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A large superconducting magnet, used for magnetic resonance imaging, has a 50.0 H inductance. If you want current through it to be adjustable with a 1.00 s characteristic time constant, what is the minimum resistance of system?
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Final Answer

$50.0 \Omega$

Solution Video

OpenStax College Physics Solution, Chapter 23, Problem 71 (Problems & Exercises) (0:33)

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Video Transcript

This is College Physics Answers with Shaun Dychko. A circuit has an inductor in it with inductance of 50 henrys and the characteristic time constant we want is one second and so the question is what resistance should the circuit have? So, the time constant for an RL circuit is inductance divided by resistance and we can solve for <i>R</i> by multiplying both sides by <i>R</i> over tau and then we will get <i>R</i> equals inductance divided by time constant. So, that’s 50 henrys divided by 1 second which is 50 ohms.