A wire of resistance $R$ is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points $A$ and $B$ is $R / n$. The value of $n$ is :

• A

  16
• B

  14
• C

  10
• Correct answer
  D

  12

Solution

As $r=\frac{R}{6}$

(As balanced wheat stone bridge is formed) Now, Equivalent resistance between A and B can be written as
$\frac{1}{\mathrm{R}_{\mathrm{AB}}}=\frac{1}{2 \mathrm{r}}+\frac{1}{2 \mathrm{r}}+\frac{1}{\mathrm{r}}=\frac{2}{\mathrm{r}}$
$\mathrm{R}_{\mathrm{AB}}=\frac{\mathrm{R}}{12}$

Hence, the correct answer is option: 'D'.