JEE Mains · Physics · STD 12 - 3. current electricity
Equivalent resistance between the adjacent corners of a regular \(n\)-sided polygon of uniform wire of resistance \(R\) would be:
- A \(\frac{(n-1) R}{n^2}\)
- B \(\frac{(n-1) R}{(2 n-1)}\)
- C \(\frac{n^2 R}{n-1}\)
- D \(\frac{(n-1) R}{n}\)
Answer & Solution
Correct Answer
(A) \(\frac{(n-1) R}{n^2}\)
Step-by-step Solution
Detailed explanation
Suppose resistance of each arm is \(r\), then \(r = R / n\) \(R _{ eq(AB )}=\frac{ R _1 R_2}{R_1+R_2}\) \(\frac{ r ( n -1) r }{ r +( n -1) r }\) \(=\frac{ r ( n -1) r }{ nr }\) \(=\frac{ n -1}{ n } r\) \(=\frac{( n -1) R }{ n ^2}\)
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