Resistance and Resistivity: The length of a certain wire is doubled while its radius is kept constant. What is the new resistance of this wire?

Explanation:

The formula for calculating the resistance of a material in terms of its resistivity is expressed as where;

R is the resistance of the material

is the resistivity of the material

L is the length of the wire

A is the area = πr² with r being the radius

If the length of a certain wire is doubled while its radius is kept constant, then the new length of the wire L₁ = 2L

The new resistance of the wire R₁ will be expressed as

since the radius is constant, the area will also be the same i.e A = A₁ and the resistivity also will be constant. The new resistance will become

Taking the ratio of both resistances, we will have;

This shoes that the new resistance of the wire will be twice that of the original wire

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