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Capacitors in series are like resistors in parallel, the total capacitance is the inverse of the sum of the inverses.

CSERIES = 1 / Summation1toN (1 / CN)

For this question ...

1 / 12 = 1 / 30 + 1 / x

1 / 12 - 1 / 30 = 1 / x

0.05 = 1 / x

x = 20

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Q: What capacitance must be connected in series with a 30microfarad's capacitor for the equivalent capacitance to be 12microfarad's?
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