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 is

Options

A. `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

A

Explanation

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)]`