question_answer

A dielectric of dielectric constant K is introduced such that half of its area of a capacitor of capacity C is occupied by it. The new capacity is

A)  \[2\,C\]          

B)  \[C/2\]

C)  \[(1+K)C/2\]   

D)  \[2C(1+K)\]

Correct Answer: C

Solution :

The dielectric is introduced such that, half of its area is occupied by it. In the given case the two capacitors are in parallel. \[\therefore \] \[C'={{C}_{1}}+{{C}_{2}}\] \[{{C}_{1}}=\frac{A\,\,{{\varepsilon }_{0}}}{2d}\] and \[{{C}_{2}}=\frac{KA{{\varepsilon }_{0}}}{2d}\] Thus, \[C'=\frac{A{{\varepsilon }_{0}}}{2d}+\frac{KA\,\,{{\varepsilon }_{0}}}{2d}\] \[C'=\frac{C}{2}(1+K)\]