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If the diameter of a wire is halved, then it's resistance _____.

The electric resistance of a material is a property that represents the opposition to the passage of the electric current. From the microscopic point of view the resistance depends on the atomic structure of the material. From the macroscopic point of view, the resistance depends on the linear dimensions of the material.


The value of the resistance of a wire can be calculated using the following expression:


R = ρL/s


Where:


ρ, is the specific resistance which is related to the material; also has a temperature dependence.


L, is the length of the wire.


S, is the area of cross section of the wire.


For a circular cross section wire, we have:


R1 = ρL/πr1^2 = (4ρL)/(πd1^2)


If the diameter is halved, we have for the resistance:


R2 = (4ρL)/[π(d1/2)^2] = (16ρL)/(πd1^2)


By comparing the values of resistance:


R2/R1 = (16ρL/πd1^2)/(4ρL/πd1^2)


R2/R1 = 16/4 = 4


R2 = 4R1


So, the resistance increases four times.

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