question_answer

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) \[5.2\]

Correct Answer: C

Solution :

 Let the equivalent resistance be\[x\], circuit can be redrawn as Then, \[x=1+\frac{x}{1+x}+1\] or \[{{x}^{2}}-2x-2=0\] \[\therefore \] \[x=\frac{2\pm \sqrt{4+4\times 1\times 2}}{2\times 1}\] 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 \[I=\frac{V}{x}=\frac{12}{2.732}=4.4\,A\]