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A parallel plate air capacitor has capac...

A parallel plate air capacitor has capacitance C. Half of space between the plates is filled with dielectric of dielectric constant K as shown in figure . The new capacitance is C . Then

A

`C=C[(K)/(K+1)]`

B

`C'=C[(2K)/(K+1)]`

C

`C'=(2C)/(K+1)`

D

`C'=C[1+(K)/(2)]`

Text Solution

Verified by Experts

The correct Answer is:
B
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)/(2epsilon_(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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