# Capacitors in a circuit / Calculate total capacitance

## Homework Statement

Capacitors are connected as shown in this diagram:

http://o3xn.files.wordpress.com/2012/04/c4.png

C1 = 2 μF, C2 = 1 μF. What is the total capacitance of the system in between the terminals A and B?

## Homework Equations

For capacitors C1 and C2 connected in series, $\dfrac{1}{C_\Sigma}=\dfrac{1}{C_1}+\dfrac{1}{C_2}$

For capacitors C1 and C2 connected in parallel, $C_\Sigma=C_1+C_2$

## The Attempt at a Solution

The problem here is that my answer doesn't match that in the book. So I just wanted to check if you guys get the same answer as me.

The three rightmost capacitors C1 have a total capacitance of 2/3 μF.
They are connected in parallel to a C2-capacitor, their overall capacitance is 1+2/3=5/3 (μF).
Then we have a C1 in series with what we calculated above in series with yet another C1, which yields 1/(1+3/5)=5/8 (μF).
Last, we have a C2 in parallel with what we calculated above, which yields 1+5/8=13/8=1.625 (μF).

The book gives 1.58 μF.