In “Back to the Future”, the time machine is said toneed 1.21 gigawatts of power
ID: 1756074 • Letter: I
Question
In “Back to the Future”, the time machine is said toneed 1.21 gigawatts of power. Doc Brown runs a cable to the top ofthe town hall to make a connection to a wire hanging over thestreet thus providing a connection to the DeLorean as it speedspast. Assume the entire length (from the lightning rod to the car)is a 100 m iron cable of resistivity = 9.7 x 10-8?m.a) The typical lightning bolt has a current of about 40.0 kA. Whatis the voltage needed to transfer 1.21 gigawatts of power?
b) If the cable is 1.5 cm in diameter, how much power is lost with40.0 kA running through the cable?
c) Assume the resistance in part (b) was calculated at 20°C.What would the power loss through the cable have been on a cold daywhen it is 0°C? (use = 5.0 x 10-3 /°C)
Explanation / Answer
a) 1.21gigawatt is equal to 1.21*109 W power. P = V*I V = 1.21*109W / 40*103 = 3.025*104 V = 30.25kV b) Resistance of the cableis: R = *l/A = 9.7*10-8 * 100/(*(1.5*10-2/2)2 c) Power lost= I2*R = (40*103)2* 5.325*10-2 = 8.52* 107 W = 85.2 MW d) Rt = R(1+t)With: = temp. coefficient ofresistivity = 6.0*10-3/ 0C R0 = 5.325*10-2(1 + (0-20)* 6.0*10-3) = 4.686*10-2 => Powerlost = (40*103)2* 4.868*10-2
= 74.97MW