8 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



trodes A and B, as shown in Fig. (1-1)1, can be determined from the 

 measurement of its resistance R. 



R = 



t 



a 



(1) 



where a is the cross-sectional area of the prism and of the electrodes. 

 The method requires the knowledge of the resistivity of the test 

 object and is applicable for the measurement of isotropic and homo- 

 geneous test objects having a resistivity less 

 than of the order of 10 6 ohm-cm. If the re- 

 sistivity of the test object is much higher, 

 the resistance between the electrodes is fre- 

 quently influenced by surface conduction. 



If the cross section of the test object 

 changes abruptly, Fig. (1-1)2, or if the elec- 

 trodes are smaller than the test object, Fig. 

 (1-1)3, the current flow pattern will be non- 

 uniform, and the resistance between the contacts will be larger than 

 that expressed by Eq. (1). The additional resistance ("spreading 

 resistance") can be computed in simple cases. 1 



Fig. (1-1)1. Resistive 



thickness gauge, principle. 



Fig. (1-1)2. Non- 

 uniform current flow 

 pattern caused by 

 abrupt change of the 

 cross section of the 

 test object. 



Fig. (1-1)3. Non- 

 uniform current flow 

 pattern caused by 

 electrodes that are 

 smaller than the test 

 object. 



Surface conduction effects can be eliminated by means of the 

 guard-ring arrangement illustrated in Fig. (1-1)4. This consists of a 

 circular electrode A (guarded electrode: radius r x ) on one side of the 

 sample, concentrically surrounded by an annular electrode B (guard 

 electrode: inner radius r 2 , outer r 3 ). Thegapr 2 — ?\ should be small. 

 On the other side of the sample is a circular electrode C (unguarded 

 electrode: radius r 3 ). The guard-ring electrode B prevents the flow 



1 W. Schrader, Wied. Ann., 44, 222 (1891), and W. B. Kouwenhoven and 

 W. T. Sackett, Jr., Welding Research Sup pi., 14, 466s (1949). 



