If `C_(AB)` ( equivalent ) `= (C )/(2)` and capactance of all the capacitors are C in vacuum without dielectric . Find the relation between `k_(1) , k_(2),k_(3)`

Explanation

`:. C_(AB) = ((C_(1) xx Ck_(2))/(Ck_(1)+Ck_(2))) + Ck_(3)`
`implies (C)/(2) = (C^(2))/(C ) ((k_(1)k_(2))/(k_(1)+k_(2)))+ Ck_(3)`
`implies (1)/(2) = (k_(1)k_(2))/(k_(1)+k_(2))+ k_(3)`
`implies (1)/(2) = (k_(1)k_(2) + k_(1)k_(3) + k_(2)k_(3))/(k_(1)+k_(2))`
`implies (k_(1)+k_(2))/(2) = (k_(1)k_(2) + k_(1) k_(3) + k_(2) k_(3))`