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A typical AAA battery can move 2000 C of charge at 1.5 V. How long will this run a 50 mW LED?
  1. 1000 minutes
  2. 120,000 seconds
  3. 15 hours
  4. 250 minutes
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OpenStax College Physics for AP® Courses Solution, Chapter 19, Problem 7 (Test Prep for AP® Courses) (1:26)

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This is College Physics Answers with Shaun Dychko. We are told that a AAA battery can move 2000 coulombs of charge at one and a half volts and the question is how long can it be used to run a 50 milli-watt light bulb or light emitting diode. So, we are going to re-arrange the power formula to solve for time because the question is asking us for time, how long will it run and then we will substitute for <i>w</i> by calculation the amount of energy stored in the battery. So, power is work over time and we solve for <i>t</i> by multiplying by <i>t</i> over <i>P</i> on both sides and we get time equal the work divided by power and the potential energy stored in the battery is the amount of charge multiplied by the energy per charge which is voltage, joules per coulomb and that is going to be the work factor in this equation. So, substitute for <i>w</i> by writing <i>q v</i> in its place and we have <i>t</i> equals <i>q v</i> over <i>P</i>. So, we have 2000 coulombs times 1.5 volt divided by 50 milli-watt which is ten to the minus three watts and that equals 60,000 seconds and that’s not an option listed here and so we have to convert into either minutes or hours. Lets try minutes first by multiplying by one minute for every 60 seconds and we get 1000 minutes, which is option A.