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Math Help - application 3

  1. #1
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    application 3

    A direct current generator has an electromotive force of E volts and an internal reistance of r ohms. E and r are constants. If R ohms is the external resistance, the total resistance is (r + R) ohms and if P watts is the power then
    [html]
    ER
    P = ----------
    (r + R)
    [/html]
    What external resistance will consume the most power?
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  2. #2
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    Quote Originally Posted by cazimi View Post
    A direct current generator has an electromotive force of E volts and an internal reistance of r ohms. E and r are constants. If R ohms is the external resistance, the total resistance is (r + R) ohms and if P watts is the power then
    [html]
    ER
    P = ----------
    (r + R)
    [/html]
    What external resistance will consume the most power?
    You want to solve:

    dP/dR = 0,

    well:

    dP/dR = E^2/(r+R)^2 -2 E^2 R/(r+R)^3 = 0

    which may be rearranged (as E != 0) to:

    2R/(r+R) = 1,

    or R=r.

    RonL
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