Question

Calculate the resistance of 2 km long copper wire of radius 2 mm. (Resistivity of copper = 1.72 x 1 0-8)​

Answer 1

Given,

radius of wire (r) = 2 mm = 2 × 10-³ m

Length of wire (L) = 2Km = 2 × 10³ m

resistivity of copper wire(P) = 1.72 × 10^-8 Ohm. m

use formula ,

R = pL/A

where , R is resistance

p is resistivity of wire and A is cross section area of wire .

A = πr² = 3.14 × (2 × 10-³)²

= 3.14 × 4 × 10^-6 m²

= 12.56 × 10^-6 m²

R = 1.72 × 10^-8 × 2 × 10³/12.56 × 10^-6

= { 1.72× 2 /12.56} × 10^(-8+3 +6)

= 1.72 × 2 × 10/12.56

= 34.4/12.56

=2.7388 Ohm

hence, resistance of copper wire = 2.74 Ohm

Answer 2

• Length of copper wire=2 km = 2000 m
• Radius of copper wire=2 mm = 2×
• Resistivity of copper=1.72x10⁻⁸
• Resistance=(Resistivity of copper × Length)/(Area)
• Resistance=(Resistivity of copper × Length)/(πr²)
• Resistance=[1.72×10⁻⁸*2000]/[22/7×(2×10⁻³)²]
• Resistance=(0.0000344)/(22/7)(0.000004)
• Resistance=0.0000344/0.00001256
• Resistance=2.73 ohm

HOPE this helps ☺️