A power plant produces 1000 MW to supply a city 40 km away. Current flows from the power plant on a single wire of resistance 0.050Ω/km, th

Question

A power plant produces 1000 MW to supply a city 40 km away. Current flows from the power plant on a single wire of resistance 0.050Ω/km, through the city, and returns via the ground, assumed to have negligible resistance. At the power plant the voltage between the wire and ground is 115 kV.What is the current in the wire?What fraction of the power is lost in transmission?

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Thanh Thu 3 years 2021-09-03T05:57:22+00:00 1 Answers 2 views 0

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  1. minhkhoi
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    2021-09-03T05:59:07+00:00
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    Answer:

    Current = 8696 A

    Fraction of power lost = \dfrac{80}{529} = 0.151

    Explanation:

    Electric power is given by

    P=IV

    where I is the current and V is the voltage.

    I=\dfrac{P}{V}

    Using values from the question,

    I=\dfrac{1000\times10^6 \text{ W}}{115\times10^3\text{ V}} = 8696 \text{ A}

    The power loss is given by

    P_\text{loss} = I^2R

    where R is the resistance of the wire. From the question, the wire has a resistance of 0.050\Omega per km. Since resistance is proportional to length, the resistance of the wire is

    R = 0.050\times40 = 2\Omega

    Hence,

    P_\text{loss} = \left(\dfrac{200000}{23}\right)^2\times2

    The fraction lost = \dfrac{P_\text{loss}}{P}=\left(\dfrac{200000}{23}\right)^2\times2\div (1000\times10^6)=\dfrac{80}{529}=0.151

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