Question

Two resistors, with resistances R and 2R are connected to a voltage source as shown in this figure. If the power dissipated in R is 10 W, what is the power dissipated in 2R?

- 1 W
- 2.5 W
- 5 W
- 10 W

Final Answer

(c)

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 21, Problem 4 (Test Prep for AP® Courses)

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Video Transcript

This is College Physics Answers with Shaun Dychko. Two resistors are connected in parallel to some voltage source here and we are told that the power dissipated in this resistor

*R*is 10 watts and the question is knowing that what will be the power dissipated in this resistor which has a resistance 2 times*R*? So the power dissipated in the resistor*R*is the voltage across it squared divided by its resistance and that is 10 watts we are told. The power dissipated across the 2*R*resistor is going to be the same voltage because resistors connected in parallel have the same voltage drop across them so the*V*is the same in this case as it is before and it's being divided by this new resistance 2*R*. But*V squared*over*R*is 10 watts so we can substitute*V squared*over*R*as 10 watts and we're still dividing it by 2 so our answer is 5 watts. And we expected less power to be dissipated because with a greater resistance, given the same voltage, we'll expect less current through here. Anyway the answer is (c).