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 consant of the slab?

Options

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

Answer

D

Explanation

`C_("air")=C,C_(m)=4/3C_("air")=4/3C`
`C_(m)=(Ain_(0))/(d-t(1-1/k))`
`=(Ain_(0))/(d-d/2(1-1/k))=(Ain_(0))/(d(1-1/2+1/k))`
`C_(m)=(Ain_(0))/(d(1/2+1/k))" "(therefore(Ain_(0))/d=C)`
`(4C)/3=C/(1/2+1/k)" "thereforek=2`