Question

An infinite sequence of resistance is shown in the figure. The resultant resistance between A and B will be, when $R_{1} = 1ohm$ and $R_{2} = 2ohm$

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

Answer 1

Answer: (C)

$2\Omega$

Answer 2

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 $R = 2ohm$