Question

PLEASE SHOW STEP BY STEP WORK . NO SHORTCUT.

1.

Calculate the ratio of the resistance of 15.0 m of aluminum wire 2.1 mm in diameter, to 23.0 m of copper wire 1.8 mm in diameter. The resistivity of copper is 1.68×10−8Ω⋅m and the resistivity of aluminum is 2.65×10−8Ω⋅m.

PART A:   Determine at what temperature aluminum will have the same resistivity as tungsten does at 24 ∘C.

PART B: An electric car uses a 80-kW motor. If the battery pack is designed for 340 V, what current would the motor need to draw from the battery? Neglect any energy losses in getting energy from the battery to the motor.

Answer 1

Resistance R = rho L/A resistance of aluminium R = 2.65 times 10^- 8 times 15/pi r^2 = 2.65 times 10^- 8 times 15/3.14 times (1.05 times 10^- 3)^2 = 0.1148 Ohm resistance of copper R = 1.68 times 10^- 8 times 23/3.14 times (0.9 times 10^- 3)^2 = 0.1519 Ohm Ratio of resistance R_AL/R_cu = 0.1148/0.1519 = 0.7557 a) The resistivity of aluminium = the resistivity of tungsten rho_AL = rho_T rho_AL(1 + alpha(T_T_0)) = rho_oT (1 + alpha(24 - T_0)) 2.65 times 10^- 8 (1 + 0.00429(T - 20)) = 5.6 times 10^- 8 (1 + 0.0045(24 - 20)) T = 288 degree C b) power P = VI I = P/V = 80 times 10^3/340 = 235.29 A