A dielectric of constant K is slipped between the plates as parallel plate condenser in half of the space as shown in the figure. If the capacity of air condenser is C, then new capacitance between A and B with be-

Options

A. `C/2`
B. `C/(2K)`
C. `C/2[1+K]`
D. `(2[1+K])/(C)`

Explanation

This system is equivalent to two capacitors in parallel with area of each plate `A/2`.
`C=C_(1)+C_(2)`
`=(epsi_(0)A)/(2d)+(epsi_(0)AK)/(2d)`
`=(epsi_(0)A)/(2d) [1+K]=C/2 [1+K]`
Hence the correct answer will be (C).