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14 April, 00:29

What inductance l would be needed to store energy e=3.0kwh (kilowatt-hours) in a coil carrying current i=300a?

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  1. 14 April, 00:31
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    The formula for the energy stored in the magnetic field of an inductor is:

    E = (1/2) (inductance) (current) ².

    In the present situation:

    Energy = (3 kilo-watt-hour) x (1,000 / kilo) x (joule/watt-sec) x (3,600 sec/hr)

    = (3 · 1000 · 3,600) (kilo·watt·hr·joule·sec / kilo·watt·sec·hr)

    = 1.08 x 10⁷ joules.

    Now to find the inductance:

    E = (1/2) (inductance) (current) ²

    (1.08 x 10⁷ joules) = (1/2) (inductance) (300 Amp) ²

    (2.16 x10⁷ joules) = (inductance) (300 Amp) ²

    Inductance = (2.16 x10⁷ joules) / (300 Amp) ²

    = 2.16 x10⁷ / 90,000 Henrys

    I get 240 Henrys.

    This is a big inductance. Possibly the size of your house.

    To get a big inductance, you want to wind the coil

    with a huge number of turns of very fine wire, in

    a small space.

    In this case, however, if you plan on running 300A through

    your coil, it'll have to be wound with a very thick conductor ...

    like maybe 1/4-inch solid copper wire, or even copper tubing,

    You have competing requirements.

    There are cheaper, easier, better ways to store 3 kWh of energy.

    In fact, a quick back-of-the-napkin calculation says that

    3 or 4 car batteries will do the job nicely.
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