Question

The resistivity of copper is 1.7×10^-8ohm metre.(a) what length of copper wire of diameter 0.1 mm will have a resistance of 238 Ohm?

Answer 1

Answer:i'm not sure

resistance=resistivity*length of the wire/area

so length=resistance*area/resistivity

=238*3.14*(5*10^-5)^2/1.7*10^-8

=110m

Explanation:

Answer 2

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Resistivity of copper ${\sf (\rho)=1.7×10^{-8}ohm.m}$
• Diameter of wire (d) = 0.1mm or ${\sf 10^{-4}m}$
• Resistance of wire (R) = 238Ω

$\color{darkblue}\underline{\underline{\sf To\:Find-}}$

• Lenght of copper wire ${\sf (\ell)}$

$\color{red}\blacksquare\boxed{\sf R=\rho\dfrac{\ell}{A}}$

$\implies{\sf 238=1.7×10^{-8}×\dfrac{\ell}{πr^2}}$

$\implies{\sf 238=1.7×10^{-8}×\dfrac{\ell}{3.14×\left(\dfrac{10^{-4}}{2}\right)^2}}$

$\implies{\sf 238=1.7×10^{-8}×\dfrac{\ell×4}{3.14×10^{-8}}}$

$\implies{\sf \ell =\dfrac{238×3.14×10^{-8}}{1.7×10^{-8}×4}}$

$\color{red}\implies{\sf \ell = 109.8m}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Lenght of copper wire is $\color{red}{\sf 109.8m}$.