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 $R$.

$\therefore \frac{ RR _{2}}{ R + R _{2}}+ R _{1}= R$
$\Rightarrow RR _{2}+ RR _{1}+ R _{1} R _{2}= R ^{2}+ RR _{2}$
$\therefore R ^{2}- R _{1} R _{2}- RR _{1}=0$
$\therefore R ^{2}-2-2 R =0$
$\therefore R ^{2}-2 R -2=0$
$\quad R =-1, R =2$
Hence, $R =2 \Omega$