Calculate the resistance per metre length of a wire of diameter 40 mm and specific resistance of 3.14 × 10^-4 Ω-m:

Concept:

The resistance offered by a wire of unit length and unit area of cross-section is called resistivity or specific resistance (r).​

Mathematically, this is defined as:

\(R = \frac{\rho l}{A}\)

R is the resistance of the wire

A is the area of cross-section of the wire

l is the length of the wire.

Calculation:

With d = 40 mm, l = 1 m and ρ = 3.14 × 10-4 Ω-m

so, r = 20 mm

\(A = \pi \times r^2 = 3.14 \times 20 \times 10 ^{-3}\)

\(R = \frac{\rho l}{A} = \frac{3.14 \times 10 ^{-4}}{3.14 \times 400 \times 10 ^{-6} } =\frac{1}{4 }~\Omega\)