A finite ladder circuit is constructed by connecting several sections of 6 µF, 8 µF capacitor combinations as shown in the figure. Circuit is terminated by a capacitor of capacitance C. Find the value of C, such that the equivalent capacitance of the ladder between the points A and B becomes independent of the number of sections in between?
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(12 µF)
Sol. If capacitance of C is equal to 12 µF. Then equivalent capacitance of the ladder between points A and B is becomes in dependent of the number of section in between points.
⇒ 
+ 8 = C
⇒ C 2 – 8C – 48 = 0
⇒ C = 12 µF
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