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 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.

The $2\mu F$ and C are in series with each other and they are in parallel to $1\mu F$ capacitor,

For finding the equivalent capacitance we can write

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

$\Rightarrow C=\frac{2C+2+C}{2+C}$

Now solving

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

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

After solving this quadratic equation

$C=-1or2$

-1 will be neglected

So, the correct answer is $2\mu F$