Answer to Question #302752 in Electric Circuits for ilovephysicssolman

Question

A uniform piece of wire has a diameter of 0.30 mm and length 2.25 m has a resistance of 28 Ω. Find the resistivity of the wire. 

Answer 1

The resistivity of a conductor is given by

$R=\rho \dfrac{L}{A}$

Where 

$A$ is the Area

$\rho$ is the Resistivity

$L$ the length

the radius is 

$r=\dfrac{d}{2} \\ r=\dfrac{0.30mm}{2}\\ r=0.15mm$

Converting from millimeters to meters

$r=0.15mm\times\dfrac{1m}{1000mm}=0.00015m$

The wire area is

$A=\pi r^{2}$

Evaluatin numerically

$A=\pi (0.00015m)^{2}$

$A=7.07\times10^{-8}m^{2}$

Getting the expression for the resistivity

$R=\rho \dfrac{L}{A}$

$\dfrac{A}{L}R=\rho$

$\rho=\dfrac{A}{L}R$

Evaluating numerically

$\rho=\dfrac{7.07\times10^{-8}m^{2}}{2.25m}\times 28 \Omega$

The resistivity is

$\rho=8.80\times10^{-7}\Omega m$