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Q.
The ring shown in the figure has zero resistance. The equivalent resistance between the points $A$ and $B$ will be,
NTA AbhyasNTA Abhyas 2022
Solution:
Clearly, all the resistances of $6R$ are in parallel and their combination is in series with $2R$ .
Hence, the circuit will look as given:
The parallel equivalent resistance of all $6R$ units is,
$\frac{1}{R '}=\frac{1}{6 R}+\frac{1}{6 R}+\frac{1}{6 R}\frac{1}{R '}=\frac{3}{6 R}\frac{1}{R '}=\frac{1}{2 R}R^{'}=2R$
Now, $R^{'}$ and $2R$ are in series, so their effective resistance will be,
$\Rightarrow R^{'}+2R=2R+2R=4R$
