Re: parallel feeders
Originally posted by steve66: Don, I see you have taken the current divider formula and simplified it to use raw lengths instead of resistances.
Actually, he simplified it even further than that. I would call Don?s calculation process a good ?rule of thumb,? but it has its limits. And it is not, strictly speaking, the ?current divider formula.? You can use this simplified process to estimate the currents in three parallel legs, and get an answer within 1% of the answer you would get by using the long-hand formulas for three parallel resistors and the current divider formula. But I did not analyze the rule of thumb, to see how accurate it could be for four or more parallel legs.
Just in case anyone has an interest in the exact formulas, I will give them to you. Let?s call the three cable lengths L1, L2 and L3. Lets call the three currents I1, I2, and I3, and call the total current I-tot. In Don?s example, L1 was 19 feet, L2 was 20 feet, and L3 was 21 feet. Don used the following simplification:
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- <font size="2" face="Verdana, Helvetica, sans-serif">I1 = I-tot times (L3) / (L1 + L2 + L3)</font>
<font size="2" face="Verdana, Helvetica, sans-serif"></font>
- <font size="2" face="Verdana, Helvetica, sans-serif">Result: I1 = 35.000% of I-tot</font>
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- <font size="2" face="Verdana, Helvetica, sans-serif">I2 = I-tot times (L2) / (L1 + L2 + L3)</font>
<font size="2" face="Verdana, Helvetica, sans-serif"></font>
- <font size="2" face="Verdana, Helvetica, sans-serif">Result: I1 = 33.333% of I-tot</font>
<font size="2" face="Verdana, Helvetica, sans-serif"></font>
- <font size="2" face="Verdana, Helvetica, sans-serif">I3 = I-tot times (L1) / (L1 + L2 + L3)</font>
<font size="2" face="Verdana, Helvetica, sans-serif"></font>
- <font size="2" face="Verdana, Helvetica, sans-serif">Result: I3 = 31.667% of I-tot</font>
<font size="2" face="Verdana, Helvetica, sans-serif">Now here are the actual formulas, based on the long-hand formulas for three parallel resistors and the current divider formula:
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- <font size="2" face="Verdana, Helvetica, sans-serif">I1 = (L2 times L3) / (L1 L2 plus L1 L3 plus L2 L3)</font>
<font size="2" face="Verdana, Helvetica, sans-serif"></font>
- <font size="2" face="Verdana, Helvetica, sans-serif">Result: I1 = 35.029% of I-tot</font>
<font size="2" face="Verdana, Helvetica, sans-serif"></font>
- <font size="2" face="Verdana, Helvetica, sans-serif">I2 = (L1 times L3) / (L1 L2 plus L1 L3 plus L2 L3)</font>
<font size="2" face="Verdana, Helvetica, sans-serif"></font>
- <font size="2" face="Verdana, Helvetica, sans-serif">Result: I2 = 33.278% of I-tot</font>
<font size="2" face="Verdana, Helvetica, sans-serif"></font>
- <font size="2" face="Verdana, Helvetica, sans-serif">I3 = (L1 times L2) / (L1 L2 plus L1 L3 plus L2 L3)</font>
<font size="2" face="Verdana, Helvetica, sans-serif"></font>
- <font size="2" face="Verdana, Helvetica, sans-serif">Result: I3 = 31.693% of I-tot</font>
<font size="2" face="Verdana, Helvetica, sans-serif">As I say, Don?s thumb rule formula is very close to being perfect. But if you want do this for four or more resistors, the real formulas start getting very complicated.