Four identical rectangular plates with length, l=2 cm and breadth, $b = \frac{3}{2}$ cm are arranged as shown in figure. The equivalent capacitance between A and C is $\frac{x ε_{0}}{d}$ . The value of x is _______. (Round off to the Nearest Integer)

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answer is 2.

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Detailed Solution

If label the each surface of given figure as follows

Equivalent diagram to above diagram is as follows

$C_{AC} = \frac{C \times 2 C}{3 C} = \frac{2 C}{3} = \frac{2}{3} \frac{ε_{0} A}{d} = \frac{ε_{0}}{d} (lb . \frac{2}{3}) = \frac{ε_{o}}{d} (2 \times \frac{3}{2} \times \frac{2}{3}) = 2 \frac{ε_{0}}{d}$

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