Voltage Across Two Capacitors In Series

[Brilliant]

Homework Statement

Homework Equations

Q=CV

The Attempt at a Solution

For part A, I've tried working out the algebra, with the assumptions that V₁ + V₂ = V and Q₁ + Q₂ = Q

Basically, I solved Q by finding the equivalent capacitance, then said Q₁=C₁*V₁ and Q₂=C₂*V₂
Then by my second assumption, said Q - Q₂=C₁*V₁.

Next I eliminated Q₂ by combining those equations. At this point the only two unknowns were V1 and V2 which I solved for using the first assumption. As you can imagine this resulted in an algebra nightmare. I'm afraid that I am completely off track with this problem. I there an easier way to solve this?

Thanks

 

[Delphi51]

You are missing the key: the charges on the two capacitors are equal. That is because any electrons taken away from one go onto the other.

(a) is a strange question, assuming you can't use the C1 = 10C2 info given in (b). I guess the (a) answers will be messy and include Q, V, C1 and C2 in their expressions.
The (b) answers will be very simple.

 

[Brilliant]

Thank you very much for your reply. That makes the problem MUCH simpler. I had actually been stumped before about how current was even able to flow across a capacitor at all, then I read about how charge collecting on one plate would cause charge to move off the opposing plate, causing a current. I just didn't realize that this would imply that the charge across the two capacitors would be the same.

I did have one other question, and that was if my assumption that V₁ + V₂ = V is correct. I can't think how this could be proven, and I know that it's not true if the capacitors are in parallel, but it seems like it should be, just by intuition. But it seems that my intuition and physics are rarely the same.

Thanks so much for your help.

 

[Delphi51]

V1 + V2 = V

No doubt about that.

 

[rwisz]

for your question! Solving for the voltage across two capacitors in series can definitely be a tricky problem. It seems like you have the right idea by using the equations Q=CV and the assumption that the total voltage (V) is divided between the two capacitors (V1+V2=V). However, it looks like you may have made a mistake in your algebra by assuming that Q-Q2=C1*V1. This is not correct because Q2 is not equal to C2*V2, it is equal to C2*(V-V1). So the correct equation would be Q-Q2=C1*V1+C2*(V-V1). By substituting this into your original equation and solving for V1 and V2, you should be able to find the voltage across each capacitor. Keep in mind that this is just one method of solving this problem and there may be other approaches that are easier or more efficient. It's always a good idea to double check your work and equations to make sure they are correct. Good luck!