Charged capacitors connected together, find the final potential difference

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SUMMARY

The discussion centers on the calculation of the final potential difference when two charged capacitors are connected in series. The key equations used are the charge-voltage relationship (C = Q/V) and the conservation of charge (Q1 = Q2). The final potential difference was calculated to be 71.4 V for the first capacitor (C1) when the total potential difference across both capacitors is 100 V. The participants clarified that although the capacitors are charged separately, they share the same charge when connected in series.

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The Blind Watchmaker
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Homework Statement


upload_2018-3-6_21-55-34.png


Homework Equations


C = Q/V

The Attempt at a Solution


Q1 = Q2
C1*V1 = C2*V2
2*V1 = 5*V2
V2 = 2/5*V1

V1+V2 =100
7/5*V1 = 100
V1 = 71.4 V

Can someone verify my working? Thanks!
 

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The Blind Watchmaker said:

The Attempt at a Solution


Q1 = Q2 ← How do you conclude this?
C1*V1 = C2*V2
2*V1 = 5*V2
V2 = 2/5*V1

Two different valued capacitors with the same potential difference will have the same charge?
 
Note that before the switches are closed, Q1 ≠ Q2. What is the total charge on the two bottom plates before the switches are closed? What is the total charge on the two bottom plates after the switches are closed?
 
gneill said:
Two different valued capacitors with the same potential difference will have the same charge?
They are in series thus Q1=Q2. I do not get why they have the same potential difference as I assume only 1 battery is used
 
The Blind Watchmaker said:
They are in series thus Q1=Q2. I do not get why they have the same potential difference as I assume only 1 battery is used
There are two issues in your understanding. When we connect two capacitors in series using only one battery q for each is taken to be the same. Just make such a connection with two different capacitors and then argue why we take charge stored by these capacitors to be the same. But in this problem they have been charged separately to the same potential difference.
 
The Blind Watchmaker said:
They are in series thus Q1=Q2. I do not get why they have the same potential difference as I assume only 1 battery is used
Read the problem statement carefully as to how the capacitors are prepared *before* they are connected to each other.
 

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