Substituting the numerical values and performing the calculations we find the value of C_eq1, or:

Look at the Figure 03-05.2 as the redesigned circuit was. It's also easy to recognize that the capacitors of 14 and 16 µF are in parallel. In order to calculate the equivalent capacitance of a parallel circuit, sum the value of all the capacitors that make up the circuit. In our case, adding 14 and 16 µF we have the result of C_eq2 = 30 µF

In the Figure 03-05.3 we see how C_eq2 is in series with the capacitor of 60 µF. Again we have the case of capacitors in series. So just apply the equation mentioned above and we can calculate the value equivalent of the association. After the calculation, we find the value of 20 µF.

Substituting these two capacitors (C₂ e C_eq2) by a single 20 µF, we have to do the parallel of this capacitor with that of 30 µF and finally adding its values we find the value of the total capacitance between the points a - b, or:

Item b

In this item we will calculate the voltages in each capacitor of the circuit. As C₁ is in parallel with the voltage source of 90 volts, of course the voltage on it is also 90 volts. Let's recall the eq. 03-02 linking charge, voltage and capacitance. See below:

In this way, looking at the Figure 03-05.4 we know that C_eq2 and C₂ are in series. To calculate the voltage across each capacitor of a series circuit is enough to know that the voltage is inversely proportional to the value of the capacitance, since the charge of the capacitors is the same.

So, we can write:

In the same way we can C_eq2, or:

As we can see in the Figure 03-05.5, the voltage V_Ceq2, voltage on C_eq2, is the same about C_eq1 and C₃, since C_eq2 is the equivalent capacitance of the parallel association of C_eq1 and C₃. Therefore:

On the other hand, we know that C_eq1 is the equivalent capacitance of the series between the capacitors C₄ and C₅. Therefore, applying the same technique that we use to calculate the voltage on the capacitors C_eq2 and C₂, we find the values of:

With this, and following the notation of the initial figure we can write that:

Item c

To calculate the item c let's recall the eq. 03-05 which relates the energy of a capacitor as a function of the voltage on the capacitor and its capacitance.

Then, to calculate the energy accumulated in each capacitor it is enough to apply the formula. So:

Adendo

Note that by adding the energy accumulated by each capacitor we must find the total energy of the system. In addition, we find:

On the other hand, we calculate in the item a the total capacitance of the system, whose value is 50 µF, and we know that the voltage on this capacitance is 90 volts. Let's calculate what the energy accumulated by the total capacitance.

As it could not be, the Energy Conservation Law prevailed.