How do you calculate the equivalent capacitance of capacitors in series and parallel?

In series, 1/Ceq = 1/C1 + 1/C2 +…+ 1/Cn. In parallel, Ceq = C1 + C2 +…+ Cn. Series Ceq is smaller, while parallel Ceq is the sum of individual values.

Calculating Equivalent Capacitance in Series and Parallel

In an electric circuit, capacitors can be connected in series or parallel configurations. The equivalent capacitance of such connections is calculated differently for each configuration.

Series Connection

In a series connection, capacitors are connected end-to-end so that the same charge accumulates on each capacitor. The formula for calculating the equivalent capacitance (C_eq) of capacitors connected in series is:

1. 1/C_eq = 1/C₁ + 1/C₂ + … + 1/C_n
2. C_eq = 1 / (1/C₁ + 1/C₂ + … + 1/C_n)

Here, C₁, C₂, …, C_n are the capacitances of the individual capacitors.

Parallel Connection

In a parallel connection, capacitors are connected side by side, so that the voltage across each capacitor is the same. The formula for calculating the equivalent capacitance (C_eq) of capacitors connected in parallel is:

1. C_eq = C₁ + C₂ + … + C_n

Here, C₁, C₂, …, C_n are the capacitances of the individual capacitors.

Example

Let’s consider an example with two capacitors, C₁ = 4 μF and C₂ = 6 μF.

For a series connection, the equivalent capacitance is:

C_eq = 1 / (1/4 + 1/6) = 1 / (5/12) = 12/5 μF ≈ 2.4 μF

For a parallel connection, the equivalent capacitance is:

C_eq = 4 + 6 = 10 μF

As seen in the example, the equivalent capacitance for series connection is smaller than the individual capacitances, while in parallel connection, it’s the sum of the individual capacitances.