An aluminum bar 3.83m long has a rectangular cross section 1.33cm by 5.02cm .A) What is its resistance?B) What is the length of a copper wire 1.45mm in diameter having the same resistance?
The formula to use is: R rho*L/A where R is the resistance, rho is the resistivity, L is the length, A is the cross sectional area. In part A: R rho_Al * L/(w*h) In part B: R rho_Cu * Lcu/(Pi*d^2/4) Equate the two R's, as per instructions of the problem: rho_Al * L/(w*h) rho_Cu*Lcu/(Pi*d^2/4) Solve for Lcu: Lcu rho_Al*L*Pi*d^2/(4*rho_Cu*w*h) Data: L:3.83 m; h:0.0133 m; w:0.0502 m; d:0.00145 m; rho_Al:2.82e-8 Ω-m; rho_Cu:1.72e-8 Ω-m; assumed ambient temperature. Results: A) R 161.8 microOhms B) Lcu 0.01553 meters, or Lcu 1.553 cm
