Question

Find the resistance (in mega of a wire of length 0.5 m, cross sectional area 1 cm2 and made of a material of resistivity 0.002 m.

Answer 1

Hi there.

Given conditions ⇒

Length of the wire (l) = 120 cm.
Diameter of the cross section of the wire wire = 0.04 mm.
∴ Radius of the cross section of the wire(r) = 0.02 mm.
   = 0.002 cm.

Area of the cross-section of the wire = πr²
= 22/7 × (0.002)²
= 22/7 × 0.000004
= 12.57 × 10⁻⁶ cm²

Resistance of the wire (R) = 25 Ω

Using the Formula,

 Specific Resistance (ρ) = Ra/l
∴ ρ = (25 × 12.57 × 10⁻⁶) ÷ 120
⇒ ρ = (314.25 × 10⁻⁶)/120
∴ ρ = 2.61875 × 10⁻⁶
∴ ρ = 2.62 × 10⁻⁶ Ω-cm.


Hence, the Specific Resistance of the Resistivity of the wire is 2.62 × 10⁻⁶ Ω-cm.