An AC power generator produces 51.7 A (rms) at 3630 V (rms). (a) Find the power

Question

An AC power generator produces 51.7 A (rms) at 3630 V (rms).

(a) Find the power produced by this generator.

(b) If this power is transmitted through a long-distance power line that has a resistance of 11.3 , find the power dissipated as heat in the power line.

(c) If the voltage of the power generator is stepped up to 175 kV by an ideal transformer before being transmitted, find (c) the current in the power line and (d) the power dissipated as heat in the power line.

Hint: In an ideal transformer, the power output is equal to the power input. Note: As you can see, the power dissipated by a power line is greatly reduced if the power is transmitted at high voltage. Source: Serway and Faughn, College Physics, 5th edition, Problem 21.38

Explanation / Answer

a) The power produced by this generator is (P) =Irms*Vrms =51.7* 3630 =187671W=187.671kW

b) The power dissipated in the power line is (P) =I2*R =(51.7)2*(11.3ohms) =30203.657W=302.03kW

c) The current in the power line is given by

P =V*I then I =P/V

similarly Power dissipated as heat in the power line is P =V2/R

Substituting the values you get the required answer

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