Calculate the ratio of the resistance of 12.0 m of aluminum wire 2.5 mm in diameter, to 30.0 m of copper wire 1.6 mm in diameter. the resistivity of copper is 1.68×10−8ω⋅m and the resistivity of aluminum is 2.65×10−8ω⋅m.

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Explanation:

The resistance of a wire is calculated by the following formula:

   (1)

Where:

is the resistivity of the material the wire is made of. For aluminium is  and for copper is

is the length of the wire, which in the case of aluminium is , and in the case of copper is

is the transversal area of the wire. In this case is a circumference for both wires, so we will use the formula of the area of the circumference:

 (2) Where  is the diameter of the circumference.

For aluminium wire the diameter is    and for copper is

So, in this problem we have two transversal areas:

For aluminium:

  (3)

For copper:

   (4)

Now we have to calculate the resistance for each wire:

Aluminium wire:

    (5)

    (6)  Resistance of aluminium wire

Copper wire:

    (6)

    (7)  Resistance of copper wire

At this point we are able to calculate the  ratio of the resistance of both wires:

  (8)

  (9)

Finally:

 This is the ratio

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explanation:

the first, second, and fifth options