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A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10–8 Ω m. What will be the length of this wire to make its resistance 10 Ω? How much does the resistance change if the diameter is doubled?

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Resistance (R) of a copper wire of length l and cross-section A is given by the expression,

If the diameter (radius) is doubled, the new radius r = 0.5 mm = 0.0005 m
=2=3.14×(0.0005)2=0.000000785 2
So, the new resistance will be

Hence, the new resistance will become ¼ times the original resistance.

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