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Two parallel plate air capacitance of same capacity C are connected in series to a battery of emf E. Then one of the capacitors is completely filled with dielectric material of constant K. The change in the effective capacity of the series combination isA. `C/2[(K-1)/(K+1)]`B. `2/C [(K-1)/(K+1)]`C. `C/2[(K+1)/(K-1)]`D. `C/2[(K-1)/(K+1)]^(2)`

Answer» Correct Answer - A
Initial effective capacity of the series combination is
`1/(C_(1)) = 1/(C ) + 1/(C ) = 2/C`
`= C_(1) = C/2 `
Effective capacity of the series combination with dielectic material is
` 1/(C_(1)) = 1/C + 1/(KC)`
`1/(C_(2)) = 1C [1+1/K]`
`:. C_(2) = C/(1+1/K) = (CK)/((K + 1))`
The change in the effective capacitance is `DeltaC = C_(2) - C_(1)`
`= (CK)/((K+1)) - C/2 = C [K/(K+ 1) - 1/2]`
`=C [(2K - K - 1)/(2(K+1))] = C/2[(K-1)/(K+ 1)]`


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