Question

determine the resistance of a copper wire of length 500 m and its diameter is 2mm. (Given = resistivity of copper = 1.7x10^-8 ohm metre)​

Answer 1

Answer: R = 2.7 × 10² Ω.

Explanation:

Given, d = 0.2 mm => r = 0.1 mm

So, area = πr² = π/100 mm²

We know,

R = ρL/A

Now,

R = (1.7 × 10^-8 Ω-m)(500 m)/(π/100 mm²)

=> R = (1.7 × 10^-8 Ω-m)(500 m)/(π × 10^-2 mm²)

=> R = (1.7 × 10^-8 Ω-m)(500 m)/[π × 10^-2 × (10^-3)² m²]

=> R = (1.7 × 10^-8 Ω-m)(500 m)/[π × 10^-8 m²]

=> R = 1.7 × 5 × 10^(- 8 + 2 + 8)/π Ω

=> R = 1.7 × 5 × 10^2/π Ω

=> R = 8.5 × 10²/π Ω or 2.7 × 10² Ω approximately.

More:

• If length of a wire is increased from L1 to L2, then R′ = (L1/L2)R.
• And if area is changed from A1 to A2, then R′ = (A2/A1)R
• In a circular wire, in radius is changed from r1 to r2, then R′ = (r1/r2)⁴R.
• Resistance depends on length of conductor and area of it and not resistivity.
• Magnitude of resistance = magnitude of specific resistance if magnitude of length and area is one or equal.