Question

An infinite ladder of capacitors, each $1\mu F$, is made as shown in figure. The capacitance between A and B (in $\mu F$) is

• A. $1$
• B. $1.6$
• C. $3.4$
• D. $0$

Answer 1

The correct option is B $1.6$

From the figure,

$\frac{X}{X+1}+1=X$

$X+X+1=X(X+1)$

$2X+1=X^2+X$

$X+1=X^2$

$X^2-X-1=0$

$X=\frac{1+\sqrt{5}}{2}$

$X=\frac{1+2.236}{2}=1.6\mu F$