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Q.
In the infinite grid, if the value of $r=2(\sqrt{5}-1) \Omega$, find the equivalent resistance between the points $a$ and $c$.
Current Electricity
Solution:
Due to symmetry, the line of resistors passing through $b$ will be useless.
$r_{e q}=2 r+\frac{2 r r_{e q}}{2 r+r_{e q}}$
$ \Rightarrow r_{e q}=(1+\sqrt{5}) r$
$=(\sqrt{5+1}) 2(\sqrt{5}-1)=4 \,\Omega$
