Four identical rectangular plates with length l=2 cm and breadth b=3/2 cm are arranged as follows: the plates A, B, C, D stand parallel in a row with an equal gap d between successive plates, and plates B and D are joined by a wire. The equivalent capacitance between A and C is (xε₀)/d. The value o…

Question

Four identical rectangular plates with length l=2 cm and breadth b=3/2 cm are arranged as follows: the plates A, B, C, D stand parallel in a row with an equal gap d between successive plates, and plates B and D are joined by a wire. The equivalent capacitance between A and C is (xε₀)/d. The value of x is . (Round off to the nearest integer; take the plate area in cm².)

Accepted Answer

2. Let C₀=(ε₀ S)/d be the capacitance of one facing pair, where S=l× b=2×3/2=3 cm². The three gaps give three capacitors: AB, BC and CD, each C₀. The wire makes B and D a single node. So from A we go through AB to node BD, and from node BD there are two routes to C: the gap BC and the gap CD — these two are in parallel, 2C₀. C_AC=(C₀·2C₀)/(C₀+2C₀)=2/3C₀=2/3·(3ε₀)/d=(2ε₀)/d. x=2.

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