Q. An infinite sequence of resistances is shown in the figure. The resultant resistance between $A$ and $B$ will be, when $R_{1} = 1\ ohm$ and $R_{2} = 2\ ohm$
A) Infinity
B) $1\ \Omega$
C) $2\ \Omega$
D) $1.5\ \Omega$
Explanation
(c) Let the resultant resistance be $R.$ If we add one more branch, then the resultant resistance would be the same because this is an infinite sequence
$\therefore\frac{RR_{2}}{R + R_{2}} + R_{1} = R \Rightarrow 2R + R + 2 = R^{2} + 2R$
$\Rightarrow R^{2} - R - 2 = 0 \Rightarrow R = - 1$ or $R = 2ohm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.