversely proportional to capacitance values.
Tolerance Effects
Component tolerances affect voltage distribution. Use capacitors with similar tolerances for predictable behavior.