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

$\rho = 1.72 \times {10}^{-8} \\ r = 2mm \; or \; 2 \times {10}^{-3}\: m \\ l = 2km \; or\; 2 \times {10}^{3}\: m \\ We \: know \: that, \\ \qquad \qquad \qquad \boxed{R = \frac{\rho l}{A}} \\ \\ \Rightarrow \qquad R = \frac{1.72 \times {10}^{-8} \times 2 \times {10}^{3}}{\pi {r}^{2}} \\ \\ \Rightarrow \qquad R = \frac{3.44 \times {10}^{-5}}{12.56 \times {10}^{-6}} \\ \\ \Rightarrow \qquad R = 0.273 \times {10}^{(-5+6)} \\ \\ \mathfrak{Answer \: :} \quad \mathtt{\red{2.73 \; \Omega}}$

Answer 2

GIVEN THAT

• Length of copper wire = 2 km = 2000 m
• Radius of copper wire = 2 mm = 2 × 10-³ m
• Resistivity of copper = 1.72 x 10⁻⁸

CALCULATION OF RESISTANCE

• (Resistivity of copper × Length)/(Area)
• (Resistivity of copper × Length)/(πr²)
• [1.72×10⁻⁸*2000]/[22/7×(2×10⁻³)²]
• (0.0000344)/(22/7)(0.000004)
• 0.0000344/0.00001256
• 2.73 ohm