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

This is an infinite series and hence deletion or addition of any repetitive portions of the arrangement does not affect the overall effect. So, let’s convert this into a simpler figure for calculation.

In the above figure, ‘C’ represents the effective capacitance of the infinite ladder. For the calculations, we have added a 1μF and a 2μF as shown since they both constitute the repetitive portion of the question figure. Hence C and 2μF are in series and they instead is parallel to 1μF.

Now, we calculate the value of C as,

Which is equals to C itself,

So,

Or,

Or,

Or,

Or,

Or,

Since capacitance value cannot be negative, we neglect C=-1μF. Hence the equivalent capacitance of the infinite ladder is 2μF.

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