A generating station is producing 1.3*10^6 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 5.0*10^-2 /km.
(a) Find the power lost in heating the wires if the power is transmitted at 1100 V.
(b) A 140:1 step-up transformer is used to raise the voltage before the power is transmitted. How much power is now lost in heating the wires?
power = voltage * current
P = V * i
1.3*10^6 = 1.100 *10^3 i
i = (1.3/1.1) * 10^3 = 1.182 * 10^3 amps (heavens!)
R = 14 km * 5*10^-2 ohms
R = 7 * 10^-1 ohms
Power lost = V i = (i R) i = i^2 R = 9.777 *10^5 watts (most of our power lost in transmission :( )
b. Mr Westinghouse told Mr. Edison to use AC so he could step up the voltage and lose less.
V = 140 * 1100 = 1.54 * 10^5 volts
(now we are talking)
i = 1.3*10^6 / 1.54 * 10^5
i = 8.44 amps
power lost = i^2 R = 8.44^2 (.7) = more like 50 Watts. Half a light bulb - Alright!