The resistance of a wire varies with its diameter.

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Detailed Solution

The given statement is true.
The resistance of a conductor is inversely proportional to its area of cross-section as well as the square of the diameter. That is,

R \propto \frac{1}{A}

(Where R is resistance and A is the area of the cross-section of conductor).
And

R = \frac{4}{π d^{2}}

(d is diameter of the wire)
The resistance of a wire is inversely proportional to the square of its diameter. If the diameter of a wire is halved, then its resistance becomes four times. The characteristic of a conductor due to which it opposes the flow of current is known as resistance.

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