physics

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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?

  • physics -

    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!

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