quick circuit question with potential energy from old AAMC

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knooch

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From AAMC 7. Old paper tests, not sure if they threw this Q out in the CBT.

Assume switch is closed to left. Q: as capacitor is charged, the electrical potential energy it gains
(A) equals the work done by the battery throughout the charging process
(B) is less than the work done by the battery throughout the charging process

Answer is B because "since the energy is lost by heating the small resistor, r, the energy stores in the capacitor must be less than the work done by the battery during the charging process".

I thought current would flow to path of least resistance (capacitors have less resistance than resistors). So, the current would flow to the capacitor till that is charged, than charging it "more" is harder since the capacitor would already have build the same (same charges repel) charge. What does the resistor have to do with anything?
 
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