Question

For a resistance `R` and capacitance `C` in series the impedance is twice that of a parallel combination of the same elements What is the frequency of applied emf .
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Answer 1

Series: `Z_(1) = sqrt(R^(2) + X_(C)^(2)) , X_(C) =1//omegaC`
Parallel
`(i_(r))_(0) = V_(0) //R,( i_(C))_(0) = (V_(0))/(X_(C)) `
` i_(0) = sqrt((i_(R))_(0)^(2) + (i_(C))_(0)) = sqrt(((V_(0))/(R))^(2) + ((V)/(X_(C)))^(2))`
`(V_(0))/(Z^(2)) = V_(0) sqrt((1)/(2^(2)) + (1)/X_(C)^(2))`
`Z_(1) = 2Z_(2) implies sqrt(R^(2) + X_(C)^(2)) = (2RX_(C))/(sqrt(R^(2) + X_(C)^(2)`
`R^(2) + X_(C)^(2) = 2RX_(C) implies (X_(C) -R)^(2) =0`
`X_(C) =R implies (1)/(omegaC) =R`
`omega = (1)/(RC) implies 2pi f = (1)/(RC)`
`f = (1)/(2 pi RC)`
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