Question

Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.

Answer 1

Let the equivalent capacitance of the infinite ladder be C.

Because it is an infinite ladder, the change in the equivalent capacitance will be negligible if we add one more ladder at point AB, as shown in the given figure.

From the given figure, the equivalent capacitance can be calculated as :-

${\displaystyle C_{eq}=\frac{2\times C}{2+C}+1=C}$

${\displaystyle \Rightarrow (2+C)C=3C+2}$

${\displaystyle \Rightarrow 2C+C^2=3C+2}$

${\displaystyle \Rightarrow C^2-C-2=0}$

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

${\displaystyle \Rightarrow C=-1\text{or}C=2}$

${\displaystyle \Rightarrow C=-1}$         (It is not possible)

${\displaystyle \therefore C=2 \text{uF}}$