**Problem 3.10** Fonte:
Problem elaborated by the author of the site.

Suppose we have a capacitor, called C_{1}, with a capacity of 1 F. And
a voltage between its terminals of V_{1} = 10 volts.
Imagine another capacitor, called C_{2}, also with a capacity of 1 F, but completely discharged.
Now we connect the two capacitors in parallel. Determine the voltage that arises between the terminals of the capacitors.
Calculate the initial energy of the system and the final energy. Explain the discrepancy in energy values.

__Solution of the Problem 3-10__

To calculate the initial energy of the capacitor C_{1} we use eq. 03-05. So:

Now we must calculate the new voltage between the capacitor terminals when they are in parallel.
As the capacitors have the same capacitance, the charge will be distributed evenly between the two.
Therefore, each capacitor has half the initial charge of the capacitor C_{1} given by eq. 03-02 or,
Q = (1/2) C_{1} V_{1} = (1/2) x 1 x 10 = 5 coulombs.
Thus, we can calculate the voltage between the terminals of the capacitors. Rearranging the eq. 03-02 and,
assuming the capacitor C_{2} as a reference, we obtain:

The final energy of the system will be the sum of the energy of each capacitor. Using the energy of the capacitor C_{2} and
multiplying the result by 2, we have:

We can easily see that there is a difference of 25 joules between the initial energy of the system and the final energy.
The explanation for this difference is that when we connect the two capacitors in parallel, the energy transfer
from one capacitor to another does not happen in a linear way and, this in itself, invalidates the equations that we have studied until now.
moment. Thus, in addition to there being a joule effect, with the dissipation of energy due to the circulation of
current through the wires that connect the capacitors, there is also the emission of electromagnetic waves. Therefore, this difference
of energy of 25 joules between the initial and final value was used in this process.