Q.

Resistance of a metal wire of length 1 m is 26 Ω at 20°C. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature?

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a

1.84 × 10–6 Ω m

b

1.96 × 10–6 Ω m

c

2.34 × 10–6 Ω m

d

1.72 × 10–6 Ω m

answer is A.

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Detailed Solution

Resistance R of the wire = 26 Ω, the diameter
d = 0.3 mm = 3 × 10-4 m, and the length l of the wire = 1 m. Therefore, the resistivity of the given metallic wire is ρ = (RA/l) = (Rπd2/4l)
Substitution of values in this gives
ρ = 1.84 × 10–6 Ω m

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