A parallel plate capacitor has an area of 6 , | vedclass

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(C) The capacitor is divided into three parallel capacitors,each with area $A' = A/3$ and the same plate separation $d$.The equivalent capacitance $C_

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$12$

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(C) The capacitor is divided into three parallel capacitors,each with area $A' = A/3$ and the same plate separation $d$.The equivalent capacitance $C_{net}$ is the sum of the individual capacitances:$C_{net} = C_1 + C_2 + C_3$Using the formula for a parallel plate capacitor $C = \frac{K \epsilon_0 A}{d}$,we have:$\frac{K_{eq} \epsilon_0 A}{d} = \frac{K_1 \epsilon_0 (A/3)}{d} + \frac{K_2 \epsilon_0 (A/3)}{d} + \frac{K_3 \epsilon_0 (A/3)}{d}$Canceling the common terms $\frac{\epsilon_0 A}{3d}$ from both sides:$K_{eq} = \frac{K_1 + K_2 + K_3}{3}$Substituting the given values:$K_{eq} = \frac{10 + 12 + 14}{3} = \frac{36}{3} = 12$Thus,the equivalent dielectric constant is $12$.

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