resistance is inversely proportional to square of diameter . prove it.
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The very property of Resistance being inversely proportional to the area of the conductor=> area of any circular section being proportional to square of its diameter => The resistance is inversely proportional to square of the conductor's diameter. It is simple.
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Cross sectional area is the area of the end of the wire (assuming a perfectly flat right angle cut). So it's proportional to the square of diameter. Resistance is inversely proportional to cross sectional area. So if the diameter is halved the cross-sectional area is quartered and the resistance is quadrupled
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