Question

The current (in ampere) drawn from a $12 \,V$ supply by the infinite network shown in the following figure is

• A. $2.7$
• B. $3.3$
• C. $4.4$
• D. $5.2$

Answer 1

Answer: (C)

$4.4$

Answer 2

Let the equivalent resistance be $x$, circuit can be redrawn as
Then, $x=1+\frac{x}{1+x}+1$ or
$x^{2}-2 x-2=0$
$\therefore$ $x=\frac{2 \pm \sqrt{4+4 \times 1 \times 2}}{2 \times 1}$
or $x=\frac{2 \pm 2 \sqrt{3}}{2}$
or $x=(1 \pm \sqrt{3})=1+1.732$
$=2.7323$
Current drawn by the cell $I=\frac{V}{x}$
$=\frac{12}{2.732}=4.4 \,A$