Resistance of a composite conducting wire

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SUMMARY

The resistance of a composite conducting wire made from a 20-cm-long copper wire and a 60-cm-long iron wire, both with a diameter of 5.50 mm, is calculated using the formula R = pL/A. The resistivity values for copper and iron are applied separately to determine the resistance of each segment, which are then summed to yield a total resistance of 10.4 milliohm. The calculation confirms that the resistances of the two materials add linearly, as they are in series. The diameter of the wire is correctly converted to radius for area calculations, affirming that r equals d/2.

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  • Understanding of electrical resistance and Ohm's Law
  • Familiarity with the concept of resistivity and its units
  • Knowledge of geometric calculations for cross-sectional area
  • Basic principles of series circuits in electrical engineering
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Linus Pauling
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1. An 80-cm-long wire is made by welding a 5.50 mm-diameter, 20-cm-long copper wire to a 5.50 mm-diameter, 60-cm-long iron wire. What is the resistance of the composite wire?
2. p = resistivity, R = pL/A 3. r = 0.001375 m goes into A = pi*r2. I used the above equation for R separately for the length of the wire for each metal, then added them together. I figured they would just add linearly like resistors in series.

My calculation came out to be 9.80*10-3 ohm + 5.72*10-4ohm = 0.0104 ohm = 10.4 milliohm
 
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Isn't r equal to d/2 ?

The method you described is OK, but I couldn't get the same result. Could you give
a more detailed calculation?
 

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