Question

Find the capacitance of the infinite ladder between point $X\text{and}Y.$

• A. $1\mu F$
• B. $2\mu F$
• C. $3\mu F$
• D. $4\mu F$

Answer 1

The correct option is B $2\mu F$

Let the equivalent capacitance between $X\text{and}Y\text{be}C.$
Since the ladder is infinite. Capacitance between $A\text{and}B$ (right part) will be $C.$ Because it is same as ladder between $X\text{and}Y.$
So, circuit can be shown as:
$C$ and $2\mu F$ are in series . so, their equivalent will be = $\frac{C\times 2}{C+2}=\frac{2C}{C+2}$

Both are in parallel, so equivalent capacitance between $X\text{and}Y,$
$C$= $1+\frac{2C}{C+2}$
$\Rightarrow C=1+\frac{2C}{C+2}$
$\Rightarrow C^2+2C=3C+2$
$\Rightarrow C^2-C-2=0$
$\Rightarrow (C-2)(C+1)=0$
$C=2\mu F$