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??Ωm copper ρ = 1.72×10??Ωm So the aluminum bar with rectangular cross section has a resistance of R = ρ?l/(a?b) = 2.82×10??Ωm ? 3.8m / (0.01m ? 0.05m) = 2.1432×10??Ω The resistance of copper wire with circular cross section is given by R = ρ?l/(π?d?/4) = 4?ρ?l/(π?d?) Hence a wire of same resistance as the aluminum bar has a length of l = R?π?d? / (4?ρ) = 2.1432×10??Ω ? π ? (0.0015m)? / (4?1.72×10??Ωm) = 0.0220m = 2.2cm
I used ρ=2.63 ×10??Ωm for aluminum and got the right answer. The wikipedia page says your aluminum ρ = 2.82×10??Ωm 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. ===============================
