Series and Parallel Capacitor Calculator

Calculate Total Capacitance

Enter the capacitance values to calculate the total equivalent capacitance for capacitors connected in series or parallel.

How to Calculate Series and Parallel Capacitance

Capacitors can be connected in series or parallel configurations, each resulting in different total capacitance. This calculator helps you determine the total capacitance based on the values of individual capacitors and their connection type.

Capacitance Formulas

Series Capacitance Formula

When capacitors are connected in series, the total equivalent capacitance is always less than the smallest individual capacitance. The formula for calculating the total capacitance of series capacitors is:

\[\frac{1}{C_T} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \cdots + \frac{1}{C_n}\]

Parallel Capacitance Formula

When capacitors are connected in parallel, the total equivalent capacitance is the sum of all individual capacitances. The formula for calculating the total capacitance of parallel capacitors is:

\[C_T = C_1 + C_2 + C_3 + \cdots + C_n\]

Where:

  • CT is the total equivalent capacitance in farads (F)
  • C1, C2, C3, ..., Cn are the individual capacitances, also in farads (F)

Calculation Steps

For Series Capacitors:

  1. Identify the values of the individual capacitances (C1, C2, C3, ..., Cn) in farads
  2. Calculate the reciprocal (1/C) of each individual capacitance
  3. Add the reciprocals together to find the sum of the reciprocals
  4. Take the reciprocal of the sum to obtain the total equivalent capacitance (CT)

For Parallel Capacitors:

  1. Identify the values of the individual capacitances (C1, C2, C3, ..., Cn) in farads
  2. Add all the individual capacitances together
  3. The sum is the total equivalent capacitance (CT)

Example Calculations

Series Capacitors Example:

Given: C1 = 10 µF, C2 = 20 µF, C3 = 30 µF

Step 1: Convert to farads and calculate reciprocals:

\[\frac{1}{C_1} = \frac{1}{10 \times 10^{-6}} = 100,000\] \[\frac{1}{C_2} = \frac{1}{20 \times 10^{-6}} = 50,000\] \[\frac{1}{C_3} = \frac{1}{30 \times 10^{-6}} = 33,333.33\]

Step 2: Add the reciprocals:

\[\frac{1}{C_T} = 100,000 + 50,000 + 33,333.33 = 183,333.33\]

Step 3: Take the reciprocal of the sum:

\[C_T = \frac{1}{183,333.33} = 5.45 \times 10^{-6} \text{ F} = 5.45 \text{ µF}\]

Parallel Capacitors Example:

Given: C1 = 10 µF, C2 = 20 µF, C3 = 30 µF

Step 1: Add the capacitances:

\[C_T = 10 \text{ µF} + 20 \text{ µF} + 30 \text{ µF} = 60 \text{ µF}\]

Capacitor Connection Diagrams

Series Capacitors C1 C2 C3 Parallel Capacitors C1 C2 C3

These diagrams illustrate capacitors connected in series and parallel. Remember, the total capacitance in series is always less than the smallest individual capacitance, while in parallel, it's the sum of all capacitances.

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