Question

calculate the resistance of 2.5 km long aluminium wire of radius 0.5mm resistivity of al is 2.7×10^-8....

pls help fast
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Answer 1

resistance of aluminium wire is 86Ω

it is given that length of aluminium wire, l = 2.5 km = 2500 m , radius of wire, r = 0.5mm = 5 × 10¯⁴ m and resistivity , ρ = 2.7 × 10^-8 Ωm

using formula, R = ρl/A

where A is cross sectional area of wire

so, A = πr² = π(5 × 10¯⁴)² = 25π × 10^-8 m²

now R = 2.7 × 10^-8 × 2500/(25π × 10^-8)

= 270/(π)

= 85.98 Ω ≈ 86 Ω

therefore, resistance of aluminium wire is 86 Ω

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Answer 2

Given:

Length of Aluminium wire is 2.5 km which radius is 0.5 mm. Resistivity of material is $\mathbf{2.7\times 10^{-8} \ \Omega -m}$.

To Find:

What is resistance of Aluminium wire?

Solution:

$\mathbf{\textrm{Resistivity of Aluminium material}(\rho )=2.7\times 10^{-8} \ \Omega -m}$

Length of wire (L) = 2.5 km = 2500 m

Radius of wire (r) = 0.5 mm = 0.0005 m

$\mathbf{\textrm{Value of pie}(\pi )=\dfrac{22}{7}}$

$\mathbf{\textrm{Cross-sectional area of wire}(A )=\pi \times r^{2}}$

Resistance of wire can be find out from below formula:

$\mathbf{R=\dfrac{\rho \times L}{A}}$

$\mathbf{R=\dfrac{2.7\times 10^{-8} \times 2500\times 7}{22\times 0.0005^{2}}}$

On simplify:

Resistance (R) = 85.9 Ω

Means resistance of wire is 85.9 Ω.