Calculating Capacitance in a Mixed Circuit?

AI Thread Summary
The discussion revolves around calculating the equivalent capacitance of a mixed circuit with three capacitors: C1 = 10.3 microfarads, C2 = 41.1 microfarads, and C3 = 95.5 microfarads. Initially, the user attempted to calculate the total capacitance but made errors in the application of series and parallel formulas. After clarification, it was confirmed that capacitors in series should be treated similarly to parallel resistors, leading to a corrected understanding of the calculations. Ultimately, the user arrived at a final equivalent capacitance of 9.55 microfarads. The conversation highlights the importance of correctly applying the rules for series and parallel capacitor combinations.
brinstar
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Homework Statement


Please calculate the equivalent capacitance if C1 = 10.3 microfarads, C2 = 41.1 microfarads, and C3 = 95.5 microfarads in the diagram.

Homework Equations


1 / Ctotal for Parallel = (1/C1) + (1/C2) + ...
Ctotal for Series = C1 + C2 + ...

The Attempt at a Solution


So I tried to split it up. The total for the parallel part was 28.73389458 microfarads. Then the series was 10.3 microfarads, so when I add it up, I get 39.03389458 microfarads. Is this right?
 

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brinstar said:
1 / Ctotal for Parallel = (1/C1) + (1/C2) + ...
Ctotal for Series = C1 + C2 + ...
Are you sure?
 
cnh1995 said:
Are you sure?

Oops, sorry! It's the opposite, my bad >.<

Now I'm getting 146.9 microfarads?
 
Are you sure you should add the 10.3 microfarad directly to the parallel combination?
 
A quick reality check is to realize that any time you have capacitors in series the result must be less than the smallest in the string. In your figure capacitor C1 is definitely in series with whatever net capacitance follows it...
 
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cnh1995 said:
Are you sure you should add the 10.3 microfarad directly to the parallel combination?

Well, being that I have absolutely no idea how to face this situation, I'm as sure as can be with a wild guess :/ I'm guessing I did it wrong, though, right?

So should I be adding its inverse?
 
brinstar said:
Well, being that I have absolutely no idea how to face this situation, I'm as sure as can be with a wild guess :/ I'm guessing I did it wrong, though, right?

So should I be adding its inverse?
Yes. Series capacitors add like parallel resistors.
 
cnh1995 said:
Yes. Series capacitors add like parallel resistors.
Ah okay, I think I got it: 9.55 microfarads

Thank you!
 
brinstar said:
Ah okay, I think I got it: 9.55 microfarads
Good! In such addition, the result is always less than the least of the component values, as gneill mentioned in #5.
 
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cnh1995 said:
Good! In such addition, the result is always less than the least of the component values, as gneill mentioned in #5.

thank you for the help!
 

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