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If C(AB) (equivalent ) = (C ) /(2) and c...


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

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`because C_(AB)=((Ck_(1)xxCk_(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))`
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