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# aluminum bar resistance in physics

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• ### aluminum bar resistance in physics

AlinaVarle > 01-13-2020, 07:14 AM

An aluminum bar 3.80 m long has a rectangular cross section 1.00 cm by 5.00 cm, what is the resistance and what is the length of a copper wire 1.50 mm in diameter having the same resistance?Resistance equals resistivity times length divided by cross-sectional area. R = ρ∙l/A The resistivities at 20°C are aluminum ρ = 2.82×10⁻⁸Ωm copper ρ = 1.72×10⁻⁸Ωm So the aluminum bar with rectangular cross section has a resistance of R = ρ∙l/(a∙b) = 2.82×10⁻⁸Ωm ∙ 3.8m / (0.01m ∙ 0.05m) = 2.1432×10⁻⁴Ω The resistance of copper wire with circular cross section is given by R = ρ∙l/(π∙d²/4) = 4∙ρ∙l/(π∙d²) Hence a wire of same resistance as the aluminum bar has a length of l = R∙π∙d² / (4∙ρ) = 2.1432×10⁻⁴Ω ∙ π ∙ (0.0015m)² / (4∙1.72×10⁻⁸Ωm) = 0.0220m = 2.2cmResistance Of AluminumI used ρ=2.63 ×10⁻⁸Ωm for aluminum and got the right answer. The wikipedia page says your aluminum ρ = 2.82×10⁻⁸Ωm is used for high voltage power lines.first ,we will find out the cross sectional area Area= width* height =5.3*2.1=11.13cm^2 Area=11.13 *10^-4 m^2 shear stress = force /area =3.3*10^5/11.13*10^-4=0.296*10^9 Shear stress=2.96*10^8 N/m^2 shear modulus of aluminum=2.6*10^10 pa Shear strain =stress/modulus =2.96*10^8 / 2.6*10^10 =1.14*10^-2 =0.0114 from figure, strain=x/length 0.0114=x/220 (length in mm) x=0.0114*220 x=2.508 mm Ans: Shear deformation is 2.508 mm. ===============================Other related question