Question

calculate the resistance of 2km long wire of radius 2mm

Answer 1

Answer:

Explanation:

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

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Answer 2

Given:

The length of the wire is $l = 2 \times 10^3m.$

The radius of the wire is $r = 2 \times 10^{-3}m.$

To Find:

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

Explanation:

We know the relation between resistance and resistivity can be formulated as:

$R= \frac{ \rho \times l}{A}$

Where ρ is the resistivity of the material, l is the length of the material, and A is the area of the same material.

It is known that resistivity of copper is $\rho =1.72 \times 10^{-8} \Omega m.$

$R= \frac{ \rho \times l}{\Pi \times r^{2} }\\R= \frac{1.72 \times 10^{-8} \times 2 \times 10^{3}}{ \Pi \times (2 \times 10^{-3})^{2} } \\R=2.73 \Omega$

Hence, the resistance is calculated to be $2.73 \Omega.$