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(D) The capacitor can be modeled as a combination of three capacitors. Capacitors with dielectrics $K_1$ and $K_2$ are in parallel with each other,and

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) The capacitor can be modeled as a combination of three capacitors. Capacitors with dielectrics $K_1$ and $K_2$ are in parallel with each other,and this combination is in series with the capacitor containing dielectric $K_3$. For the top part,the area is $A/2$ and the distance is $d/2$: $C_1 = \frac{K_1 \varepsilon_0 (A/2)}{d/2} = \frac{K_1 \varepsilon_0 A}{d}$ $C_2 = \frac{K_2 \varepsilon_0 (A/2)}{d/2} = \frac{K_2 \varepsilon_0 A}{d}$ Since $C_1$ and $C_2$ are in parallel,their equivalent capacitance is $C_p = C_1 + C_2 = \frac{\varepsilon_0 A}{d} (K_1 + K_2)$. For the bottom part,the area is $A$ and the distance is $d/2$: $C_3 = \frac{K_3 \varepsilon_0 A}{d/2} = \frac{2 K_3 \varepsilon_0 A}{d}$. Now,$C_p$ and $C_3$ are in series: $C_{eq} = \frac{C_p C_3}{C_p + C_3} = \frac{\left[ \frac{\varepsilon_0 A}{d} (K_1 + K_2) \right] \left[ \frac{2 K_3 \varepsilon_0 A}{d} \right]}{\frac{\varepsilon_0 A}{d} (K_1 + K_2 + 2K_3)} = \frac{2 K_3 (K_1 + K_2)}{K_1 + K_2 + 2K_3} \frac{\varepsilon_0 A}{d}$. This expression does not match any of the given options,so the correct answer is $(d)$.

In the figure,a capacitor is filled with dielectrics. The resultant capacitance is

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