Question

Find the equivalent capacitance of the infinite ladder shown in figure (31-E17) between the points. A and B.

Answer 1

Let the equivalent capacitance be C, since it is an infinite series, So, there will be negligible change if the arrangement is done as in Figure.

From Figure

$C_{eq}=1$

$\Rightarrow (2+C)C=3C+2$

$\Rightarrow 2C+C^2=3C+2C$

$\Rightarrow C^2-C-2=0$

$\Rightarrow (C-2)(C+1)=0$

$\Rightarrow C=-1$ (impossible),

So, $C=2MF$