# Plate capacitor connected to a battery (what does a battery do)

• I
I have a plate capacitor connected to a battery with a known potential difference. Now the plates are moved apart by dx and I must figure out the change in energy stored in the battery.

Question 1: When a plate capacitor is connected to a battery charges must flow until the potential difference between the plates is equal to the difference between the "parts" of the battery. Is it generally assumed that in such cases the batteries voltage will remain constant?

Question 2: The solution seems to assume that the charges induced on the capacitor are equal in magnitude and opposite in sign. Why is this?

Question 3: When the plates are moved apart the potential difference rises. This means charges must flow until equilibrium is restored. So if it is assumed that the battery maintains constant voltage, which path do these charges take? My idea of a battery is a positive charge and a negative charge separated my some medium where no charge can pass through.

But after the plates are separated either some of the positive charge must flow from the positive plate to the negative plate(or the other way around or both). The charges don't seem to have a path though..How does this happen?

(I didn't mean to post three questions in one thread but I kept thinking of new things)

Does this sound somewhat correct? The battery has two parts which each maintain a charge equal in magnitude and opposite in sign. By symmetry this explains why the charges on the plates must be equal in magnitude and opposite in sign. When the plates are moved apart work is being put into this system. This work will at first manifest itself as an increase in the potential energy of the plates. Since the potential difference between the plates is too high though, some positive charge will flow to the positive part of the battery and some negative charge will flow to the negative part of the battery. Since the battery(for some reason) maintains its charges the excess positive charge and excess negative charge will somehow be stored as extra energy in the battery.

By conservation of energy the mechanical work done on the plates will be equal to the increase of potential energy of the plates combined with the increase of (chemical?) energy stored in the battery.

gleem
Keep in mind that the electrons are the only charges that move in the circuit. So when the plates are separated because there is a fixed relationship between the charge on the plates ,the separation of the plates and the potential difference if the battery remains affixed when the separation take place the potential difference across the capacitor remains fixed. To retain the proper relationship between the voltage and charge on the capacitor the charge must be redistributed. Some of the electrons on the negative side leave the capacitor and return to the battery's cathode while on the positive side an equal number of electron leave the battery's anode and enter the capacitor. This results in the charging of the battery.

• Fibo112
So after the battery receives these extra charges, it converts the extra potential energy into some other form of energy until the original charges, and thereby the original voltage, is restored?

CWatters
Homework Helper
Gold Member
I have a plate capacitor connected to a battery with a known potential difference. Now the plates are moved apart by dx and I must figure out the change in energy stored in the battery.

Question 1: When a plate capacitor is connected to a battery charges must flow until the potential difference between the plates is equal to the difference between the "parts" of the battery. Is it generally assumed that in such cases the batteries voltage will remain constant?
Yes. You can assume the voltage of the battery remains constant for this type of question. There isnt enough info provided to calculate any change in battery voltage.

Question 2: The solution seems to assume that the charges induced on the capacitor are equal in magnitude and opposite in sign. Why is this?
Like charges repel each other. So if you put positive charge on one plate it will repel positive charge out of the other plate leaving it with a negative charge. If both plates had the same charge/same polarity there wouldn't be a voltage difference.

Question 3: When the plates are moved apart the potential difference rises. This means charges must flow until equilibrium is restored. So if it is assumed that the battery maintains constant voltage, which path do these charges take? My idea of a battery is a positive charge and a negative charge separated my some medium where no charge can pass through.
Q=CV

If you increase the plate separation you reduce C. The Voltage V is held constant by the battery (which behaves a bit like a voltage source), so the charge Q must reduce by flowing back into the battery (eg charging it slightly).

What actually happens... The battery isn't an ideal voltage source, nor are the wires. This allows the voltage on the capacitor to rise a bit causing charge to flow back into the battery.

But after the plates are separated either some of the positive charge must flow from the positive plate to the negative plate(or the other way around or both). The charges don't seem to have a path though..How does this happen?

(I didn't mean to post three questions in one thread but I kept thinking of new things)
When batteries are charged current flows the "wrong" way through them. Eg positive charge goes into the positive terminal of the battery.

CWatters
Homework Helper
Gold Member
Gleem is correct in that only electrons actually move.

Edit: I mean around the circuit. Positive ions do move in the battery.

Last edited:
Mister T
Gold Member
Question 1: When a plate capacitor is connected to a battery charges must flow until the potential difference between the plates is equal to the difference between the "parts" of the battery. Is it generally assumed that in such cases the batteries voltage will remain constant?
If by "parts" you mean the battery terminals, yes.

Question 2: The solution seems to assume that the charges induced on the capacitor are equal in magnitude and opposite in sign. Why is this?
Initially (before the battery is connected) it is assumed the capacitor is uncharged, that is, there is zero charge on each plate. The battery, when connected, moves some charge from one plate to the other. Since charge cannot be created or destroyed, the deficiency of charge on one plate is equal to the excess charge on the other.

Question 3: When the plates are moved apart the potential difference rises.
Not if the battery stays connected during that process. What happens instead is that the battery moves charge from one plate to the other to maintain a constant potential difference.

davenn
Gold Member
The battery, when connected, moves some charge from one plate to the other.
no

What happens instead is that the battery moves charge from one plate to the other to maintain a constant potential difference.

again ... no

charge DOES NOT move between plates ... it's a capacitor, the plates are isolated from each other

For every negative charge (electron) that moves onto one plate from the battery ( other supply), one negative charge moves off the other plate and back towards the battery

At ALL TIMES, the net charge on the capacitor is zero ....
an equal number of negative charges on one plate to the number of positive charges on the other plate

Dave

Last edited:
jbriggs444
Homework Helper
charge DOES NOT move between plates
Yes, it does. Through the wires connected to the plates -- the long way 'round.

• davenn
Mister T
Gold Member
... it's a capacitor, the plates are isolated from each other
Not according to the the OP ...

I have a plate capacitor connected to a battery
The battery provides a connection between the capacitor plates. For an ideal battery the potential difference across the terminals remains constant as the capacitor's plates are moved further apart. The only way this can happen is if the charge on each capacitor plate changes.

davenn
Gold Member
Yes, it does. Through the wires connected to the plates -- the long way 'round.

yes the long way around agreed … BUT not directly between the plates ( across the gap …. many people think that happens)

and if one wants to be REALLY pedantic … then there still isn't a complete path around the circuit vial the battery … the electrons entering the + terminal do not travel across the electrolyte to the negative side
As there is charge separation occurring in the electrolyte

• jbriggs444