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Find the capacitance of the infinite la...

Find the capacitance of the infinite ladder shown in figure.

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Let the equivalent capacitance `C`. Since it is an infinite series, there there will be negligible change if the arragement is done as in . So
`C=1+(2xxC)/(2+C) =((2+C)+2C)/(2+C)`
`=(3C+2)/(C+2)`

or `(2+C)C=(3C+2)`
or `2C+C^(2)=3C+2C`
or `C^(2)-C-2=0`
or `(C-2)(C+1)=0`
Since `C=-1` is impossible, so `C=2 mF`.
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