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I have a few questions about charging capacitors with DC circuits that I would like to check.

1, 2, 3, correct.

4. The power supply voltage is always U. When charging starts, the voltage on the capacitor = 0, so at the beginning, the voltage difference between the power supply and the capacitor (this is the electrical appliance) is U, but as the charging process As the voltage across the capacitor increases, the voltage difference between the power supply and the electrical appliance will become smaller, until finally, the voltage difference gradually becomes zero. This is like work done by a variable force in mechanics. Therefore, the work done by the power supply is not Uq, but (1/2) U*q; this is related to your next question: the electric field energy stored in the fully charged capacitor is also (1/2) U*q, which is Consistent.

We often use the following formula to describe the electric field energy stored in a capacitor: E=(1/2)CU^2. This formula is consistent with: (1/2)U*q.