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(C) In the given arrangement, there are four plates. Let the plates be numbered $1$, $2$, $3$, and $4$ from top to bottom.Plate $1$ and $4$ are connec

Vedclass · Accepted Answer

$\frac{3\varepsilon_0 A}{d}$

Vedclass · Answer

(C) In the given arrangement, there are four plates. Let the plates be numbered $1$, $2$, $3$, and $4$ from top to bottom.Plate $1$ and $4$ are connected to point $A$.Plate $2$ and $3$ are connected to point $B$.This creates three capacitors in parallel between points $A$ and $B$.Specifically, the space between plate $1$ and $2$ forms a capacitor, the space between plate $2$ and $3$ forms a capacitor, and the space between plate $3$ and $4$ forms a capacitor.However, looking at the connections: Plates $1$ and $4$ are connected to $A$, and plates $2$ and $3$ are connected to $B$. This forms three parallel capacitors, each with capacitance $C = \frac{\varepsilon_0 A}{d}$.Thus, the total equivalent capacitance is $C_{eq} = C + C + C = 3C = \frac{3\varepsilon_0 A}{d}$.

Four metallic plates are arranged as shown in the figure. If the distance between each plate is $d$ and the area of each plate is $A$, then the capacitance of the given system between points $A$ and $B$ is (Given $d << \sqrt{A}$):

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