Find the unknown capacity of two capacitors

[Kirill Vlaksov]

Homework Statement

We consider two capacitors with the unknown capacitances C1 and C2. If
one connects the capacitors in series and applies a voltage of 100 V, finds
that two positively charged plates in total have the charge 1.5 · 10-4 C. If
one switches the capacitors in parallel and again applies a voltage of 100 V, finds
that two positively charged plates, in total have the charge charge 4 · 10-4 C. Which
capacities have the two capacitors?

Homework Equations

Q=C*V

Q=Charge
C=Capacitance
V=Voltage

The Attempt at a Solution

[/B] My attepmpt to solve this is attached in the photos bellow. In general , I was trzing to apply Q=C*V to the first and the second case and then tried to combine my answers

 

[TSny]

Hello.

I don’t think you are using the correct charge for each capacitor when they are in series. Read the second sentence of the problem statement carefully. Otherwise, your work looks good so far.

 

[epenguin]

It seems to me OK. You realize that in series the charge is the same on both capacitors; and that the potentials add up to the known totaL potential. The rest is an algebraic exercise. I would now express in terms of C₁ and the ratio r of capacitances. You should be able to eliminate C₁ and find two capacitances, but from these measurements you will not know capacitor has which capacitance.

 

[TSny]

It seems to me OK.

Hi, epenguin.

The problem states that when the two capacitors are in series, the "two positively charged plates in total have the charge 1.5 · 10^-4 C".
To me, this is different than saying that "each positively charge plate has a charge of 1.5 · 10^-4 C".

[If each positively charged plate has 1.5 · 10^-4 C, then I get that there is no real solution to the set of equations for C₁ and C₂.]

 

[Kirill Vlaksov]

Hello.

I don’t think you are using the correct charge for each capacitor when they are in series. Read the second sentence of the problem statement carefully. Otherwise, your work looks good so far.

It seems to me OK. You realize that in series the charge is the same on both capacitors; and that the potentials add up to the known totaL potential. The rest is an algebraic exercise. I would now express in terms of C₁ and the ratio r of capacitances. You should be able to eliminate C₁ and find two capacitances, but from these measurements you will not know capacitor has which capacitance.

Thank you for your replies. I indeed missed a part concerning a total charge. Attached is the new calculations that I did. So in my calculations instead of 1.5 · 10-4 C i used 7.5 · 10-5 C ( which I got by deviding a total charge when capacitors were connected in series by 2 ). Then all calculations work out just fine. Thank you again for your help.

 

[epenguin]

Hi, epenguin.

The problem states that when the two capacitors are in series, the "two positively charged plates in total have the charge 1.5 · 10^-4 C".
To me, this is different than saying that "each positively charge plate has a charge of 1.5 · 10^-4 C".

[If each positively charged plate has 1.5 · 10^-4 C, then I get that there is no real solution to the set of equations for C₁ and C₂.]

You have to be right about that what the question means. I guess I had resistance in accepting that because in that case that part of the question seemed so artificially contrived - testing examsmanship rather than physics understanding. Why would anyone add those charges, to what physics, or what straightforward measurement would that correspond? The pair combines as one equivalent capacitance of 0.75 μF.

More constructively at least this made me realize something I had never heard of or thought, nor had occasion to: that two capacitors In series cannot have more than a quarter of the capacitance as the same two in parallel (the ≤ becoming = when the two capacitances are equali. Likewise two resistors in parallel cannot have more than a quarter the resistance of the two in series, which I don't remember having particularly heard of. )
1.5 is more than quarter of 4 so without needing to solve equations we should have been able to see immediately that the physically meaningful charge is not meant to be 1.5.