Question

The resistance between the terminal points A and B of the given infinitely long circuit will be

• A. $(\sqrt{3}-1)$
• B. $(1+\sqrt{3})$
• C. $(2+\sqrt{3})$
• D. $(1-\sqrt{3})$

Answer 1

The correct option is B $(1+\sqrt{3})$


Let the equivalent resistance between A and B be R then since it is extending to infinity, equivalent resistance between C and D is also R ( The circuit appears the same when seen from C-D and when seen from A-B due to the infinite number of similar branches).


Equivalent resistance across AB will be

$\therefore R_{AB}=1+\frac{R}{R+1}+1=R$

$\frac{R+2(R+1)}{R+1}=R$

$2+3R=R^2+R$

$R^2-2R-2=0$

$R=\frac{2\pm \sqrt{4+8}}{2}$

$R=\sqrt{3}+1,1-\sqrt{3}$

(Negative value of resistance is not possible)

Thus, equivalent resistance between A and B is $(\sqrt{3}+1)\Omega$

Hence, option (c) is correct.