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IN-WATER ELECTRicAL MEASUREMENTS 9 AC Power Source (voltage) J plied Voltage (V.) Air I Voltmeter Insulated wire IDpth (D) Bares wire Ijy ?w at tip V Electrode A Electrode B v Distance - M Fig. 8. Circuit configuration and metering for measuring voltage profiles. wire probe as the probe is moved throughout the volume of water. A voltage profile is produced by plotting the voltmeter readings as a function of the probe's location. For example, the probe might be moved through the water along a transect between the centroids of the two electrodes; along this particu- lar path, the voltage readings at three locations are predictable. With the probe at zero distance (i.e., touching the "A" electrode), the voltage reading is zero; both voltmeter leads are electrically con- nected to the same piece of metal. When the probe is midway between the two electrodes, the geomet- ric symmetry of the apparatus requires the voltage reading to be one-half the applied voltage (50% of Vs). And finally, when the probe makes contact with the "U' electrode, the meter will read the applied voltage (Vs). The interspatial readings be- tween these predicted values can also be measured with the voltmeter, and Fig. 9 shows a generalized voltage profile for the two identical electrodes. The S-shaped voltage curve depicted in Fig. 9 results from the decreasing values of effective in- water resistance as described in the quasi-techni- cal discussion. The S-curve can be interpreted as showing that one-half the supply voltage and one- half of the available power are dissipated in the volume of water surrounding each of the elec- trodes. In fact, electrofishing systems operating with two identical electrodes are often described as being a "balanced" electrode array. This conclusion 100 v ay t)A s0 a sy d Fig. 9. Generalized voltage profile for two identical electrodes. is substantiated by applying the analysis tech- niques previously described and noting that any balanced electrode system implies that R'm = RN; similar electrodes must have equal resistances (Fig. 4). Furthermore, the relative curvatures along each end of the S-curve reflect a reversed geometric symmetry, and the two halves of the S appear balanced. Voltage profiles can also be measured for elec- trode arrays that are dissimilar or unbalanced. Dissimilar electrodes simply displace and alter the shape of the S-profile, and the two halves of the S-curve will no longer display the same relative curvatures or the same percentages in applied volt- age. The voltage profiles can be used to graphically demonstrate spatial differences between the elec- tric fields generated by various electrode configura- tions. In fact, an electrode design can purposely be chosen to dissipate more voltage or power at one particular electrode. For example, backpack elec- trofishing equipment can be designed to direct more power into the hand-held electrode for captur- ing fish than into the trailing electrode. A voltage profile can be developed into a voltage gradient profile by noting that voltage gradient is defined by the derivative of the voltage profile (E = dV/dx). In words, the slope of the tangential line at any point on the voltage profile is the value of the voltage gradient at that location. The S-shape of the voltage profile will always produce a voltage gradient profile having a U-shaped curve (Fig. 10). The two arms of the U will be symmetric or non- symmetric depending on whether the system is balanced or unbalanced. The shape of the U-curve is highly significant in electrode design. If the U rises sharply and bottoms quickly, the electrode O X/2 X Distance