In the figure,the area of each plate is A and | vedclass

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(A) The given system consists of four plates. Let the plates be numbered $1, 2, 3, 4$ from top to bottom. From the figure,plates $1$ and $3$ are conne

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$\frac{2 A \varepsilon_0}{d}$

Vedclass · Answer

(A) The given system consists of four plates. Let the plates be numbered $1, 2, 3, 4$ from top to bottom. From the figure,plates $1$ and $3$ are connected to point $A$,and plates $2$ and $4$ are connected to point $B$. This forms three parallel plate capacitors connected in parallel: $1$. Capacitor formed by plates $1$ and $2$ with separation $2d$: $C_1 = \frac{A \varepsilon_0}{2d}$ $2$. Capacitor formed by plates $2$ and $3$ with separation $d$: $C_2 = \frac{A \varepsilon_0}{d}$ $3$. Capacitor formed by plates $3$ and $4$ with separation $2d$: $C_3 = \frac{A \varepsilon_0}{2d}$ Since these capacitors are connected in parallel,the equivalent capacitance $C_{AB}$ is: $C_{AB} = C_1 + C_2 + C_3$ $C_{AB} = \frac{A \varepsilon_0}{2d} + \frac{A \varepsilon_0}{d} + \frac{A \varepsilon_0}{2d}$ $C_{AB} = \frac{A \varepsilon_0 + 2A \varepsilon_0 + A \varepsilon_0}{2d} = \frac{4A \varepsilon_0}{2d} = \frac{2A \varepsilon_0}{d}$ Thus,the correct option is $(A)$.

In the figure,the area of each plate is $A$ and the distance between consecutive plates is as shown in the figure. What is the effective capacitance between points $A$ and $B$?

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