Question

An infinite sequences of resistances is shown in the figure. The resultant resistance between A and B will be when $R_1=1\Omega$ and $R_2=22\Omega$

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

Answer 1

Answer: (C)

In case of infinite sequence of resistances if we add another branch, effective resistance of circuit .would be same. Let effective resistance be $R$.

$\therefore \frac{R{R}_2}{R+R_2}+R_1=R$
$\Rightarrow R{R}_2+R{R}_1+R_1{R}_2=R^2+R{R}_2$
$\therefore R^2-R_1{R}_2-R{R}_1=0$
$\therefore R^2-2-2R=0$
$\therefore R^2-2R-2=0$
$R=-1,R=2$
Hence, $R=2\Omega$