The equivalent capacitance of three capacitors of capacitance `C_(1):C_(2)` and `C_(3)` are connected in parallel is `12` units and product `C_(1).C_(2).C_(3) = 48`. When the capacitors `C_(1)` and `C_(2)` are connected in parallel, the equivalent capacitance is `6` units. then the capacitance are

Options

A. `2, 3, 7`
B. `1.5, 2.5, 8`
C. `1, 5, 6`
D. `4, 2, 6`

Answer

D

Explanation

`C_1+C_2+C_3 = 12`
`C_1 +C_2 = 6 implies C_1C_2=8`
`C_1 C_2 C_3 = 48 implies C_1C_2 =8`
`(C_1-C_2)^2 +4C_1C_2=(C_1+C_2)^2`
`implies C_1-C_2 = sqrt(36-32) =2`
`C_1 = 4 , C_2 = 2`