How Should a Copper Wire Be Cut to Achieve Specific Resistances?

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SUMMARY

The discussion centers on determining how to cut a copper wire with a resistance of 10.0 Ω into two pieces such that one piece has a resistance 5.0 times greater than the other. Using the formula R = ρ * (L/A), where resistance (R) is proportional to length (L), it is established that the wire must be divided into a ratio of 5:1. Consequently, the longer piece will have a resistance of 8.33 Ω, while the shorter piece will have a resistance of 1.67 Ω.

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  • Understanding of electrical resistance and Ohm's Law
  • Familiarity with the formula R = ρ * (L/A)
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  • Concept of proportionality in physical equations
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Questions: A certain copper wire has a resistance of 10.0 Ω. At what fraction of the length L must the wire be cut so that the resistance of one piece is 5.0 times the resistance of the other?

What is the resistance of the longer piece? Shorter piece?

I am completely lost on this. i know it should be fairly simple and I think I have to use the equation R= p*l/A
 
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Resistance is proportional to length, so you just need one piece to be 5 times the length of the other.
 

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