A generating station is producing 17 x 106 W of power that i

A generating station is producing 1.7 x 106 W of power that is to be sent to a small town located 6.8 km away. Each of the two wires that comprise the transmission line has a resistance per length of 5.5 x 10-2/km. (a) Find the power lost in heating the wires if the power is transmitted at 1600 V. (b) A 100:1 step-up transformer is used to raise the voltage before the power is transmitted. How much power is now lost in heating the wires?

Solution

the total resistance of the two wires = 5.5 * 10^-2 * 2 * 6.8 km = 0.748 ohm

I = P / V = 1.7 * 10⁶ / 1600 = 1.063 * 10³ A

delta P = I² R = 1.063 * 10³ * 1.063 * 10³ * 0.748

= 8.44 * 10⁵ W

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The step-up transformer ratio of 100:1 means that power is transmitted at a voltage of

1600 * 100 = 160,000 V

I = P / V = 1.7 * 10⁶ / 160,000 = 10.625 A

delta P = I² R = 10.625² * 0.748

= 84.4 W