Two capacitors of unknown capacities can produce maximum capacity 45 farad and minimum 10 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) = 45 F`
`rArr C_(1) + C_(2) = C_(P) = 45`…..(1)
These can produce minimum capacitance when connected in series combination
`rArr C_(s) = 10 F`
and `1/C_(1) + 1/C_(2) =1/C_(s)`
`(C_(1)+ C_(2))/(C_(1)C_(2))=1/10`
`45/(C_(1)C_(2)) =1/10` [Using eqn. (1)]
`C_(1)C_(2) = 45 xx 10 = 450`
We know that,
`(C_(1)-C_(2))^(2) =(C_(1)-C_(2))^(2) = (C_(1) + C_(2))^(2) -4 C_(1)C_(2)`
`(C_(1)-C_(2))^(2) = (45)^(2) - 4(450)`
`C_(1) - C_(2) = sqrt(225)`
Adding eqns. (1) and (2)
`2C_(1) = 50`
`rArr C_(1) = 30 F`
Put value of `C_(1)` in eq. (2) `30-C_(2) = 15`
`rArr C_(2) = 30-15 = 15 F`
`rArr C_(2) = 15F`