A copper wire has a diameter 0.5 mm and resistivity 1.6 108 m. What will be the length of this wire to make the resistance of 12 ? How much will be the resistance of another copper wire of same length but half the diameter?
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Given,
diameter of copper wire = 0.5mm = 5 × 10-⁴ m
resistivity = 1.6 × 10^-8 ohm.m
resistance = 10 ohm
Length = ?
we know,
R = dL/A
where R , d , L and A are resistance , resistivity , length and cross section area.
10 = 1.6 × 10^-8 × L/(πr²)
L = 10 × 3.14 × (2.5 × 10^-4)² × 10^8/1.6
L = 10× 3.14 × 6.25/1.6=122.656
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