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A 24V battery of internal resistance of 10ohms is connected to a variable resistor. At what value of current drawn from battery the rate of heat produced by the resistor is maximum? Hence find its value.

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    Delivered power is a maximum when the internal and external resistances are equal, as I recall. Therefore
    Rexternal(optimum) = 10 ohms.
    Current with that external resistance
    = V/Rtotal = 24/20 = 1.2 Amps

    Maximum power produced in external resistor =
    I^2*Rexternal = (1.2)^2 * 10 = 14.40 W

    Check: If I use Rexternal = 11 ohms instead, Rtotal = 21 ohms and I = (24/21) = 1.143 A
    I^2 * Rext = 14.37 W

    If you use Rexternal = 9 ohms, your will still get a power less than 14.4 W

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