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Question
The capacitors, each of 4 µF are to be connected in such a way that the effective capacitance of the combination is 6 µF. This can be achieved by connecting ______.
Options
All three are in parallel.
All three are in series.
Two of them connected in series and the combination in parallel to the third.
Two of them connected in parallel and the combination in series to the third.
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Solution
The capacitors, each of 4 µF are to be connected in such a way that the effective capacitance of the combination is 6 µF. This can be achieved by connecting two of them connected in series and the combination in parallel to the third.
Explanation:
When the capacitors are connected in parallel the equivalent capacitance is given by
`C_{eq} = C_1 + C_2 + C_3`
in series `1/C_{eq} = 1/C_1 + 1/C_2 + 1/C_3`
here `C_1 = C_2 = C_3 = 4muF`
`C_{eq} = 6muF`
So, Ceq = 6µF can only be get if two capacitors are connected in series with the third one in parallel as shown.
`C_{eq} = (4 xx 4)/(4 xx 4) + 4`
= 2 + 4 = 6µF
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