In early 2016, I published a paper, “Spheres, rings and rods in electrofishing: Their effects on system resistance and electrical fields” (Transactions of the American Fisheries Society 145:239-248, 2016). My aim was to elucidate the relative importance of size and shape of common electrodes in determining electrical resistance of electrofishing systems and the intensity and size of the electrical fields they produce. In that paper, I did not cover the relationship of electrode surface area to resistance; instead, I am reporting that information in this blog.
The methods used in the designed experiment are detailed in my paper. However, a summary of the method is given here in order to provide the reader with context. Two sizes of spheres, 15 cm and 30 cm diameter (Figure 1), were selected to represent the minimum and maximum sizes used in electrofishing; these were also the diameters of rings used. Two lengths of rods, 48 and 96 cm, equal to the circumference of the rings, were also selected. Rings and rods were constructed with four diameters of stock diameter (material thickness): 3, 6, 10 and 13 mm (Figure 2). This resulted in 18 combinations of size, shape and stock diameter: two spheres, eight rings and eight rods. Two electrodes of identical size, shape and stock were suspended in a hatchery raceway [ambient conductivity (σa) 655-690 µS/cm, water temperature 15° C] and electrified with 120-V (RMS), 60-Hz, AC. Measurement of voltage (V, volts) and current (I, amperes) applied to each pair of identical electrodes yielded 18 values of total resistance (R, ohms) by Ohm’s Law (R = V/I), then divided by 2 to give the R of one electrode. Because electrode resistance is inversely proportional to water conductivity, R was standardized to 100 µS/cm (R100) so that the resistance of a single electrode could be re-calculated to any other conductivity.
Figure 1. The pairs of 15-cm and 30-cm sphere electrodes used in the study. [Click on image to enlarge it.]
Figure 2. The pairs of 15-cm and 30-cm rings, and 48-cm and 96-cm rods, used in the study. [Click on image to enlarge it.]
Given that surface area of a solid geometric form increases as the square of its linear dimension, and that resistance decreases with surface area, I plotted resistance (R100) of each electrode as a function of the log of surface area (semi-log plot, Figure 3). The points formed a linear function with a correlation coefficient of 0.77 meaning that surface area accounted for 59% of the variability between resistance and surface area. I concluded that surface area determined about three-fifths of resulting electrode resistance. The remaining two-fifths was due to the size, shape, stock and a small amount of measurement error. Data points for the smaller rings and rods fell above the regression line, indicating above-average resistance; those for the larger electrodes were below average indicating below-average resistance. Resistance of both spheres was above average. Stock diameter had a smaller effect on resistance than overall electrode size but did cause a regular increase in resistance as it increased from 3 mm to 13 mm within a size-shape set (e.g., 15-cm rings). Resistance of rings and rods with equal surface area depended on size and stock diameter. For example, the smaller ring (15 cm) and rod (48 cm) with 6-mm stock had a surface area (about 100 cm2) equal to the larger ring (30 cm) and rod (96 cm) with 3-mm stock, but had higher resistance (Figure 3). I interpret this to mean that the larger electrodes have more circumference or length to radiate a field and reduce resistance.
Figure 3. Single-electrode resistance (R) plotted as a function of electrode surface area (SA, log scale) for 18 sizes and shapes of electrodes. The linear regression results and line (dashed) are embedded in the plot. The numbers by data points are stock diameter (mm). [Click on image to enlarge it.]
Although surface area is somewhat more important than the size-shape effect in determining electrode resistance, the effect of electrode size and shape cannot be ignored. Knowledge of electrical resistance is important if one wants to know the power limitations of an electrofishing system.