Question

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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Answer 1

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 !

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

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

Answer 2

$\mathcal{\huge{\underline{\underline{\red{Question:-}}}}}$

✒ 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.

$\mathfrak{\huge{\underline{\underline{\green{Answer:-}}}}}$

⭐ The resistivity of wire is 86.6Ω.

$\mathbb{\huge{\underline{\underline{\orange{SOLUTION:-}}}}}$

GᏆᐯᗴᑎ :-

Length l = 1.0 km = 1000 m

Diameter d = 0.50 mm

тo find :-

☑ The resistivity of copper wire.

ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ :-

We, know that

r = d / 2. {here d is 0.50mm}

r =

$\dfrac{0.50 }{2}$

r = 0.25 mm

r = 0.00025mm

We know resisivity,

ϱ = 1.7 × 10^-8Ωm

Resistance R = ϱ × length/area

=> ϱ × l /a

=> R = 1.7 × 10^-8 × 1000/πr²

$=> \dfrac{1.7 \times {10}^{ - 5} }{3.14 \times 0.00025 \times 0.00025}$

$= > r = \dfrac{1.7 \times {10}^{3} }{3.14 \times 6.25}$

$= > r = \cancel{\dfrac{1700}{19.625}}$

=> R = 86.6Ω

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