Physics
Physics
Problem
Two identical capacitors, each of capacitance , are first connected in parallel to a battery of potential and fully charged. Keeping them isolated, they are then disconnected from the battery and reconnected in series so that plates carrying like charges are joined together. State whether the total energy stored in the system increases, decreases or remains the same after this reconnection, and calculate the ratio of the final energy to the initial energy.Intuitive explanation
The key insight is that charge is conserved when you reconnect the capacitors, but the voltage distribution changes dramatically. When identical capacitors charged in parallel (each holding charge ) are reconnected in series with like charges facing each other, those charges partially cancel at the junction, leaving less total charge to store. Since energy stored in a capacitor depends on , the reduction in charge means the final energy will be significantly less than the initial energy—you can find the ratio by tracking how charge redistributes.
Intuitive explanation
The key insight is that charge is conserved when you reconnect the capacitors, but the voltage distribution changes dramatically. When identical capacitors charged in parallel (each holding charge ) are reconnected in series with like charges facing each other, those charges partially cancel at the junction, leaving less total charge to store. Since energy stored in a capacitor depends on , the reduction in charge means the final energy will be significantly less than the initial energy—you can find the ratio by tracking how charge redistributes.