Three capacitors are having capacity in the ratio of `1 : 2 : 3`. Their equivalent capacity when connected in parallel is greater than that when in series by `5(5/11)muF`. Find the individual capacities.

Explanation

Here, ratio of capacities is `1 : 2 : 3`. So let
`C_(1) =C`
`C_(2) = 2C`
`C_(3) = 3C`
In series
`1/C_(s) =1/C_(1) + 1/C_(2) + 1/C_(3)`
`1/C_(s) =1/C + 1/(2C) + 1/(3C)`
or `1/C_(s) = (6 + 3 +2)/(6 C) = 11/(6C)`
or `C_(s) = 6/11 C`
In parallel combination
`C_(P) = C_(1) + C_(2) + C_(3)`
`C_(P) = C_(1) + C_(2) + C_(3)`
`C_(P) = C + 2C + 3C = 6C`
Given, `C_(P) - C_(s) = 60/11`
or `60/11 C = 60/11`
`rArr C =1 muF`
Hence, capacitance are `1muF, 2muF` and `3 muF`.