The formula for the power output P of a battery is P = VI – RI2, where V is the electromotive force in volts, R is the resistance in ohms, a

Question

The formula for the power output P of a battery is P = VI – RI2, where V is the electromotive force in volts, R is the resistance in ohms, and I is the current in amperes. Find the current that corresponds to a maximum value of P in a battery for which V = 12 volts and R = 0.5 ohm.

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Diễm Kiều 3 years 2021-08-22T13:26:36+00:00 2 Answers 82 views 0

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    0
    2021-08-22T13:27:47+00:00

    Answer:

    The current that corresponds to a maximum value of P in a battery = 12 A.

    That maximum power is 72 W.

    Explanation:

    The power output of a battery is given as

    P = VI – RI²

    V = 12 V

    R = 0.5 ohm

    P(I) = 12I – 0.5I²

    The current that corresponds to a maximum value of P in the battery

    P(I) = 12I – 0.5I²

    For any function, at maximum point, the derivative of the dependent variable with respect to the independent variable is equal to 0.

    At maximum power,

    P'(I) = (dP/dI) = 0

    P'(I) = (dP/dI) = 12 – I = 0

    I = 12 A

    That maximum power is

    P(I=12) = 12(12) – 0.5(12²) = 144 – 72 = 72 W

    Hope this Helps!!!

    0
    2021-08-22T13:27:54+00:00

    Explanation:

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