Assuming 100% efficient energy conversion, how much water stored behind a 50 centimetre high hydroelectric dam would be required to charge b

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Assuming 100% efficient energy conversion, how much water stored behind a 50 centimetre high hydroelectric dam would be required to charge battery

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Thiên Di 2 weeks 2021-09-01T11:25:37+00:00 1 Answers 0 views 0

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    2021-09-01T11:27:12+00:00

    Complete question is;

    Assuming 100% efficient energy conversion how much water stored behind a 50 centimeter high hydroelectric dam would be required to charge the battery with power rating, 12 V, 50 Ampere-minutes

    Answer:

    Amount of water required to charge the battery = 7.35 m³

    Explanation:

    The formula for Potential energy of the water at that height = mgh

    Where;

    m = mass of the water

    g = acceleration due to gravity = 9.8 m/s²

    H = height of water = 50 cm = 0.5 m

    We know that in density, m = ρV

    Where;

    ρ = density of water = 1000 kg/m³

    V = volume of water

    So, potential energy is now given as;

    Potential energy = ρVgH = 1000 × V × 9.8 × 0.5 = (4900V) J

    Now, formula for energy of the battery is given as;

    E = qV

    We are given;

    q = 50 A.min = 50 × 60 = 3,000 C

    V = 12 V

    Thus;

    qV = 3,000 × 12 = 36,000 J

    E = 36,000 J

    At a 100% conversion rate, the energy of the water totally powers the battery.

    Thus;

    (4900V) = (36,000)

    4900V = 36,000

    V = 36,000/4900

    V = 7.35 m³

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