Question
What will be the ratio of the resistance of a 120 W, 220 V lamp to that of a 100 W, 110 V lamp?
Final Answer
Solution video
OpenStax College Physics for AP® Courses, Chapter 20, Problem 15 (Test Prep for AP® Courses)
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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 R. We can solve this for R by multiplying by R over P 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 R two is voltage squared over power two. We can take the ratio of these resistances by going V one squared over P one multiplied by reciprocal of R two which is P two over V one squared, sorry, P two over V two 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.