Calculate the resistance of a copper wire 1.0 km long and 0.50 mm diameter if th...

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June 2021 1 18 Report

Calculate the resistance of a copper wire 1.0 km long and 0.50 mm diameter if the resistivity of the copper is 1.7×10‐⁸ ohm meter..solve and explain the calculation also

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Brâiñlynêha

Verified answer

Given :-

• Length of wire = 1km = 1000m

• Diameter= 0.5mm or 0.0005m

$\implies\sf 5\times 10^{-4}m\\ \\ \implies\sf Radius= \dfrac{\cancel5\times 10^{-4}}{\cancel2}\\ \\ \implies\sf Radius = 2.5\times 10^{-4}m$

• Resistivity of wire = $\sf 1.7\times 10^{-8}\Omega$

To find :-

The Resistance of copper wire

According to the formula

$\boxed{\sf \ R= \rho \dfrac{l}{A}}$

Where ,

R= Resistance

$\sf \rho$ = Resistivity

l= Length of wire

A = Area of cross section

Now find the value of A (Area of cross section)

$\sf \ Area \ of \ cross \ section= \pi r^2\\ \\ \longrightarrow\sf Area = 3.14\times (2.5\times 10^{-4})^2\\ \\ \longrightarrow\sf Area = 3.14\times 6.25\times 10^{-8}m\\ \\ \longrightarrow\sf Area = 19.625\times 10^{-8}m^2$

Let's find the Resistance !

$\longrightarrow\sf R= \dfrac{\rho l}{A}\\ \\ \longrightarrow\sf R= \dfrac{1.7\times 10^{-8}\times 1000}{19.625\times 10^{-8}}\\ \\ \longrightarrow\sf R= \dfrac{1.7\times 10^{-8}\times 10^{3}\times 10^8}{19.625}\\ \\ \longrightarrow\sf R= \dfrac{1.7\times 10^{(-8+11)}}{19.625}\\ \\ \longrightarrow\sf R= \dfrac{1.7\times 10^{3}}{19.625}\\ \\ \longrightarrow\sf R= \cancel{\dfrac{1700}{19.625}}\\ \\ \longrightarrow\sf R= 86.6 \Omega$

$\underbrace{\sf\ \ Resistance= 86.6 \Omega}$

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