Question

A wire of length 2.0 m . has a resistance of 30 Ω.if its diameter is 0.8mm,calculate its resistivity(π=3.14).

Answer 1

Answer: 7.536 × $10^{-4}$ Ω-cm.

Explanation:

Length of the wire (l) = 200 cm.

Diameter of the cross section of the wire wire = 0.8 mm.

∴ Radius of the cross section of the wire(r) = 0.4 mm.

  = 0.04 cm.

Area of the cross-section of the wire = πr²

= 3.14 × (0.04)²

= 3.14 × 1.6 x $10^{-3}$

= 5.024 × $10^{-3}$ cm²

Resistance of the wire (R) = 30 Ω

Using the Formula,

 Specific Resistance (ρ) = Ra/l

∴ ρ = (30 × 5.024 × $10^{-3}$) ÷ 200

⇒ ρ = (150.72 × $10^{-3}$) / 200

∴ ρ = 7.536 × $10^{-4}$

∴ ρ = 7.536 × $10^{-4}$ Ω-cm.

Hence, the Specific Resistance of the Resistivity of the wire is 7.536 × $10^{-4}$ Ω-cm.