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Building on the current and rate-of-change-of-current equations derived for an LR circuit, Bobby determines the circuit's time constant: matching the derived equations to the standard exponential form shows the time constant equals inductance divided by resistance, tau = L/R. Bobby then explains what the time constant actually means: one time constant is the amount of time it takes for a 63.2 percent change to occur. Substituting one time constant into the current equation confirms that after one time constant the current has risen to 63.2 percent of its final, maximum value (since e to the power negative 1 equals 0.368, and 1 minus 0.368 equals 0.632); substituting into the rate-of-change equation shows the rate of change of current has fallen by 63.2 percent from its initial, maximum value. The video closes by relating both results back to their graphs of current and its rate of change over time. http://www.flippingphysics.com/lr-circuit-time-constant.html Next Video: Analogies Between LR Circuits and Falling Objects http://www.flippingphysics.com/lr-circuit-falling.html Thank you to Beth Baran and the rest of my wonderful Patreon supporters. Please consider supporting me monthly at http://patreon.com/FlippingPhysics Thank you to Julie Langenbrunner, Carl Hansen, Lou Jisonna, and Jonathan Everett for being my Quality Control Team for this video. http://flippingphysics.com/quality-control.html Chapters: 0:00 Introduction 0:30 Determining the LR circuit time constant 1:20 What is the time constant? 1:45 The Graphs!! Curriculum Standards: AP Physics C: Electricity and Magnetism, Unit 13 Electromagnetic Induction, Topic 13.5 Circuits with Resistors and Inductors (LR Circuits) 13.5.A.3: "The time constant is a significant feature of the behavior of an LR circuit." 13.5.A.3.i: "The time constant of a circuit is a measure of how quickly an LR circuit will reach a steady state and is described with the equation tau = L/R." 13.5.A.3.iii: "For an inductor that has zero initial current, the time constant represents the time required for the current in the inductor to reach approximately 63 percent of its final asymptotic value." JEE Main & NEET, Unit 14 Electromagnetic Induction and Alternating Currents "Electromagnetic induction: Faraday's law, induced emf and current, Lenz's law, eddy currents, self and mutual inductance." #LRcircuit #TimeConstant #Derivation
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