Four metal plates are arranged as shown. Capacitance between $ X $ and $ Y $ (A $ \rightarrow $ Area of each plate, $ d \rightarrow $ distance between the plates)

Question

Four metal plates are arranged as shown. Capacitance between $ X $ and $ Y $ (A $ \rightarrow $ Area of each plate, $ d \rightarrow $ distance between the plates), $ \frac{3}{2} \frac{\varepsilon_{0} A}{d} $, $ \frac{2 \varepsilon_{0} \mathrm{~A}}{d} $, $ \frac{2}{3} \frac{\varepsilon_{0} A}{d} $, $ \frac{3 \varepsilon_{0} \mathrm{~A}}{d} $

MARKS App · Accepted Answer

Area of each plate = A There are $ 3 $ plates between $ X $ and $ Y $ and each will have a contribution of $ \frac{C}{3} $ Therefore, capacitance between $ \mathrm{X} $ and $ \mathrm{Y}=2 \times \frac{C}{3}=\frac{2}{3} \frac{\varepsilon_{0} A}{d} $

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