Discussion
In the given figure, the effective Capacitance between point A and point B is __________.
Answer: A
The effective capacitance is 3 µF.
Each branch is a series pair, and capacitors in series combine like resistors in parallel. The two branch results then add, because capacitors in parallel add directly.
\[ \begin{aligned} C_{1} &= \frac{3 \times 6}{3 + 6} = 2\ \mu\text{F} \\ C_{2} &= \frac{2 \times 2}{2 + 2} = 1\ \mu\text{F} \\ C_{AB} &= 2 + 1 = 3\ \mu\text{F} \end{aligned} \]
9 µF comes from adding 3 and 6 as if they were in parallel; the rules for capacitors are the reverse of those for resistors. 6 µF and 12 µF are more than the two branches can give together, since the upper branch can be no larger than its smaller capacitor, 3 µF, and the lower no larger than 2 µF.
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