A2 Daily A Level Physics question
A 9.0 V ideal DC supply is used to charge the same capacitor to steady state through either a 1.0 kΩ resistor or a 4.0 kΩ resistor. Ignore internal resistance and leakage. After each charge is complete (steady state reached), which statement about the total thermal energy released in the resistor during the charging process must be true?
Answer
The correct answer is A.
Correct: A — The total heat in the resistor is the same with 1.0 kΩ and with 4.0 kΩ. A This follows because the battery supplies energy CV^2 while the capacitor ends with 1/2 CV^2, so the remainder (1/2 CV^2) is dissipated as heat, independent of R; changing R only alters the rate, not the total. B Although the charge takes longer with 4.0 kΩ, the current is proportionally smaller throughout, so the longer duration does not increase the total heat. C Focusing only on the smaller current ignores the longer charging time; these effects balance so the total heat is not reduced to one quarter. D The idea that a longer time necessarily means more heat is incorrect here because the instantaneous power is lower at every moment with 4.0 kΩ, leading to the same total heat as with 1.0 kΩ.