A uniform metal wire of length l has 10 Ω resistance. Now this wire is stretched to a length 2l and then bent to form a perfect circle.

Question

A uniform metal wire of length \(l\) has \( 10 \ \Omega\) resistance. Now this wire is stretched to a length \(2 l\) and then bent to form a perfect circle. The equivalent resistance across any arbitrary diameter of that circle is

(1) \(10 \ \Omega\)

(2) \(5 \ \Omega\)

(3) \(40 \ \Omega\)

(4) \(20 \ \Omega\)

Answer 1

Correct option is : (1) \(10 \ \Omega\)

\(R_{0}=10 \ \Omega\)

After stretching its length up to \(2l\)

\(\begin{aligned} R_{1} & =n^{2} R_{0}\end{aligned}\)

\(\begin{aligned} =4 R_{0} \end{aligned}\)

\(\begin{aligned} =40 \ \Omega\end{aligned}\) 

\(R_{A B}=\frac{20 \times 20}{20+20}=10 \ \Omega\)