The Electrical Properties of Solids — Question 1

Question 1

Separating intrinsic resistivity from specimen geometry

A uniform bar has length $L=12.0\,\mathrm{mm}$, cross section $A=.300\,\mathrm{mm^2}$ and resistance $R=8.00\,\Omega$. Contacts are ideal and the response is ohmic.

1. Find resistivity and conductivity.

2. Find the resistance of a same-material bar twice as long with twice the diameter.

Question 1 - Solution

Separating intrinsic resistivity from specimen geometry

(a) Method and calculation

$$R=\rho L/A\Rightarrow\boxed{\rho=RA/L=2.00\times10^{-4}\,\Omega\,\mathrm m}.$$$$\boxed{\sigma=1/\rho=5.00\times10^3\,\mathrm{S/m}}.$$

(b) Interpretation and further calculation

$$L\prime=2L,\quad d\prime=2d\Rightarrow A\prime=4A.$$$$\boxed{R\prime/R=(L\prime/L)(A/A\prime)=1/2,\quad R\prime=4.00\,\Omega}.$$

Physical check

Resistivity is a material parameter at the specified conditions; resistance also depends on shape. Doubling a diameter quadruples area.