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8 BIoLoGICAL REPORT 11 <br />concentric ring act as a group of parallel resistors, <br />and these successive groups become effectively <br />wired in series as the electrical charge moves ra- <br />dially from one concentric ring to the next. There- <br />fore, the circuit diagram for this axial segment of <br />the cylindrical electrode can be reduced to a series <br />circuit (Fig. 7), where Rl, R2, RQ...RN represent the <br />equivalent resistances of the first, second, <br />third ...Nth group of concentric (parallel) resistors. <br />As the radii of the concentric rings increase, the <br />number of cubes per concentric ring also in- <br />creases. In this manner, the effective resistance <br />for each consecutive ring decreases as more par- <br />allel resistors are added; that is, Rl > % > Ra >...> <br />RN. This phenomenon of decreasing resistance <br />implies that the incremental voltages generated <br />across the successive concentric rings must de- <br />crease in some nonlinear manner as the distance <br />away from the surface of the electrode is in- <br />creased. Furthermore, it is the shape and size of <br />an electrode that determines how the cubes in- <br />itially become "inter-wired" into the water to gen- <br />erate a unique electric field pattern. <br />This conceptualization of concentric rings sur- <br />rounding the cylindrical electrode provides a men- <br />tal image of what is meant by the term voltage <br />gradient; voltage gradient is the in-water voltage <br />that exists across an individual concentric ring. <br />The first concentric ring always has the greatest <br />incremental resistance (RI) and must, therefore, <br />exhibit the largest voltage gradient. When com- <br />paring electrodes of different size, it is helpful to <br />consider that larger-surfaced electrodes expose <br />more metal to the water, and this exposure de- <br />creases the initial resistance value of R,. Any <br />reduction in the initial resistance means that less <br />voltage is dissipated near the electrode. It be- <br />comes a matter of algebra. If voltage is not dissi- <br />pated close to an electrode, it becomes available at <br />distances away from the electrode. Thus, larger- <br />surfaced electrodes inherently extend their elec- <br />tric fields a greater distance by reducing the volt- <br />age gradient near the electrodes, and smaller <br />R1 R2 R3 RN <br />Metal <br />Cylinder' ----W---- <br />Fig. 7. Equivalent series circuit for a cylindrical <br />electrode. <br />electrodes collapse their fields by increasing the <br />voltage gradients near the electrodes. The above <br />discussion is based on a circular geometry, but the <br />reader can readily expand the basic tenets to any <br />electrode configuration. With these mental per- <br />ceptions, equipment operators can develop intui- <br />tive guidelines for modifying electrodes to particu- <br />lar field applications. <br />In-water Voltage Measurement <br />Techniques <br />I present two empirical methods for determin- <br />ing the distribution of voltages in water. One <br />method measures the in-water voltage as a func- <br />tion of distance, and the second method measures <br />the incremental voltages (voltage gradients) at <br />discrete locations in a volume of water. The first <br />method develops a voltage versus distance profile <br />with the same instrumentation described for <br />measuring the resistance of electrodes. The second <br />method requires a special probe that connects to a <br />voltmeter or cathode ray oscilloscope and directly <br />measures voltage gradient. Voltage gradient can <br />also be converted to a power density measurement <br />with the equation <br />D = cE2 (11) <br />where, <br />D = power density (NW/cm), <br />c = conductivity of the water (µS/cm), and <br />E = voltage gradient (V/cm; Kolz 1989). <br />At present, there are no instruments marketed <br />that directly measure power density, but I predict <br />that power density information will eventually <br />prove valuable in providing electrofishing thresh- <br />old data for comparing various species of fish. <br />Method 1: Voltage Profiles <br />It is convenient to describe what is meant by a <br />voltage profile through illustration. Figure 8 <br />shows an experimental setup having two identical <br />electrodes (A and B) immersed in water to some <br />convenient depth (D) and separated by a distance <br />(X). The electrodes are driven by an AC power <br />source similar to that depicted in Fig. 2. One test <br />lead of the voltmeter has a direct wire connection <br />to the 'A electrode, and the second lead is fitted <br />with an extended length of insulated wire (about <br />#20 gauge) that has the end of its conductor ex- <br />posed for approximately 2 mm. With this appara- <br />tus, the voltmeter can measure the electrical po- <br />tential between the "A" electrode and the tip of the