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By what factor does the resistance of a copper wire change if its length quadruples and...

By what factor does the resistance of a copper wire change if its length quadruples and its diameter quadruples? (If the resistance doubles, enter "2"; if it decreases by a factor of three, enter "1/3", etc.)

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Answer #1

Resistivity of copper =

Initial length of the copper wire = L1

Initial diameter of the copper wire = D1

Initial cross-sectional area of the copper wire = A = D12/4

Initial resistance of the copper wire = R1

New length of the copper wire = L2 = 4L1

New diameter of the copper wire = D2 = 4D2

New cross-sectional area of the copper wire = A2 = D22/4

The resistance of the copper wire changes by a factor of 1/4.

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