Question

# A wire of diameter 0.750 mm and length 45.0 m has a measured resistance of 1.20...

A wire of diameter 0.750 mm and length 45.0 m has a measured resistance of 1.20 Ω. What is the resistivity of the wire?

The resistance of a wire is defined as
$R=\rho \frac{L}{A}$
where, L is the length of the wire. A is the cross section of the wire. $\rho$ is the resistivity of the wire. So, we get
$\rho=\frac{RA}{L}$
And as we know for a circular section of diameter d, the cross sectional area is given by
$A=\frac{\pi d^2}{4}$
And so, the resistivity is
$\rho=\frac{\pi d^2 R}{4L}$
And given the values,
$d=0.75\times 10^{-3}~m$
$L=45.0~m$
$R=1.20~\Omega$

We get the resistivity as
$\rho=\frac{\pi \times (0.75\times 10^{-3})^2\times 1.20}{4\times 45}$
$\Rightarrow \rho=1.178\times 10^{-8}~\Omega .m$

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