3. jumper cables are used to start an automobile can get hot if usedfor more tha

Question

3.           jumper cables are used to start an automobile can get hot if usedfor more than a few seconds. The jumper cables are 3 meters longwith a radius of 5mm, and they are composed of copper. Copper has aresistivity of 1.72*10^ (-8) ( ohm-m) at 20C, temperaturecoefficient of 0.0039(1/C), and a density of 9000 kg/m3.

a. What is thetotal resistance of the pair of wires when the temperature is20C?

b. How muchdoes the resistance increase if the temperature becomes 100C?

c. What is themagnetic force magnitude and direction between the wires of thewire centers are separated by 20 mm and the current is 40amperes?

Explanation / Answer

   R = 2 L /A
  here is resistivity, L is length , Ais area = R2
   R = 2 L/ R2  
   = 2 ( 1.72x10-8)(3m)/ (5x10-3m)2   
   = 1.314x10-3 ohms
-------------------------------------------------------------------------------------------------------------- The increase in resistance of the two wiresis
   R ' = R [ 1 + (t2 - t1) ]
   =(1.314x10-3 ohms ) [ 1 + (0.0039)(100-20)]
   = 1.724x10-3 ohms
----------------------------------------------------------------------------------------------------------- The force between the wires is
   F = o I1I2 L / 2d
   =(4x10-7)(40)(40)(3) /2(20x10-3m)
   = 1.527x10-2N

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