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# A certain copper wire has a resistance of $10.0 \Omega .$ 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?

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According to the equation (18-3), the resistance is directly proportional to the length. This implies the wire need to be cut so that the long piece must be 4 times the length of the short piece.

$L=L_S+L_L=L_S+4L_S=5L_S,$

thus:

$L_S=\frac{1}{5}L=0.2L,$

$L_L=\frac{4}{5}L=0.8L.$

So cut the wire at $20\%$ of the total length of the copper wire.

Let's denote with $R_S$ and $R_L$ the resistances of the shorter and longer piece respectively. As we said $L\propto R$ so:

$R_S=0.2R=0.2(10\Omega)=2\Omega,$

$R_L=0.8R=0.8(10\Omega)=8\Omega.$

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