Question

Calculate the resistance of 2 km long copper wire of radius 2 mm

Answer 1

Length of copper wire=2 km = 2000 m

Radius of copper wire=2 mm = 2×$10^{-3}$

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 

Answer 2

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