# Capacitance in a Complicated Mixed Circuit

1. Feb 10, 2016

### brinstar

1. The problem statement, all variables and given/known data
Find the capacitance of the circuit if C1 = 10.3, C2 = 41.1, C3 = 95.5, C4 = 299.9, and C5 = 525.7, with all the units being in microfarads.

2. Relevant equations
1/Series Ctotal = 1/c1 + 1/c2 ....
Parallel Ctotal = C1 + C2 + ...

3. The attempt at a solution
I tried to combine all the parallel units first and then put it together in series, but I feel like I did it wrong. The answer I got was 241.524 microfarads. I'm pretty sure it could be right given that it's less than the smallest series capacitor (the only one I'm seeing is C5), but I'm not sure. Thank you for any help!

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2. Feb 10, 2016

### BvU

Well, I get a different result. So one of us is making a mistake. Perhaps you can post your steps ?

3. Feb 10, 2016

### brinstar

Basically, what I did was:

(1/c5) + (1/[c1+c2+c3+c4])

Then let's say the result is x.
x^-1 = Ctot.

And from that, I got around 241, give or take a few mistypes in the calculator should there be.

4. Feb 10, 2016

### cnh1995

You can combine only two capacitors in either series or parallel at a time. Start with with C1 parallel with C3..

5. Feb 10, 2016

### brinstar

Ah, okay. So C1 + C3 = 10.3 + 95.5 = 105.8 microfarads?

6. Feb 10, 2016

### cnh1995

Right. Replace this parallel combination with 105.8 microfarad and proceed.

7. Feb 10, 2016

### brinstar

Okie doke. So now do I add that with C4 as if they are in series?

8. Feb 10, 2016

### cnh1995

9. Feb 10, 2016

### brinstar

I meant C2, sorry! I was looking at the diagram and wrote the wrong thing >.<

So (1/105.8) + (1/41.1) = 0.0337826961 => 0.0337826961^-1 = 29.60095303 microfarads?

10. Feb 10, 2016

### cnh1995

Right. I don't know the answer but 29.600 looks correct (it is less than the least!).

11. Feb 10, 2016

### cnh1995

I believe you have understood the logic now. You can proceed with this technique and find the final answer. It's almost 12:30 am here, got to sleep now! Good luck!

12. Feb 10, 2016

### brinstar

Thank you so much for the help! :D I truly appreciate it! Have a good night!

For anyone else out there, is 202.547 microfarads the correct final answer?

13. Feb 10, 2016

### BvU

Isn't that great ! If the exercise has 4 digits max, then the answer should generally have no more than 4 digits.

14. Feb 10, 2016

### brinstar

Ah okay, so 202.5?

15. Feb 10, 2016

### BvU

PF isn't really in the business of approving answers . If you think you did it right, you did it right, right ?

16. Feb 10, 2016

### brinstar

I mean, just because I think I did it right doesn't mean I did it right and got it right :/ if I went with that form of logic, I don't think I'd be here asking for help and unsure of myself. I probably would've just spouted whatever I thought was logical and stuck with that answer, unaware of whether I'm objectively correct or not.

17. Feb 10, 2016

### BvU

Have some faith !
And you were right when you didn't trust yourself in post #1, so maybe you are also right when you think this is the right answer!

More important: do you understand what you did and why it's correct ?

18. Feb 10, 2016

### brinstar

I understand what I did, but I don't know if it's correct?

19. Feb 10, 2016

### donpacino

you can write your answer out using variables without plugging in numbers (which is a "better way" to solve these problems in general) then check that your units are correct. Looking at the units will help you tell if you made a mistake.

the units of C1/(C2+C3) are F/F which is unitless

You can also do a sanity check, which is saying "does this answer make sense". In some cases you might not be able to answer that question. If your answer was 500 F, you can make an argument that it doesn't make sense.

20. Feb 10, 2016

### BvU

There is a meta-approach: suppose you were mistaken, then wouldn't someone have reacted and put a finger on that ? From my evasive replies you could have deduced that I got the same result as you did

Have some faith !
And your reward is the fact you understand it now; the proper answer is only the cherry on the cake.