Question

wire is 2.0 m long, 2 mm in diameter, and has a resistance of 20 ohms. Its resistivity (in Ohm - meter) will be​

Answer 1

Given :-

• length of wire , L = 2 m
• diameter of wire = 2 mm = 0.002 m

        radius of wire , r = 0.001 m

• Resistance of wire, R = 20 Ω

To find :-

• Resistivity of wire , ρ = ?

Formula required :-

• Relation b/w Length (L) , area of cross section (A) , resistance (R) and resistivity (ρ) of any conductor

     ρ = R × A / L

Solution :-

Radius of wire is 0.001 m

Calculating area of cross section (A) of wire

→   A = π r²

→   A = 22 / 7  × (0.001)²

→   A = 3.14 × 10⁻⁶  m²

Calculating resistivity of wire

Using formula

→   ρ = R × A / L

→   ρ = 20 × 3.14 × 10⁻⁶ / 2

→  ρ = 3.14 × 10⁻⁵    Ω m

Therefore,

Resistivity of wire will be 3.14 × 10⁻⁵  ohm - metre.