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Energy of a charged capacitor is U. Now it is removed from the battery and then connected in parallel to another uncharged capacitor having capacitance twice that of the first one. The energies of the first and second capacitors respectively are ______.

Asked in GUJCET 2016 · Redistribution of charge

• (1) 1/9U, 2/9U
• (2) 2/9U, 1/9U
• (3) 1/9U, 1/9U
• (4) 2/9U, 2/9U

Step-by-step solution

Why the other options are wrong

• (2) Swaps the two. At the common voltage U = 1/2CV² is proportional to C, so the capacitor of capacitance 2C holds twice the energy of the first.
• (3) Gives the two capacitors equal energies, which would need equal capacitances. Here one is twice the other, so at the same voltage their energies are in the ratio 1:2.
• (4) No single slip gives equal energies of 2/9U each. Sanity check: the energies must be in the ratio 1:2 (same V, capacitances C and 2C), and together they come to 1/3U.

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