Two capacitors of unknown capacities can produce maximum capacity 25 farad and minimum 6 farad when connected together. Find the capacity of each capacitor.

Explanation

Let we have two capacitors `C_(1)` and `C_2`
These, can produce maximum capacitance when connected in parallel
`rArr C_(P) = C_(1) + C_(2)`
`C_(1) + C_(2) = 25` ….....(1)
These can produce minimum capacitance when connected in series combination:
`rArr C_(s) = 6F`
and `1/C_(1) + 1/C_(2) = 1/C_(s)`
`(C_(1)C_(2))/(C_(1)C_(2)) = 1/6`
`25/(C_(1)C_(2)) = 1/6` [Using eq. (1)]
We know that,
`(C_(1)-C_(2))^(2) = (C_(1)+C_(2)) =-4C_(1)C_(2)`
`C_(1) -C_(2) = sqrt(25) =5`........(2)
Adding eqns. (1) and (2)
`2C_(1) =30`
`rArr C_(1) = 15 F`
Put value of `C_(1)` in eq. (2)
`15-C_(2)=5`
`C_(2) = 15-5= 10 F`
`rArr C_(2) = 10 F`