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Q.

Four thin metallic plates have rectangular shapes with dimensions $L \times a o r L \times 2 a .$ All those plates are placed parallel to each other with equal spacing d between consecutive neighboring plate as shown at the picture below. Top and bottom plates are connected with wire. Determine effective capacitance $C_{A B}$ measured between contacts A and B connected to the middle plates. If $C_{A B} = \frac{x ε_{0} a L}{d},$ find x.

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answer is 1.6.

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Detailed Solution

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$C (x - v) + \frac{l}{2} (x - 0) + C (x - 0) = 0 \frac{5 x}{2} = V x = \frac{2 V}{5}$

Q on plate connected to +ve terminal $= C (V - \frac{2 V}{5}) T C (V - 0)$ $= \frac{8 C V}{5} = C_{e q} V$

$\Rightarrow C_{e q} = \frac{1.6 ε_{0} L a}{d}$

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Four thin metallic plates have rectangular shapes with dimensions L×a or L×2a. All those plates are placed parallel to each other with equal spacing d between consecutive neighboring plate as shown at the picture below. Top and bottom plates are connected with wire. Determine effective capacitance CAB measured between contacts A and B connected to the middle plates. If CAB=xε0aLd, find x.