A thin uniform wire of length 25 m and area of cross-section 5mm2 has resistivity 2 × 10^–6 Ω – m. If the wire is bent to form a circle

Question

A thin uniform wire of length 25 m and area of cross-section \(5mm^2\) has resistivity \(2 \times 10^{-6} -m\). If the wire is bent to form a circle, the resistance across diametrically opposite points is

(1) \(5 \ \Omega\)

(2) \(2.5 \ \Omega\)

(3) \(10 \ \Omega\)

(4) \(12.5 \ \Omega\)

Answer 1

Correct option is:  (2) \(2.5 \ \Omega\) 

\(R = \rho \frac{l}{A} = \frac{ (2 \times 10^{-6} \Omega m) (25\ m) }{5 \times 10^{-6} m^2}\)

\(R = 10 \ \Omega\)

Resistance across diametrically is \(\frac{R}{4} = 2.5 \ \Omega\)