Calculating Capacitance in a Mixed Circuit?

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Homework Help Overview

The discussion revolves around calculating the equivalent capacitance in a mixed circuit involving three capacitors with specified values. Participants are exploring the relationships between capacitors in series and parallel configurations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants attempt to calculate the total capacitance by considering both series and parallel arrangements. Questions arise regarding the correct application of formulas and the order of operations in combining capacitances.

Discussion Status

The discussion is active, with participants questioning each other's calculations and assumptions. Some guidance has been provided regarding the addition of capacitors in series and parallel, but there is no explicit consensus on the final answer yet.

Contextual Notes

Participants express uncertainty about the correct approach to the problem, indicating a lack of clarity on how to combine the capacitances based on their configuration in the circuit.

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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