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In the fabrication of an electrical extension cord, the manufacturer wants to reduce the overall resistance of the wires in the extension cord.

Which of the following changes would result in the lowest resistance?
A) decrease the diameter of the wires
B) increase the diameter of the wires
C) choose a metal wire with a larger value of resistivity
D) increase the length of the extension cord

Respuesta :

skyluke89

B) increase the diameter of the wires will result in the lowest resistance

Explanation:

The electrical resistance of a wire is given by:

[tex]R=\frac{\rho L}{A}[/tex]

where

[tex]\rho[/tex] is the resistivity of the material used for the wire

L is the length of the wire

A is the cross-sectional area of the wire

From the equation, we can notice the following:

  • The resistance is directly proportional to the resistivity of the material, [tex]R\propto \rho[/tex], therefore if a metal with larger value of resistivity is used, the resistance will increase
  • The resistance is directly proportional to the length of the wire, [tex]R\propto L[/tex], therefore if the length of the wire is increased, the resistance will increase
  • The resistance is inversely proportional to the cross-sectional area of the wire, [tex]R\propto \frac{1}{A}[/tex], therefore if the cross-sectional area increases, the resistance will decrease

From these observation, it is now clear that the correct answer is

B) increase the diameter of the wires

In fact, by increasing the diameter of the wire, we also increase its cross-sectional area, and therefore we will decrease its resistance, since it is inversely proportional to the area.

Learn more about resistance:

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