How Much Work Does a Battery Charger Do to Recharge a 5V Battery?

[anonymousphys]

Homework Statement

To recharge a 5V battery, a battery charger must move 7x10^6 C of charge from the neg. to pos. terminal. How much work is done by the charger in joules?

Homework Equations

QV=U

The Attempt at a Solution

If the battery needs to be recharged, isn't the potential difference initially zero because there is no charge on either of the terminals to begin with? Therefore, isn't this similar to a parallel plate capacitor where U=(.5)QV?

 

[Borek]

No, potential difference on capacitor changes linearly with charge, in the case of battery change of potential difference is not linear and much smaller (as compared to capacitor). I suppose you are to assume ideal battery with constant potential difference.

 

[anonymousphys]

Thanks for the reply.

But..how does an electric potential exist if the two terminals are uncharged? Isn't that what the question is asking when it says to recharge the battery? Or does it mean that the battery does have charged terminals amd is only partially uncharged?

 

[Borek]

Battery stories energy not in a form of charge/potential (as capacitor does) but in the form of chemical energy - that is, charging battery you are converting one substance into other. When you are using battery reverse chemical reaction occurs and allows you to recover the energy.

Terminals in battery are charged - but only slightly. You don't need a lot of charge to build a 5V difference. You may think about it as if the charged chemical is willing to react back so strongly that to some extent it reacts on itself - producing enough charge to make the 5V difference (or whatever is battery voltage).

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