How Does Electric Potential Energy Relate to Capacitors?

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Discussion Overview

The discussion revolves around the relationship between electric potential energy and capacitors, specifically focusing on the energy stored in capacitors during charging and the associated equations. It includes theoretical considerations and mathematical reasoning related to the energy dynamics in capacitors.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant states that the energy stored in a capacitor is given by the formula 1/2 QV, noting that the other half of the energy is dissipated during the charging process.
  • Another participant argues that since Q and V are proportional (Q=CV), the equation E=QV does not apply directly, leading to a different expression for the change in energy, dU=Vdq=CVdV.
  • This participant further elaborates that the total energy stored can be derived as U=\int_0^VCV'dV'=(1/2)CV^2=(1/2)QV.
  • A later reply acknowledges a potential misinterpretation of the original question regarding the energy imparted by a battery, clarifying that while the battery imparts energy QV, the energy stored in the capacitor is only half that amount.

Areas of Agreement / Disagreement

Participants express differing views on the energy dynamics in capacitors, particularly regarding the energy stored versus the energy imparted during charging. There is no consensus on the interpretation of these energy relationships.

Contextual Notes

Some assumptions regarding the definitions of energy in the context of capacitors may be implicit, and the discussion does not resolve the mathematical steps involved in deriving the energy equations.

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all my question is listed in the file below

thanks for your help
 

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1/2 QV is the energy stored in the capacitor. The other half of the energy was dissipated during charging as heat or radiation.
 
Q and V for a capacitor are proportional to each other by Q=CV so the simple E=QV does not apply. The change in energy is dU=Vdq=CVdV.
Then U=\int_0^VCV'dV'=(1/2)CV^2=(1/2)QV.
 
Last edited by a moderator:
Clem is, of course, correct. Perhaps I misinterpreted your question (or just answered a different question!) about charging a capacitor with a battery. The energy imparted to the charge by the battery is QV, but the energy stored in the capacitor only half that. Sorry about that!
 

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