Power lines carry electricity to your house at high voltage. This problem investigates the reason for that. Suppose a power plant produces 800 kW of power and wants to send that power for many miles over a copper wire with a total resistance of 12Ω. (a) If the power is sent at a voltage of 120 V rms as used in houses in the United States, how much current flows through the copper wires? [Hint: The 12-Ω resistance of the wires is in series with the load in the house, and the 120-V rms voltage is connected across the series combination.] (b) What is the power dissipated due to the resistance of the copper wires? (c) If transformers are used so that the power is sent across the copper wires at 48 kV rms, how much current flows through the wires? (d) What is the power dissipated due to the resistance of the wires at this current? What percent of the total power output of the plant is this? (e) Although a series of transformers step the voltage down to the 120 V used for household voltage, assume you are using a single transformer to do the job. If the single transformer has 10.000 primary turns, how many secondary turns should it have?
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