capacitors

[chiddler]

---

Members don't see this ad.

I'm struggling with understanding capacitors in series.

here is the question

Going across each capacitor, the voltage drops v = q/c. So the voltage decreases based on how strong a capacitor it is, with a weaker capacitor causing more voltage drop.

1. Why does a weaker capacitor cause a stronger voltage drop?

2. How do we know that the charge on each capacitor will be the same after they are charged?

thank you!

 

[milski]

You need to start from the charge. Consider the part of the circuit which starts with one of the first capacitor's plates, the conductor and the second capacitor's plate. Before you start charging them the total charge of that part is 0. Since no charges move in or out of it, the total has to stay 0 - the positive charge in one capacitor has to match the negative in the other. (For some reason that reminds me of auto-ionization of water, where [H]=[OH] but that's neither here nor there).

Once you know that the charges are the same you can calculate the voltage from Q/C=V. Since Q is the same, the capacitor with larger Q will have lower voltage drop.

In certain ways the capacitance is more similar to a spring constant - it does not tell you how much charge can be stored as an absolute but how much charge can be stored for certain potential, the same way k does not give you one displacement but a displacement for a corresponding force.

The spring analogy in that case would be pushing two springs next to each other - it's obvious that the force on each of them would be the same (same charge) and you can probably imagine that the "softer" spring with smaller k will get compressed more than the "harder" one with larger k.

 

[chiddler]

Why does the different capacitors have to match each other?

I'm thinking of charge on each plate in a capacitor. Each plate can have equal and opposite of the other plate. So for two capacitors it might be -100 mC plate, +100 mC plate, some wire, then the second capacitor plate at -200 mC, then +200 mC.

Net = 0. So why is this not possible.

 

[milski]

----| |-----| |----
A B C

This may come up misaligned but let's try it.

The charge of the wire B in your case is 100 mC. Where did these 100 mC come from, considering that no charge goes between the plates of the capacitor?

Edit: yes, the letters got squeezed. Just put A,B,C under each wire.

 

[chiddler]

The charge must come from the wire. Oh, you're saying that the wire cannot have some nonzero charge. It must net zero.

 

[milski]

The charge must come from the wire. Oh, you're saying that the wire cannot have some nonzero charge. It must net zero.

Yes, the middle wire + the two plates attached to it have a total charge of 0.

 

[chiddler]

Yes, the middle wire + the two plates attached to it have a total charge of 0.

thank you very much