Cutting a Copper Wire for Different Resistances

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To solve the problem of cutting a copper wire with a total resistance of 10.0 Ohm into two pieces where one piece has a resistance 4.0 times greater than the other, the resistance of the smaller piece is determined to be 2 Ohm, making the larger piece 8 Ohm. The equation for resistivity, R = ρL/A, is relevant, but the user struggles with applying the total length equation (L1 + L2 = Ltotal) correctly. The key is to set up the relationship between the lengths of the two pieces in proportion to their resistances. Clarifying when to use the total length equation is crucial for finding the correct lengths of each wire segment. Understanding these relationships will lead to the correct solution for the problem.
DevilishNole
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I need help with one of my Physics homework problems please!

A certain copper wire has a resistance of 10.0 Ohm. At what point along its length must the wire be cut so that the resistance of one piece is 4.0 times the resistance of the other? What is the resistance of each piece?

I worked it out and got that R=2 Ohm, and so the other piece, 4R, has to be equal to 8 Ohm. I used the equation for resistivity, R= rho*L/A using 4R in the place of R and solved for L. I replaced this back into the original equation but end up in a loop, with R=2. I have no idea what I'm doing wrong; can anyone please help?!
 
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You need to use the fact that L1 + L2 = Ltotal.
 
I did that on my second attempt to the problem but to no avail because I do not know when to use the "L1+L2" equation and the "Ltotal"
 
Consider it as a proportion.
 
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