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when diameter of a wire is doubled what is its resistance

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Answer #1

Resistance is inversely proportional to the cross section of a conductor. Since the area of a circle is pi * radius squared the cross section of a conductor increases by the square of its diameter; so its resistance would be inversely proportional to the square of its diameter. E.g. doubling the diameter decreases resistance by a quarter, increasing the diameter 10 times reduces resistance by 99% Note that this is for plain DC resistance. Alternating current is subject to “skin effect” where the current flows near the surface of the conductor so AC impedance is far more complicated to deal with. The higher the frequency the greater the skin effect. At 60 hertz this effect can be ignored unless you are dealing with large conductors and large amounts of current. At radio frequencies skin effect comes into play and at microwave frequencies skin effect is so extreme that a thin pipe has the same impedance as a solid wire the same diameter.

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