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 capacitance doubles, but the voltage across each capacitor remains the same. The energy stored in a capacitor is given by $E = \frac{1}{2}CV^2$, where $E$ is the energy, $C$ is the capacitance, and $V$ is the voltage. When the charged capacitor is connected in parallel with an uncharged one, the charge redistributes equally between the two, effectively halving the voltage across each capacitor (since they are identical). The energy stored in each capacitor is then quartered (since energy is proportional to the square of the voltage), making the total energy $2 \times \frac{1}{4} \times 4 \, \text{J} = 2 \, \text{J}$.

Capacitors a and B Are Identical