If the radius of wire of same length is doubled (or area of cross section becomes four times), its resistance becomes one-fourth; if the radius is tripled (or area of cross section becomes nine times), the resistance becomes one-ninth and so on.
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(a) Resistance of a wire is directly proportional to the length of a wire; so if the length is doubled, resistance is also doubled.
(b) Resistance of a wire is inversely proportional to the area of cross-section the wire. Thus, if radius is doubled, area increases four times and hence the resistance becomes one-fourth.
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