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Two parallel plate air capacitance of...

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

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)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(1)/(C_(1))=1/C+1/C=2/C Rightarrow C_(1)=C/2`
`1/C_(2)=1/C+1/(KC)`
`1/C_(2)=1/C [1+1/K]`
`therefore C_(2)=(C)/((1+1/K))=(CK)/((K+1))`
`DeltaC=(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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