question_answer

A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness d \[{{d}_{1}}\]and dielectric constant \[{{k}_{1}}\]and the other has thickness \[{{d}_{2}}\]and dielectric constant \[{{k}_{2}}\]as shown in figure. This arrangement can be thought as a dielectric slab of thickness \[d\left( ={{d}_{1}}+{{d}_{2}} \right)\]and effective dielectric constant K. The K is; 

A) \[\frac{{{K}_{1}}{{d}_{1}}+{{K}_{2}}{{d}_{2}}}{{{d}_{1}}+{{d}_{2}}}\] 

B) \[\frac{{{K}_{1}}{{d}_{1}}+{{K}_{2}}{{d}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]

C) \[\frac{{{K}_{1}}{{K}_{2}}\left( {{d}_{1}}+{{d}_{2}} \right)}{{{K}_{2}}{{d}_{1}}+{{K}_{1}}{{d}_{2}}}\] 

D) \[\frac{2{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]