Question

A finite ladder is constructed by connecting several sections of $2\mu F,4\mu F$ capacitor combinations as shown in the 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 point A and B becomes independent of the number of sections in between?

• A. $4\mu F$
• B. $2\mu F$
• C. $18\mu F$
• D. $6\mu F$

Answer 1

The correct option is A $4\mu F$

From left hand side, the effective capacitance between the terminals is C and the ladder is infinite.
The effective network is shown in figure. Now, the capacitance between A and B is
$C=\frac{4C}{C+4}+2=\frac{6C+8}{C+4}$ or $C^2+4C-6C-8=0$
solving $C=4\mu F$.