$3.3$

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This is College Physics Answers with Shaun Dychko. The power dissipated by resistance in terms of voltage and resistance is voltage squared divided by <i>R</i>. We can solve this for <i>R</i> by multiplying by <i>R</i> over <i>P</i> on both sides. We get resistance is voltage squared over power. So in the first case we have voltage one squared over power one, and in the second case <i>R two</i> is voltage squared over power two. We can take the ratio of these resistances by going <i>V one</i> squared over <i>P one</i> multiplied by reciprocal of <i>R two</i> which is <i>P two</i> over <i>V one</i> squared, sorry, <i>P two</i> over <i>V two</i> squared I should say. So we have 220 volts for resistance one squared, divided by 120 watts, multiplied by the power of the second thing which is 100 watts divided by the voltage of the second thing, 110 volts squared. This gives 3.3.