Question

An infinite sequence of resistance is shown in the figu The resultant resistance between $A$ and $B$, when $R_1=$ ohm and $R_2=2$ ohm, will be

• A. Infinity
• B. $1\Omega$
• C. $2\Omega$
• D. $1.5\Omega$

Answer 1

Answer: (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.

$\therefore \frac{R{R}_2}{R+R_2}+R_1=R\Rightarrow 2R+R+2=R^2+2R$
$\Rightarrow R^2-R-2=0\Rightarrow R=-1\Omega$ or $2\Omega$
Since $-1\Omega$ does not have any sense, so neglecting it.