The Electrical Properties of Solids — Question 2

Question 2

A four-terminal measurement removes contact voltage drops

A specimen carries $I=20.0\,\mathrm{mA}$. Its end-to-end voltage is .180 V, while noninvasive voltage probes separated by $L_v=4.00\,\mathrm{mm}$ read .0800 V. The uniform specimen length is 6.00 mm and its area is $.100\,\mathrm{mm^2}$.

1. Infer the bulk resistivity from the inner probes.

2. Find the combined end-contact resistance.

Question 2 - Solution

A four-terminal measurement removes contact voltage drops

(a) Method and calculation

$$R_v=V_v/I=.0800/.0200=4.00\,\Omega.$$$$\boxed{\rho=R_vA/L_v=1.00\times10^{-4}\,\Omega\,\mathrm m}.$$

(b) Interpretation and further calculation

$$R_{\mathrm{bulk}}=\rho L/A=6.00\,\Omega,\quad R_{\mathrm{two}}=.180/.0200=9.00\,\Omega.$$$$\boxed{R_{c1}+R_{c2}=R_{\mathrm{two}}-R_{\mathrm{bulk}}=3.00\,\Omega}.$$

Physical check

Negligible probe current prevents significant voltage loss in the voltage leads. The bulk scaling requires a uniform cross section and material between all probes.