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IN-WATER ELEcTRicAL MEASUREMENT'S 5 <br />RT = R.egM + ReQN, (6) <br />Current (1) <br />Line A <br />Rle R2a R3a RM + RegM <br />Power - - - <br />Source RT <br />(voltage) - - - <br />Rib R2b Rib RN RegN <br />Une B <br />Fig. 4. Diagrams showing the analysis sequence to <br />simplify the electrical circuits for an electrofishing <br />system: (a) Generic circuit for any two-terminal <br />electrofishing system. (b) Simplified circuit showing <br />the parallel resistors attached to each line replaced <br />by their equivalent resistances (Rm and RN). <br />(c) Final circuit is reduced to a single value of <br />resistance (RT). <br />between the "M" and "N' electrodes) is provided <br />by the water; it is not a "metal-wired" connection. <br />A complete circuit analysis is possible for any <br />electrode array if the individual electrode resis- <br />tances are known. <br />Although the generic circuit appears complex, <br />the analysis is readily initiated by calculating the <br />equivalent resistance associated with each termi- <br />nal (line A or line B) of the power source. Those <br />electrodes attached to a given terminal are actu- <br />ally connected in parallel, and an equivalent resis- <br />tance can be calculated for each (Brand 1979). <br />These equivalent resistances (R m and RN) are <br />depicted in Fig. 4b where <br />Regardless of the number of electrodes, this <br />analysis technique reduces any single-phase elec- <br />trofishing system to one equivalent resistance <br />(Rr). Although more complicated, the same gen- <br />eral techniques can be applied for electrofishing <br />equipment designed with multiple power sources <br />(Harris 1955), <br />Resistance Analysis <br />A resistance analysis is now demonstrated for <br />a hypothetical electrofishing system by using the <br />electrode resistances presented in Fig. 3 for cylin- <br />ders. Consider a system designed with four cylin- <br />drical electrodes that are separated by a sufficient <br />distance to prevent mutual coupling between the <br />electric fields. Three electrodes are attached to <br />line A of the power source, and a single electrode <br />is connected to line B. Two of the cylinders on line <br />A are 1.27 cm in diameter and measure 116 ohms <br />for an immersion depth of 60 cm. The third cylin- <br />der on line A is 2.54 cm in diameter and immersed <br />to a depth of 30 cm; its resistance is about <br />169 ohms. The single cylinder on line B is 60 cm <br />long and 5.08 cm in diameter and has a resistance <br />of 81 ohms. These resistances are for a water <br />conductivity of 100 µS/cm, but the system is to <br />operate in water of 500 µS/cm. Therefore, it is <br />necessary to correct the resistance values for the <br />three sizes of electrodes by the conversion ratio of <br />c1162 = 100/500 = 0.2 (equation 3). The corrected <br />resistance values are about 23, 34, and 16 ohms <br />(Fig. 5a). Figure 5b indicates how the three paral- <br />lel electrodes connected to line A combine for an <br />equivalent resistance of 8.6 ohms, while the resis- <br />tance of the single electrode on line B remains <br />unchanged at 16 ohms. The resistance analysis is <br />completed by calculating the total circuit resis- <br />tance of 24.6 ohms (Fig. 5c). <br />RI-,M = - (4) <br />1/(1/Rza+1/R2I +1/R:I. +,,,+1/Foohms <br />and <br />R,,N_ (5) <br />1/(1/Rlb+ 1/16+ 1/R3b+,,, + 1/RN) ohms. <br />In equations 4 and 5, the individual electrodes <br />are represented by their corresponding resistance <br />value. <br />The circuit has now been reduced to a series <br />connection of two resistors: Rem and ReN (Fig. 4b). <br />The total resistance (Rr) for the system (Fig. 4c) is <br />calculated by <br />Voltage and Current Analysis <br />It is possible to extend the results from the <br />resistance analysis and to calculate how the sys- <br />tem's applied voltage (Vs) is proportioned between <br />the two electrode voltages: VA and VB in Fig. 5. <br />Each electrode's voltage is equal to the ratio of the <br />equivalent resistance for the parallel electrodes <br />(R,M or Rte,) to the total resistance (RT) times the <br />applied voltage (Vs). That is, <br />VA = (7) <br />OteqM / Rr) X Vs = (8.6/24.6) x V. = 0.35 Vs,