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A paralle plate air capacitor has capaci...

A paralle plate air capacitor has capacitance C. Now half of the space is fillel with a dielectric material with dielectric constant K as shown in figure . The new capacitance is C . Then

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Answer (2)
`(1)/(C_(AB))= (1)/(((epsilon_(0)KA)/(d/2)))+ (1)/((epsilon_(0)A)/(d/2))`
`implies (1)/(C_(AB))= (d)/( 2epsilon_(0)A) [(1)/(K) +1]`
`implies (1)/(C_(AB))= (d)/(2 epsilon_(0)A) [ (1+K)/(K)]`

`implies C_(AB) =(2epsilon_(0)A)/(d) [(K)/(1+K)]`
`= 2C [ (K)/(1+K)]`
`C_(AB) = C((2K)/(1+K))`
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