Find the ratio of potential difference that must be applied across parallel and series combination of two capacitors C1 and C2 with their capacitance in the ratio 1:2 so that the energy stored in both the cases becomes the same.

LetC1=xandC2=2xSeries combination:Cs=C1C2C1+C2     =x × 2xx+2x     =2x3Parallel combination:Cp=C1+C2     =x+2x     =3xEnergy stored in series combination =Energy stored in parallel combination12Csv12=12Cpv22122x3v12=123xv222x3v12=3xv22v1v2=9x2x       =3:2

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