Question
If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an RC discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one RC constant is acceptable, and given that the flash is driven by a $600\textrm{ }\mu\textrm{F}$ capacitor, what is the resistance in the flash tube?

$3.33\textrm{ m}\Omega$

# OpenStax College Physics for AP® Courses, Chapter 21, Problem 74 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. Often when taking a photo of fast subjects, a quick shutter speed is used to limit the exposure and limit blurring but when you are taking about super fast things like a bullet going at 500 meters per second, it's not possible to have a shutter open and close quick enough to prevent blurs. So a different strategy then is to have a very quick pulse of light, a very quick flash and that's the strategy being used in this question. So we are told that it's acceptable to have an amount of of time equal to the time constant RC such that the bullet moves 1 millimeter and given that it's traveling 500 meters per second, and we'll figure out how much time that is using our regular kinematics formula— distance equals speed times time— and we'll solve this for t by dividing both sides by v. So the time that is equal to the time constant we are told is the distance divided by the speed. So with distance divided by speed equaling the time constant RC, we can solve for R by dividing both sides by the capacitance. So the resistance then is the distance, which is 1.00 millimeter, divided by the capacitance, which is 600 microfarads, times 500 meters per second and that is 3.33 milliohms.