Capacitors A and B are identical.Capacitor A is charged so it stores 4 J of energy and capacitor B is uncharged.The capacitors are then connected in parallel.The total stored energy in the capacitors is now:
A)16 J
B)8 J
C)4 J
D)2 J
E)1 J

Question

Quizplus · Accepted Answer

When two identical capacitors are connected in parallel, the total voltage across them remains the same, but the charge is distributed equally between the two. Since energy stored in a capacitor is given by $E = \frac{1}{2}CV^2$, where $C$ is the capacitance and $V$ is the voltage, the energy stored in each capacitor after they are connected will be half of the initial energy stored in the charged capacitor (because the voltage across each capacitor will be halved when the charge is distributed equally). Therefore, each capacitor will store $2 J$ of energy, making the total energy stored $4 J$. However, due to the conservation of energy and the fact that the system is ideal (no energy loss), the total energy before and after connecting the capacitors must be the same, which is $4 J$. The error in the previous explanation is acknowledging the incorrect distribution of energy due to misunderstanding the conservation of energy in an ideal system. The correct answer, based on the conservation of energy principle, should be that the total energy remains $4 J$ because energy cannot be created or destroyed, only transferred. The initial misunderstanding was due to an incorrect application of formulas and principles.

Capacitors a and B Are Identical