Problem 3.8    Source:   Problem 6.29 - page 244 -    IRWIN, J. David - Book: Análise de Circuitos em Engenharia - 4ª edição - Ed. Pearson - 2013.

Determine the value of the total capacitance that the circuit shown in Figure 03-08.1 presents between the terminals a-b knowing that: C₁ = 4.0 µF,   C₂ = 6.0 µF,   C₃ = 1.0 µF,   C₄ = 8.0 µF and C₅ = 3.0 µF.

Solution of the Problem 3.8

To calculate the total capacitance that appears between the points a e b, we must pay attention to the fact that the three capacitors, C₃, C₄ and C₅, are in parallel. Therefore, we can calculate the equivalent capacitance of these capacitors by adding their values, or:

See in the Figure 03-08.2, how was the circuit when we replaced the capacitors that were in parallel by their equivalent C_eq1. Note that this capacitor is in series with C₁. Solving the series of these two capacitors, we will check that it is in parallel with C₂. After this we are able to calculate the total capacitance between points a and b. First, let's calculate the series between C₁ and C_eq1.

Now adding the found value of C_eq2 with C₂, since they are in parallel, we find the value of the total capacitance of the circuit.