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Asked in GUJCET 2016 · Capacitor networks
Given: ten square plates of side l (area l²) with every gap equal to d. In the figure three branches join A to B: four plates above, a pair in the middle, and four plates below.
Idea: each gap between facing plates is a capacitor C = (ε₀l²)/d.
In a four-plate branch the two inner plates are isolated, so its three gaps are in series: C/3.
The middle pair is a single gap: C.
All three branches join A to B, so they are in parallel: C_eq = C/3 + C + C/3 = (5C)/3.
So C_eq = (5ε₀l²)/(3d).
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