There are 16 nodes on a circle. Each node is connected with every other node by a resistance R. Equivalent resistance between any two consecutive nodes is R/n. Find n.

Question

There are 16 nodes on a circle. Each node is connected with every other node by a resistance R. Equivalent resistance between any two consecutive nodes is $\frac{R}{n}$ . Find $n$ .

Smart Achievers · Accepted Answer

(8)

All other 14 points are at same potential

$\frac{1}{R_{eq}} = \underset{14 terms}{\underset{⏟}{\frac{1}{2 R} + \frac{1}{2 R} + \dots + \frac{1}{R}}} \Rightarrow R_{eq} = \frac{R}{8}$

Solution

Q.
There are 16 nodes on a circle. Each node is connected with every other node by a resistance R. Equivalent resistance between any two consecutive nodes is $\frac{R}{n}$ . Find $n$ .

Ans.
(8)

All other 14 points are at same potential

$\frac{1}{R_{eq}} = \underset{14 terms}{\underset{⏟}{\frac{1}{2 R} + \frac{1}{2 R} + \dots + \frac{1}{R}}} \Rightarrow R_{eq} = \frac{R}{8}$

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Solution

Q. There are 16 nodes on a circle. Each node is connected with every other node by a resistance R. Equivalent resistance between any two consecutive nodes is Rn. Find n.

Ans. (8) All other 14 points are at same potential 1Req=12R+12R+⋯+1R⏟14 terms⇒Req=R8

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Q.
There are 16 nodes on a circle. Each node is connected with every other node by a resistance R. Equivalent resistance between any two consecutive nodes is $\frac{R}{n}$ . Find $n$ .

Ans.
(8)

All other 14 points are at same potential

$\frac{1}{R_{eq}} = \underset{14 terms}{\underset{⏟}{\frac{1}{2 R} + \frac{1}{2 R} + \dots + \frac{1}{R}}} \Rightarrow R_{eq} = \frac{R}{8}$