#1 An energy plant produces an output potential of 2700 kV and servesa city 136
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Question
#1
An energy plant produces an output potential of 2700 kV and servesa city 136 km away. A high-voltage transmission line carries 670 Ato the city. The effective resistance of a trans- mission line[wire(s)] is 3.43 /km times the distance from the plant tothe city.
a. What is the potential provided to the city, i.e., at the end ofthe transmission line? An- swer in units of kV.
b. How much power is dissipated due to resistive losses in thetransmission line? Answer in units of W.
c.Assume the plant charges $ 0.092 /kW · hr for electricenergy. At this rate, how much does it cost to trans- mitenergy to the city (by the transmission line heating theatmosphere) each hour? An- swer in units of dollars/hrConsider themoney lost by the transmission line heating the atmosphere eachhour. As- sume the energy plant produces the same amount of power;however, the output electric potential of the energy plant is 20%greater.
d.How much money per hour is saved by in- creasing the electricpotential of the power plant? Answer in units of dollars/hr
Explanation / Answer
Power at the plant is P = VI
Power loss in the wire is Ploss =I2R
Power reached to the citi is Pc =P-Ploss
But Pc =VcI Then the voltage reached to the city is Vc =Pc/I
=(P-Ploss )/I =(VI - I2R)/I = V- IR =2700kV - (670A)(3.43/km)(136km) =2700kV - 312.5kV = 2387.5 kV
(b)Ploss = I2R =(670A)2(3.43/km)(136km) = 2.09*108W
(c) Cost to transmit energy to city is (2.09*105kW)($0.092 /kW.hr) = $19,265/hr
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