Find the ratio of potential difference that must be applied across parallel and series combination of two capacitors C1 and - Physics - Electrostatic Potential And Capacitance

Question

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

Vara · Accepted Answer

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

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.