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  • A parallel plate capacitor of plate area A and separation d filled with three dielectric materials as shown in figure. The dielectric constants are <img alt="k_1, k_2\ and\ k_3" src="https://entran

A parallel plate capacitor of plate area A and separation d filled with three dielectric materials as shown in figure. The dielectric constants are k_1, k_2\ and\ k_3  respectively. The capacitance across A B will be -

Option: 1

\frac{\epsilon_{0 A}}{d} \frac{k_1 k_2 k_3}{k_1+k_2+k_3}


Option: 2

\frac{\epsilon_0 A}{d}\left(k_1+k_2+k_3\right)


Option: 3

\frac{\epsilon_0 A}{3 d}\left(k_1+k_2+k_3\right)


Option: 4

\frac{3 \epsilon_0 A}{2 d}\left(k_1+k_2+k_3\right)


Answers (1)

best_answer

\text { For parallel plate capacitor } c=\frac{k \epsilon_0 A}{d}

\begin{aligned} & c=\frac{\left(A_1 k_1+A_2 k_2+\cdots\right) \epsilon_0}{d} \\ & c=\frac{A}{3} \frac{\epsilon_0}{d}\left(k_1+k_2+k_3\right) \end{aligned}

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Nehul

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