Consider an infinite matrix of capacitors as shown in the figure. The effective capacitance between point $A$ and $B$ will be
Diffcult
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For row $1: \frac{1}{\mathrm{C}_{\mathrm{eff}}}=\frac{1}{\mathrm{C}}+\frac{1}{2 \mathrm{C}}+\frac{1}{4 \mathrm{C}}+\ldots=\frac{2}{\mathrm{C}}$
$\Rightarrow \mathrm{C}_{\mathrm{eff}}=\frac{\mathrm{C}}{2}$
Similarly for row $2: \mathrm{C}_{\mathrm{eff}}=\frac{\mathrm{C}}{4}$
$ \Rightarrow {{\rm{C}}_{{\rm{ef}}{{\rm{f}}_{net}}}} = \frac{{\rm{C}}}{2} + \frac{{\rm{C}}}{4} + \frac{{\rm{C}}}{8} + \ldots = {\rm{C}}$
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