AAMC Self Assessment Physics #33

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tripkramer

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When switch S is closed to the left, charge begins to accumulate on the capacitor. Charge cannot accumulate indefinitely because:

(A) the variable resistor inhibits current flow
(B) the battery continually loses charge
(C) successive charges brought to the plates are repelled by charges accumulated earlier
(D) the fixed resistor loses energy to heat

They say the answer is C because: The two plates of the capacitor collect charges of opposite sign. As more charge arrives it is harder and harder to fill the plates until finally an equilibrium occurs.

Can anyone explain? I thought it can't accumulate indefinitely because the capacitor will eventually become fully charged. I'm not really sure what I thought would happen then - if the capacitor will then discharge and recharge continuously until the battery is done?

Thanks

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In a parallel-plate capacitor if two parallel metallic plates are separated by a distance and connected to a battery, one plate accumulates some negative charges while the other plate accumulates equal amount of positive charges. The electric field in between the plates and especially away from the edges will essentially be uniform and the electric field lines become parallel. Such a device uses the battery in doing the work to moves positive ions to the negative plate until you reach a point when successive charges brought to the plates are repelled by charges accumulated earlier.
 
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I thought it can't accumulate indefinitely because the capacitor will eventually become fully charged.

You are correct. Answer C is explaining what happens when a capacitor eventually becomes fully charged. This is a great MCAT physics question and exemplifies why people arguing that physics is all about equations are wrong.

Imagine an uncharged capacitor which you connect to a battery and a switch. When you throw the switch, negative charges are moved by the battery from the bottom plate to the top plate. In the beginning, this requires very little work to be performed because there is no force to push the charges against. That should make sense, because in the beginning there are no charges on the top plate. However, as the battery keeps loading more charges on the top plate, the electric field increases and the work you must do increases. Eventually, the battery no longer has enough capacity to move charges (i.e., voltage) against the electric field due to the charges on the top plate, and the amount of charge on the top plate stops changing.

What this really means is that the amount of charge you can place on the top plate of a capacitor is proportional to the voltage doing the work. In other words:

Q = CV

Here's another way to do this problem.

(A) The variable resistor inhibits current flow.
Wrong. Resistance determines the rate of charging, but not the final value.
(B) The battery continually loses charge
Wrong. The charges that are used to charge the capacitor come from the plates. Now, an interesting question here is this. What does the battery continually gain?
(C) Successive charges brought to the plates are repelled by charges accumulated earlier
Must be the right answer.
(D) The fixed resistor loses energy to heat
Wrong. Resistance determines the rate of charging, but not that final value.

Anyone have any idea what the battery gains while it's charging the capacitor?
 
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May be the battery is not gaining , It is just not continually loses charge, because the capacitor is fully charged.
 
May be the battery is not gaining , It is just not continually loses charge, because the capacitor is fully charged.

This statement makes no sense. Did you even read it after you wrote it?

The battery doesn't lose or gain charge at any point while the capacitor is charging. You seem to be implying that the positive terminal of the battery is positively charged and the negative terminal is negatively charged and both of those statements are false. The battery is neutrally charged at all times. The reason it can do work is because the chemical reactions occurring within the battery cause those two points to be at different potentials.

If the battery lost charge at any point in time, it would no longer be neutrally charged when you finished. The battery is not a store of charge - it is a storage of energy.

Any takers on what IS increasing inside the battery while you discharge it?
 
Heat, lol. Entropy. Chemical products. RT ln Q.

Or were you looking for a non-thermodynamic answer?
 
Heat, lol. Entropy. Chemical products. RT ln Q.

Or were you looking for a non-thermodynamic answer?

Entropy was the big one. I talked to the battery engineer that works down the hall from me and he had no idea. Sorta surprising to me how little he understood battery chemistry.
 
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