Resistance and Resistivity — Question 7

Question 7

A pair of lengths reveals contact resistance in a two-terminal measurement

Two uniform samples of the same material and area $A=1.00$ mm$^2$ have lengths 0.20 m and 0.60 m. Their measured resistances are .140 and .340 $\Omega$. Each measurement includes the same total contact resistance $R_c$.

1. Infer resistivity and total contact resistance.

2. Predict the two-terminal resistance of a 1.00 m sample and its ideal four-terminal value, excluding contacts.

Question 7 - Solution

A pair of lengths reveals contact resistance in a two-terminal measurement

(a) Method and calculation

$$R_m=\rho L/A+R_c,\quad\rho/A=\frac{.340-.140}{.60-.20}=.500\,\Omega/\mathrm m.$$$$\rho=5.00\times10^{-7}\,\Omega\,\mathrm m,\quad R_c=.140-.500(.20)=.0400\,\Omega.$$

(b) Interpretation and further calculation

$$R_{2t}(1.00)=.500+.0400=.540\,\Omega.$$$$R_{4t}=\rho L/A=.500\,\Omega.$$

Physical check

The intercept belongs to contacts; dividing a single measured resistance by length confounds two effects.