Affect on stored energy if charge is doubled

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Homework Help Overview

The discussion revolves around the effect of doubling the charge on the stored energy in a parallel plate capacitor that is connected to a battery, maintaining a constant potential difference. Participants explore the relationship between charge, voltage, and stored energy using various formulas.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants examine different formulas for stored energy, including U = 0.5QV and U = Q^2 / 2C, and discuss how changes in charge affect energy. There is debate over whether doubling the charge results in doubled or quadrupled energy.

Discussion Status

Multiple interpretations of the problem are being explored, with some participants suggesting that stored energy would quadruple due to the relationship between charge and voltage, while others question this conclusion based on their understanding of the formulas. No explicit consensus has been reached.

Contextual Notes

Participants are working under the assumption that the capacitor is ideal and air-filled, and they are considering the implications of maintaining a constant potential difference while changing the charge.

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Homework Statement

A parallel plate capacitor is air filled and assumed to be ideal. It is connected to a battery so it has constant potential difference. By what factor does stored energy change if the charge is doubled..

The attempt at a solution

Using the formula U = 0.5QV..

If charge is doubled, then U is doubled correct?

I say the answer is stored energy is doubled, but the answer at the back reckons quadrupled. Who is right?
 
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E = Q^2 / 2C is another formula. That would yield a 4 times greater energy being stored.

Also, if E = (0.5)QV, then if Q = 2Q

Q = CV
C = Q/V

C = 2Q/2V, as C cannot change, so V must change in order to keep it constant.

E = (0.5).2Q.2V

I think.
 
well I'm given two formulas, U = (0.5)QV and U = 1/2CV^2

The second formula is not relevant as charge is not a variable, hence my above reasoning...
 
In case the charge doubles, the voltage would also get doubled. Hence stored energy would get quadrupled. All the formulas would yield the same result.
 

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