In the figure (Figure 1), let V=71V and C1=C2=C3=6.8μF. How much energy is stored in the capacitor network?

Question

I don't know how to do this one.

Answer 1

Go back to the definition of voltage.... it is the energy (or work) needed to move a unit charge between two points in a static electric field.

Therefore, total energy (or work) required to move a charge Q from the one side of the capacitor to the other (i.e. to charge the capacitor up) is simply

E = Q. V

Now, note that in a capacitor the Voltage varies during charging. At the start there is no voltage but as charges are added, the voltage keeps changing. Therefore, potential energy stored during charging changes with each element of charge placed on the capacitor. For this reason, to calculate the total charge stored on the capacitor we must add all potential energies added to the capacitor by each element of charge. That means integration.

E = ∫V.dQ

Using the capacitance formula, C= Q/V, you can follow a text book to see that the result is

E = 1/2.C.V²

You have not provided a figure to know whether C1, C2 and C3 are in series or in parallel to each other. If in parallel, the total capacitance will add to 20.4 μF. If in parallel, the total capacitance is obtained as 2.267μF. Use the appropriate value of C to figure out the stored energy.