Final answer:
By calculating the initial energy of both capacitors, finding the final combined energy, and using the conservation of charge to determine the new voltage across the capacitors after connection, we can find that the heat generated is CV^2. However, this result does not match the options given in the question, suggesting an error in the question or options provided.
Step-by-step explanation:
The question involves two capacitors with different capacitances and voltages that are connected together oppositely. The initial energies stored in the capacitors before they are connected can be found using the formula for energy stored in a capacitor, which is E = 1/2 CV^2. The energy for the first capacitor (C and V) is E1 = 1/2 CV^2 and for the second capacitor (2C and 2V) is E2 = 1/2 × 2C × (2V)^2 = 2CV^2. When connected, the total initial energy is E1 + E2 = 1/2 CV^2 + 2CV^2 = 5/2 CV^2. After connection, they share the same voltage and the combined capacitance is (C + 2C) = 3C. The final energy is E_final = 1/2 × 3C × V'^2 where V' is the new voltage across both capacitors. Charge conservation requires that CV + 2C × 2V = 3CV', leading to V' = V. Thus, E_final = 1/2 × 3C × V^2 = 3/2 CV^2. The heat generated during this process is the difference in energy: Heat = E_initial - E_final = (5/2 CV^2) - (3/2 CV^2) = CV^2. However, this result is not matching any of the given options, indicating a potential error in the question or the options provided.