Chapter 43, Problem 52P

A direct and relatively simple demonstration of zero DC resistance can be carried out using the four-point probe method. The probe shown in Figure P43.52 consists of a disk of YBa₂Cu₃O₇ (a high-T_c superconductor) to which four wires are attached. Current is maintained through the sample by applying a DC voltage between points a and b, and it is measured with a DC ammeter. The current can be varied with the variable resistance R. The potential difference ΔV_cd between c and d is measured with a digital voltmeter. When the probe is immersed in liquid nitrogen, the sample quickly cools to 77 K, below the critical temperature of the material, 92 K. The current remains approximately constant, but ΔV_cd drops abruptly to zero, (a) Explain this observation on the basis of what you know about superconductors. (b) The data in the accompanying table represent actual values of ΔV_cd for different values of I taken on the sample at room temperature in the senior author’s laboratory. A 6-V battery in series with a variable resistor R supplied the current. The values of R ranged from 10 Ω to 100 Ω. Make an I-ΔV plot of the data and determine whether the sample behaves in a linear manner, (c) From the data, obtain a value for the DC resistance of the sample at room temperature. (d) At room temperature, it was found that ΔV_cd = 2.234 mV for I = 100.3 mA, but after the sample was cooled to 77 K, ΔV_cd = 0 and I = 98.1 mA. What do you think might have caused the slight decrease in current?

Figure P43.52

Current Versus Potential Difference ΔV_cd Measured in a Bulk Ceramic Sample of YBa₂Cu₃O_7−δ at Room Temperature