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Q.
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
Current Electricity
Solution:
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.
$\therefore \frac{R R_{2}}{R+R_{2}}+R_{1}=R \Rightarrow 2 R+R+2=R^{2}+2 R$
$\Rightarrow R^{2}-R-2=0 \Rightarrow R=-1 \Omega$ or $2 \Omega$
Since $-1 \Omega$ does not have any sense, so neglecting it.
