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A2L Item 241

Meta-Information
Description: 
Identify the circuit whose battery does more work charging a capacitor.
Goal: 
Reason regarding circuits
Level: 
Undergraduate
Keywords: 
Circuits
Keywords: 
Electromagnetism
Keywords: 
Reasoning
Keywords: 
Work
Source: 
283 compare dissipated energy

Consider the following circuits. Two identical batteries are connected to two identical capacitors in series with different resistors. The capacitors are initially uncharged. Which statement is true regarding the energy supplied by the batteries to charge the capacitor?

  1. The battery in A does more work.
  2. The battery in B does more work.
  3. Both batteries do the same work.
  4. Cannot be determined
Commentary

Answer

(3) The energy dissipated in the resistor is independent of the resistance. Consider a time when the capacitor contains some charge Q. If an additional charge dq is added, the battery does work dqV and the increment of stored energy in the capacitor is (Q/C)dq. By conservation of energy, the difference must have been dissipated in the resistor. The difference, [V-(Q/C)]dq is independent of resistance.