Question

The ring shown in the figure has zero resistance. The equivalent resistance between the points $A$ and $B$ will be,

• A. $R$
• B. $2R$
• C. $3R$
• D. $4R$

Answer 1

Answer: (D)

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,
$\frac{1}{R^{\prime }}=\frac{1}{6R}+\frac{1}{6R}+\frac{1}{6R}\frac{1}{R^{\prime }}=\frac{3}{6R}\frac{1}{R^{\prime }}=\frac{1}{2R}{R}^{{}^{\prime }}=2R$
Now, $R^{{}^{\prime }}$ and $2R$ are in series, so their effective resistance will be,
$\Rightarrow R^{{}^{\prime }}+2R=2R+2R=4R$