Calculating Total Resistance & Tolerance of 2 Wires

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SUMMARY

The total resistance of two wires, one with a resistance of 50 Ohms and a tolerance of 5%, and the other with a resistance of 60 Ohms and a tolerance of 3%, is calculated to be 110 Ohms. The total tolerance is determined to be 8%, derived from the individual tolerances and the error in the sum calculated using the square root of the sum of the squares of the individual tolerances. The resistance ranges for the wires are 47.5 Ohms to 52.5 Ohms for the first wire and 58.2 Ohms to 61.8 Ohms for the second wire, leading to a total range of 105.7 Ohms to 114.3 Ohms.

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  • Understanding of electrical resistance and Ohm's Law
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  • Knowledge of statistical error propagation methods
  • Basic proficiency in using square root calculations
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If there were 2 wires, and one of the wire has a resistance of 50 Ohms with a tolerance of 5%, while the second wire has a resistance of 60 Ohms with a tolerance of 3%. The total resistance would be 110 Ohms but what about the total tolerance? Would it be 8%?
 
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The first one is 50+/-2.5, and the second is 60+/-2. The error in the sum is sqrt(2.5^2+2^2)=3 ohms. This equates to 3%.
 


Yes, the total tolerance would be 8%. This can be calculated by finding the range of possible resistance values for each wire and then adding them together. For the first wire, the range would be 47.5 Ohms to 52.5 Ohms (50 Ohms +/- 5%). For the second wire, the range would be 58.2 Ohms to 61.8 Ohms (60 Ohms +/- 3%). When added together, the total range is 105.7 Ohms to 114.3 Ohms. This means that the total tolerance is 8% (8.6 Ohms / 105.7 Ohms = 0.0815 = 8.15%).
 

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