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: [2025]

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Solution

Q.
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: [2025]

1 16

2 14

3 10

4 12

Ans.
(4)

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

(As balanced wheat stone bridge is formed)

Now, Equivalent resistance between A and B can be written as

Clearly, $R_{1} = \frac{r}{6}$

So, $R_{A B} = R_{1} ∥ 2 R_{1} ∥ 2 R_{1}$

$\Rightarrow \frac{1}{R_{A B}} = \frac{1}{R_{1}} + \frac{1}{2 R_{1}} + \frac{1}{2 R_{1}} = \frac{4}{2 R_{1}} = \frac{2}{R_{1}}$

$\Rightarrow R_{A B} = \frac{R_{1}}{2} = \frac{r}{12}$

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