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. 2
B. 4
C. 5
D. 6

Answer

A

Explanation

`C'=(4)/(3)C" "therefore (4)/(3)C=(epsi_(0)A)/((d)/(2)+(d)/(2K))=(epsi_(0)A)/((d)/(2)[1+(1)/(K)])`
`therefore (4)/(3)(epsi_(0)A)/(d)=(epsi_(0)Axx2K)/(d(K+1))`
`therefore (4)/(3)=(2K)/(K+1)" "therefore 6K=4K+4" "therefore K=2`