Phys 0175 - Lecture 29

# Phys 0175 - Lecture 29 - Lecture 29(Mar 30 2009 Induction...

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Lecture 29 (Mar. 30, 2009): Induction and Inductance (cont’d): R-L circuits Energy stored in a magnetic field Mutual induction Electromagnetic Oscillations (Ch. 31): L-C oscillations; analogy with block-on-a-spring Charge, current, and energy in an L-C circuit as functions of time Damped oscillations in an R-L-C circuit

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R-L Circuits: What happens when a resistor R and an inductor L in series are first connected to an emf (S→a)? The induced emf in the inductor L will initially oppose the increasing current passing through it. But a long time later, when the current has reached its final value, the inductor acts just like a piece of ordinary connecting wire. When the switch S is changed from position a to position b, the inductor L will again oppose the changes in the current passing through it, until the current no longer changes.
Apply the loop rule: 0 or the solution is 1 where time constant L t L di iR L dt di L Ri dt i e R L R τ - - - + = + = = - = E E E V R = i*R V L = E -V R

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Assume that the switch has been in position a sufficiently long so that the current through the inductor has reached its final constant value. When the switch position is then changed from a to b, the magnetic field energy stored in the inductor will cause a current to flow again. The loop rule gives the equation: The solution of this equation is: ( τ L = L/R) (decay of current) 0 L L t t i e i e R τ - - = = E 0 di L iR dt + =
Energy Stored in an Inductor: Establishing a current in an inductor requires an input of

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## This note was uploaded on 04/06/2009 for the course PHYS 0175 taught by Professor Koehler during the Spring '08 term at Pittsburgh.

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Phys 0175 - Lecture 29 - Lecture 29(Mar 30 2009 Induction...

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