Electric  resistance of a wire

R = (ρ ℓ) / A          

  • ℓ length wire in m
  • A cross sectional area in m2
  • ρ resistivity of the material in Ωm

Example  

50.0 cm of a constantan wire has a electric resistance of 1.125  Ω

Find the diameter of the wire

ρ of constantan : 0.45 x 10-6 Ωm

R = (ρ ℓ)/A

R A = ρ ℓ

A = (ρ ℓ)/R = ((0.45 x 10-6)( 0.50)) /1.125 = 2.0 x 10-7 m2 = 2.0 x 10-1 mm2

A = π r2

2.0 x 10-1 = πr2

r2 = (2.0 x10-1)/π = 0.06366

r = 0.25 mm

d = 2r = 2 x 0.25 = 0.50 mm

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