Question on capacitors in parallel

[binbagsss]

A capacitor is connected to a cell of emf 200V and fully charged.
Another capacitor is then connected in parallel, which has 1/100th of the capacitance of the charged capacitor.
The total charge is instantly shared between the two capacitors, and so the capacitor connected in parallel to the original capacitor will get 1/100th of the charge as components in parallel have the same voltage and so Q is proportional to C.

However, what I don't fully understand is why the charge is instantly shared, and, eventually will both capacitors obtain a voltage equal to the emf of the cell?

- Is it because intially the emf is not able to do any work, because the capacitor which is fully charged has an equal voltage across it, acting in the opposite direction. However charge is able to flow from the charged capacitor to the capacitor in parallel as this has no pd across it, and so the charge will be distributed until both capacitors reach the same voltage and no current flows.
- But, as the charge flows from the charged capacitor to the uncharged capacitor, the p.d across the charged capacitor decreases, and so the cell has the greater voltage again and is able to do work, so eventually will both capacitors reach 200v?

 

[tiny-tim]

hi binbagsss!

However, what I don't fully understand is why the charge is instantly shared, and, eventually will both capacitors obtain a voltage equal to the emf of the cell?
…
- But, as the charge flows from the charged capacitor to the uncharged capacitor, the p.d across the charged capacitor decreases, and so the cell has the greater voltage again and is able to do work, so eventually will both capacitors reach 200v?

no, you're misunderstanding p.d. (voltage) …

the p.d. across either capacitor is 200 V at all times, it doesn't change …

only its effect changes, in this case it (almost) instantly charges the second capacitor

 

[binbagsss]

That sounds cool, however the question then asks to calculate the initial reading on the voltmeter, which is connected in parallel to the second capacitor...

 

[tiny-tim]

can you clarify the original question …

is the emf cell disconnected before the second capacitor is connected, or does the emf cell remain connected the whole time? ​

 

[rwisz]

I can provide an explanation for the phenomenon you have described. When two capacitors are connected in parallel, they share the same voltage and the total charge is distributed between them based on their relative capacitances. This is because each capacitor has the same voltage drop across it, and therefore the charge stored on each capacitor is proportional to its capacitance (Q=CV).

In the scenario you have described, the first capacitor is fully charged and has a voltage of 200V. When the second capacitor is connected in parallel, the total charge is shared between the two capacitors, with the second capacitor receiving only 1/100th of the charge. This is because the capacitance of the second capacitor is 1/100th of the first one, and therefore it can only hold 1/100th of the charge.

Now, to address your question about why the charge is instantly shared and if both capacitors will eventually reach a voltage of 200V - the answer is yes, they will both eventually reach a voltage of 200V. This is because of the principle of conservation of energy. Initially, when the second capacitor is connected, the first capacitor has a higher voltage and is able to do work, but as the charge flows from the first capacitor to the second one, the voltage across the first capacitor decreases. This decrease in voltage means that the first capacitor has less energy stored in it.

At the same time, the second capacitor is gaining charge and its voltage is increasing. This means that the second capacitor is gaining energy. Eventually, the energy stored in the first capacitor will be equal to the energy stored in the second capacitor, and both capacitors will have the same voltage of 200V. This process may happen very quickly, which is why it may seem like the charge is instantly shared.

In summary, the charge is instantly shared between capacitors in parallel because of their shared voltage and the principle of conservation of energy. Both capacitors will eventually reach the same voltage as the cell, but this process may happen quickly due to the high rate of energy transfer between the two capacitors. I hope this explanation helps to clarify your understanding of capacitors in parallel.