What length of copper wire of specific resistance \(1.7\times {{10}^{-8}}\) ohm m and radius 1 mm is required so that its resistance is 1 ohm.
What length of copper wire of specific resistance \(1.7\times {{10}^{-8}}\) ohm m and radius 1 mm is required so that its resistance is 1 ohm.

According to the question,

R = 1 ohm

Specific resistance = 1.7× 10-8 ohm m

r =  10-3 m

l =?

R = ρ 1 / A

l = RA / ρ

l = Rπr2 / ρ

l = (1 × π × 10-6) / (1.7 × 10-8)

l = (1 × 3.14 × 10-6) / (1.7 × 10-8)

l = 1.847 × 102 m

Therefore,

l = 184.7 m