Please show all working out. (d) The power company strives to maximize efficienc

Question

Please show all working out.

(d) The power company strives to maximize efficiency when it delivers power to a customer, rather than maximize load power. Assume that RTH = 0.5 ohm (representing the equivalent resistance of the transmission lines to the load), RL = 5 ohm and VTH = 120 V. What is the power of the load? What is the efficiency? (e) Now assume the power company wants to increase efficiency. It cannot change RTH = 0.5 ohm (because the transmission lines are fixed structures), but it can change VTH (by adjusting generator voltage), and it can adjust the effective load resistor value. Calculate the values of VTH and RL needed to dissipate the same load power as part (d), but with an efficiency of 99%. (f) The power company uses high-voltage transmission lines with voltages of 10 kV to 200 kV to transmit power over long distances. Given your analysis from parts (d) and (e), why does it use such high voltages, despite the potential dangers that they pose?

Explanation / Answer

d)Power=(120/5.5)*2*5=2380.165W

Efficiency=2380.165/(2380.165+(120/5.5)^2*0.5)=90.9%

e)Power=V^2/(RL+0.5)^2*Rl=2380.165

efficiency=2380.165/(2380.165+V^2/(RL+0.5)^2*0.5)=0.99

gives R=49.5ohm

V=346.71V

f)since by increasing voltage we see the efficiency has increased we need high voltages for even higher efficiency.

so although it is dangerous, to save power losses, high voltage are used.

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