A finite ladder is constructed by connecting several sections of 2 μF, 4 μF capacitor combinations as shown in figure. It is terminated by a capacitor of capacitance C. What value should be chosen for C, such that the equivalent capacitance of the ladder between the points A and B becomes independent of the number of sections in between?

Question

Philoid · Accepted Answer

Given,

The capacitance C should be equal to the equivalent capacitance.

Since the arrangement is an infinite series, addition or deletion of the repetiting components which is the 2 μF, 4 μF capacitor combinations) would not make any effect on the overall capacitance.

Hence, for simplification, we represent it as shown below,

In the figure , C in μF) represents the capacitance that gives the same value for equivalent capacitance to the infinite ladder even after it is terminated at the end. So that C and 4 μF are in series, and these are parallel to 2μF.

In this case, the effective capacitance C_eff

Which is equals to C itself, since C should not alter the effective capacitance.

So,

Or,

Since capacitance value cannot be negative, we neglect C=-2μF. Hence the equivalent capacitance of the infinite ladder is 4μF.

So, the value of capacitance that should be assigned with the terminating capacitor is 4 μF.