Physics (DUE SOON)
posted by DCM .
A generating station is producing 2.00 106 W of power that is to be sent to a small town located 7.0 km away. Each of the two wires that comprise the transmission line has a resistance per kilometer of length of 5.00 102 /km.
(a) Find the power lost in heating the wires if the power is transmitted at 1300 V.
W
(b) A 120:1 stepup transformer is used to raise the voltage before the power is transmitted. How much power is now lost in heating the wires?
W

I did this yesterday for someone:
Power = V i = 1300 * i = 2*10^6
so
i = (2/1.3)*10^3 = 1.54 * 10^3 amps (big current!)
R = 2 * 7 * 5 * 10^2 = .7 Ohms
Power loss = i^2 R = (1.54)^2*10^6*.7 = 1.66*10^6 Watts (we lose about as much as we use)

Now use a high voltage line
i = 1.54*10^3/120 = 12.8 amps (reasonable now)
power loss = i^2 R = 12.8^2 (.7) = 115 Watts, about a 100 watt light bulb worth lost now.