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Math Help - Quadratic word problems

  1. #1
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    Quadratic word problems

    In a DC electrical circuit, the relationship between the power used by a device, P (in Watts, W), the electric potential difference (voltage), (in volts,V), the current,I (in amperes, A), and hte resistance, R (in ohms) is represented by the formula P=IV-I^2R.
    represent the relationship between the poer and the current when the electrical potential is 24V and the resistance is 1.5Ohms. Determine the current needed in order for teh device to use hte maximum amount of power.

    What? as a grade 12 student i am soo lost!

    Please help!
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  2. #2
    MHF Contributor
    Joined
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    I'm not much into Physics now (no practice) but it is all given in your question.

    P = IV -(I^2)R
    P = I(24) -(I^2)(1.5)
    P = 24I -1.5I^2

    If you know derivatives,
    dP/dI = 24 -3I
    For maximum P, dP/dI = 0
    0 = 24 -3I
    3I = 24
    I = 24/3 = 8 amperes ----------------answer.

    If you are not into derivatives yet, use Analytic Geometry, or the properties of a parabola.
    y = ax^2 +bx +c
    at vertex, x = -b/2a

    P = -1.5I^2 +24I +0 ---------(i)
    at vertex, I = -24 / 2(-1.5) = -24 / -3 = 8 amperes
    Since the parabola (i) has a negative coefficient for its I^2, then the parabola opens downward, so its vertex is for maximum P.
    Therefore, I = 8 amperes for maximum P. ------answer.
    Last edited by ticbol; September 23rd 2007 at 08:57 PM.
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