The capacitance of a capacitor between` 4//3` times its original value if a dielectric slab of thickness `t=d//2` is inserted between the plates (d is the separation between the plates). What is the dielectric constant of the slab?

Options

A. `8`
B. `4`
C. `6`
D. `2`

Answer

D

Explanation

`C_(air) = (epsilon_(0)A)/(d)`, with dielectric slab `C' = (epsilon_(0)A)/((d-t+(t)/(K)))`
Given `C' = (4)/(3) C rArr (epsilon_(0)A)/((d-t+(t)/(K))) = (4)/(3) xx (epsilon_(0)A)/(d)`
`rArr K = (4t)/(4t - d) = (4(d//2))/(4[(d//2)-d]) =2`