Question

An infinite sequence of resistance is shown in the figure. The resultant resistance between $A$ and $B$ will be, when $R_1=1\Omega$ and $R_2=2\Omega$

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

Answer 1

Answer: (C)

$2\Omega$

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.

$\therefore \frac{R{R}_2}{R+R_2}+R_1=R\Rightarrow 2R+R+2=R^2+2R$

$R^2-R-2=0\Rightarrow R=-1$ or $R=2$