Consider three capacitors of capacitance `C_(1),C_(2)` and `C_(3)`. If `C_(1), C_(2)` and `C_(3)` in parallel, the equivalent capacitance is `6` unit, while `C_(2)` and `C_(3)` in parallel, the equivalent capacitance is `5` unit. If `C_(1).C_(2).C_(3)=6`, then the capacitance are

Options

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

Answer

A

Explanation

`C_(1)+C_(2)+C_(3)=6`
`C_(2)+C_(3)=5`
`C_(1)=1`
`C_(1)C_(2)C_(3)=6`
`C_(2)C_(3)=6`
From (ii), `C_(3)=5-C_(2)` in (iv)
`C_(20(5-C_(2))=6`
`C_(2)^(2)-5C_(2)+6=0`
`(C_(2)-2)(C_(2)-3)=0`
`C_(2)=2 or 3, C_(3)=3or2`
Capacitance are `1,2,3`