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

Answer

C

Explanation

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