An AC power generator produces 54.5 A (rms) at 3630 V (rms). (a) Find the power

Question

An AC power generator produces 54.5 A (rms) at 3630 V (rms).

(a) Find the power (kW) produced by this generator.

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

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

Explanation / Answer

(a)the power (kW) produced by this generator= 54.5 A * 3630 V / 1000= 197.83 kW

(b)If this power is transmitted through a long-distance power line that has a resistance of 11.3 ohms, power (kW) dissipated as heat in the power line will be  54.5^2*11.3 / 1000 = 33.56 kW

(c)If the voltage of the power generator is stepped up to 175 kV by an ideal transformer before being transmitted; then  the current (A) in the power line is 197.83 kW/ 175 kV = 1.1A

(d) the power (W) dissipated as heat in the power line is 1.1^2 * 11.3 = 14.44 W

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