Calculating Capacitance in a Mixed Circuit?

In summary, the equivalent capacitance of a circuit with C1 = 10.3 microfarads, C2 = 41.1 microfarads, and C3 = 95.5 microfarads is 9.55 microfarads when the capacitors are arranged in series. The result is always less than the smallest component value in this type of addition.
  • #1
brinstar
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1

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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  • #2
brinstar said:
1 / Ctotal for Parallel = (1/C1) + (1/C2) + ...
Ctotal for Series = C1 + C2 + ...
Are you sure?
 
  • #3
cnh1995 said:
Are you sure?

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

Now I'm getting 146.9 microfarads?
 
  • #4
Are you sure you should add the 10.3 microfarad directly to the parallel combination?
 
  • #5
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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  • #6
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?
 
  • #7
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.
 
  • #8
cnh1995 said:
Yes. Series capacitors add like parallel resistors.
Ah okay, I think I got it: 9.55 microfarads

Thank you!
 
  • #9
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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  • #10
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!
 

Related to Calculating Capacitance in a Mixed Circuit?

1. How do I calculate the total capacitance in a mixed circuit?

To calculate the total capacitance in a mixed circuit, you will need to use the formula: C = C1 + C2 + ... + Cn, where C is the total capacitance and C1, C2, and Cn are the individual capacitances of each component in the circuit. Simply add up all the individual capacitances to obtain the total capacitance.

2. Can I use series or parallel equations to calculate capacitance in a mixed circuit?

Yes, you can use series or parallel equations to calculate capacitance in a mixed circuit. In a series circuit, the total capacitance is equal to the inverse of the sum of the inverse of each individual capacitance. In a parallel circuit, the total capacitance is equal to the sum of all the individual capacitances. You can use either equation depending on the configuration of your mixed circuit.

3. What is the difference between series and parallel connections in a mixed circuit?

In a series connection, components are connected one after another in a single loop. This means that the same current flows through each component, and the total resistance is equal to the sum of each individual resistance. In a parallel connection, components are connected side by side and share the same voltage. This means that the total current is equal to the sum of the individual currents, and the total resistance is less than the smallest individual resistance.

4. How do I calculate the equivalent capacitance in a mixed circuit with both series and parallel connections?

To calculate the equivalent capacitance in a mixed circuit with both series and parallel connections, you will need to simplify the circuit into smaller series and parallel sections. Then, use the appropriate equations to calculate the total capacitance of each section. Finally, use the series or parallel equations to calculate the total capacitance of the entire circuit.

5. Can I use the same method to calculate capacitance in any type of mixed circuit?

Yes, the same method can be used to calculate capacitance in any type of mixed circuit. As long as you know the individual capacitance values and the configuration of the circuit, you can use the appropriate equations to calculate the total capacitance. However, keep in mind that the equations may differ depending on the type of connection (series or parallel).

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