Physics

Problem

Capacitor

C_{1}=10\,\mu\text{F}

is charged to

200\,\text{V}

and capacitor

C_{2}=5\,\mu\text{F}

is charged to

100\,\text{V}

. Both capacitors are then isolated from their respective sources. The free plates of

C_{1}

and

C_{2}

are now connected together, and simultaneously the plates that were connected to the negative terminals of the sources are also connected together, so that their positive plates join and their negative plates join. a. (i) Determine the total charge on the system just before the capacitors are connected together. b. (ii) After connection, find the common potential difference across the combined system. c. (iii) Calculate the total energy stored in the two capacitors before connection and the energy stored after connection. d. (iv) Explain the reason for any difference in energy calculated in part (iii).

Intuitive explanation

This problem is about charge conservation and redistribution when isolated capacitors are connected in parallel. The key insight is that when you join the plates, the total charge in the system stays constant, but it redistributes until both capacitors reach the same final voltage. Calculate the initial charge on each capacitor using $Q = CV$ , add them to find total charge, then divide by the combined capacitance to find the equilibrium voltage.

Intuitive explanation

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