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Question

In the figure, capacitor is filled with dielectrics. Find the resultant capacitance.
774291_1fe064df16204dc2ab2f61b092766ad5.png


Solution

$$C_{eq}=\cfrac{C_1C_3}{C_1+C_3}+\cfrac{C_2C_3}{C_2+C_3}$$
$$\cfrac{\epsilon_oA}{d}\left\{ \left[ \cfrac { \cfrac { 1/2 }{ 1/2 } \times \cfrac { 1/2 }{ 1 }  }{ 1+\cfrac { 1 }{ 2 }  }  \right] +\left[ \cfrac { 1\times 1/2 }{ 1+1/2 }  \right]  \right\}$$
$$=\cfrac{\epsilon_oA}{d}\left(\cfrac{1}{3}+\cfrac{1}{3}\right)$$
$$C_{eq}=\cfrac{2\epsilon_oA}{3d}$$

953315_774291_ans_4c2b8a3a61f44c149b2cf287e22ecf12.png

Physics

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