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Find the ratio of potential difference that must be applied across the parallel and series combination of two capacitors `C_(1) and C_(2)` with their capacitance in the ratio 1:3 so that energy stored in the two cases becomes the same.

Text Solution

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Here, `(C_(1))/(C_(2)) = (1)/(3)`
If `C_(1) = C. C_(2) = 3C`
`C_(p) = C. C_(2) = 3C`
`C_(s) = (C_(1) C_(2))/(C_(1) + C_(2)) = (C (3C))/(C + 3C) = (3C)/(4)`
If `V_(1) and V_(2)` are potential differences applied across the parallel and series combination, then as
`(1)/(2) C_(p) V_(1)^(2) = (1)/(2) C_(s) V_(2)^(2)`
`(V_(1))/(V_(2)) = sqrt((C_(s))/(C_(P))) = sqrt((3C//4)/(4C)) = (sqrt(3))/(4)`
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