Question

Your plot your results as I versus 1/d and find that the data lie close to a straight line that has slope 600 A⋅m. What is the resistivity of the material of which the wire is made? Express your answer in ohm-meters.

Answer 1

Answer:

$\rho=4.02\times 10^{-8}\ \Omega-m$

Explanation:

Let us assume that the radius of the wire, r = 0.8 mm = 0.0008 m

EMF of the battery, V = 12 V

Slope of I versus 1/d, m = 600 A-m

The resistance of any material is given by :

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

d is the length of wire

Since, $I=\dfrac{V}{R}$

$I=\dfrac{VA}{\rho d}$

$I=\dfrac{VA}{\rho}.(\dfrac{1}{d})$

$y=slope\times x$

$\dfrac{VA}{\rho}=600$

$\rho=\dfrac{VA}{600}$

$\rho=\dfrac{12\times \pi \times (0.0008)^2}{600}$

$\rho=4.02\times 10^{-8}\ \Omega-m$

So, the resistivity of the material of which the wire is made is $4.02\times 10^{-8}\ \Omega-m$.