Question

You have a 1.0 μF, 2.0 μF and 3.0 μF capacitors. What
capacitances can you get by connecting them?

Answer 1

\[(1.0 + 2.0 + 3.0) \mu{\rm F}\]
\[\left(\frac{1.0 + 2.0}{2} + 3.0\right)\mu{\rm F}\]
\[\left(\frac{1.0 + 3.0}{2} + 2.0\right)\mu{\rm F}\]
\[\left(\frac{2.0 + 3.0}{2} + 1.0\right)\mu{\rm F}\]
\[\left(\frac{1.0 + 2.0 + 3.0}{3} \right)\mu{\rm F}\]

Answer 2

Not quite Carl. The first one is correct for all three caps in parallel. The correct formula for capacitors in series is:\[\frac{ 1 }{ C _{Eq} }= \frac{ 1 }{ C _{1} }+\frac{ 1 }{ C _{2} }+\frac{ 1 }{ C _{3} }...\] which reduces to:
\[C _{Eq}=\frac{ C _{1}C _{2} }{C _{1}+C _{2} }\] for two capacitors in series.

Answer 3

RIght you are. For some reason I had a braino and thought we were dealing with resisters. Substitute the inverses for the numbers in all the equations, and invert at the end.