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Question:

Three capacitors each of 4 μF are to be connected in such a way that the effective capacitance is 6 μF. This can be done by connecting them: all in parallel, two in parallel and one in series, all in series, two in series and one in parallel

all in parallel

all in series

two in parallel and one in series

two in series and one in parallel

Solution:

For capacitors in series, equivalent capacitance is given by:
CS = C1C2/(C1 + C2)
For capacitors in parallel, equivalent capacitance is given by:
CP = C1 + C2
In the given configuration, equivalent capacitance is given by
Ceq = Cs + C, where C = 4 μF and Cs = C × C/(C + C) = C/2
Therefore, Ceq = C + C/2 = 6 μF