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,     \[C=\frac{A{{\varepsilon }_{0}}}{2d}+\frac{KA{{\varepsilon }_{0}}}{2d}\]                 \[C=\frac{C}{2}(1+K)\]