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Filament Lamps - Quick Question

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    Name:  june 2010 phya1.PNG
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    Was just hoping for a quick explanation for 6cii from this question.
    I follow everything on the mark scheme, up until the part where it says that the power requirement of the lamp is higher?
    I really don't understand why, and would greatly appreciate some help

    The student has used the resistance at 12 V to estimate the power at 6 V using


    however the resistance at 6 V is not the same as the resistance at 12 V due to the filament having a different temperature... s/he's overestimated the resistance.

    lower number on the bottom of the fraction means the value for P is higher
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