Two copper wires, one of length 1 m and the other of length 9 m, are found to have the same resistance. Their diameters are in the ratio :

 An electrical conductor’s electrical resistance is the resistance to the passage of an electric current through it.

  • The resistance of a wire is inversely proportional to the area of the wire’s cross-section and directly proportional to the wire’s length.
  • That is, as the diameter of the wire increases and the length of the wire decreases, the resistance of the wire lowers, and as the diameter of the wire decreases and the length of the wire increases, the resistance of the wire increases.

The resistance of the conductor is given as R=ρ l/A.

The wire in this example is 9 times longer than the first. The resistance rises as the length grows, as shown above. Because the diameter of the wire is inversely related to the resistance, it may be increased to maintain the same resistance. Because the area of the cross-section is proportional to the diameter, the resistance remains constant when the diameter of the wire is raised by three times.

As a result, their diameters are in the 1:3 ratio.

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