How Do You Calculate the Equivalent Capacitance in a Complex Circuit?

[holymoly]

Homework Statement

In the diagram V = 12.0V, C1 = 23 uF, C2 = 4.00 uF, C3 = 12.0 uF and C4 = 9.00uF. Calculate the equivalent capacitance of the system.

http://img403.imageshack.us/img403/6346/eqam8.jpg

Homework Equations

Just combinding capacitors in parallel and in series.

The Attempt at a Solution

This question is giving me a headache when it should be simple. I must be overlooking something stupid, and hopefully someone will please lead me in the right direction.

I start by taking capacitors C1 and C3, which are in series, and combine them :
1/C13 = 1/24 + 1/12
1/C13 = 3/24
C13 = 8

Doesn't that leave C13, C2, and C4 in parallel? (this is where I'm getting sidetracked i think. the middle one is throwing me for a bit of a loop). In parallel, that would just be 8+4+9 = 21 uF, which is not the answer. The answer should be 5.14 uF.

I'd appreciate any pointers.

 

[berkeman]

Doesn't that leave C13, C2, and C4 in parallel?

No, only C13 and C2 are in parallel for the next step.

 

[m2003]

You are on the right track with combining capacitors in series and parallel. However, it looks like you may have made a mistake in your calculation for C13. Remember that when capacitors are in series, their equivalent capacitance is given by 1/Ceq = 1/C1 + 1/C2. So for C1 and C3, the equivalent capacitance would be 1/C13 = 1/23 + 1/12 = 5/69. Solving for C13, we get C13 = 13.8 uF.

Now, for the remaining capacitors in parallel, we can use the equation Ceq = C1 + C2 + C3. In this case, Ceq = 13.8 uF + 4.00 uF + 9.00 uF = 26.8 uF. This is the equivalent capacitance of the system. However, the question specifically asks for the equivalent capacitance of the system, not the total capacitance of the remaining capacitors in parallel. To find the equivalent capacitance of the system, we need to combine this value with the 8 uF from C13. So the final answer should be 26.8 uF + 8 uF = 34.8 uF. It is important to note that when capacitors are in series, they add inversely, while in parallel, they add directly. Keep practicing and you will get the hang of it!