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. 6
B. 8
C. 2
D. 4

Answer

C

Explanation

Original capacity, `C_(0)=(epsilon_(0)A)/(d)`
On introducing dielectric slab of thickness d/2, the capacity becomes
`C=(epsilon_(0)A)/((d-(d)/(2))+2(d)/(2K))=(epsilon_(0)A)/((d)/(2)(1+(1)/(k)))`
`"As "C=(4)/(3)C_(0)`
`therefore" "(epsilon_(0)A)/((d)/(2)(1+(1)/(k)))=(4)/(3)(epsilon_(0)A)/(d)rArr 1+(1)/(k)=(3)/(2) rArrK=2`