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` ..(i)
`C_(1)C_(2)C_(3) = 48` ..(ii)
`C_(1) + C_(2) = 6` ..(iii)
From equations (i) and (ii)
`C_(3) = 6`
From equations (ii) and (iv) `C_(1)C_(2) = 8`
Also `(C_(1) - C_(2))^(2) = (C_(1) + C_(2))^(2) - 4C_(1)C_(2)`
`(C_(1) - C_(2))^(2) = (6)^(2) - 4 xx 8 = 4`
`rArr C_(1) - C_(2) = 2` ..(iv)
On solving (iii) and (v) `C_(1) = 4, C_(2) = 2`