Lecture 23 preview april1

Lecture 23 preview april1 - Lecture 23 The LCR AC circuit...

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Lecture 23 The LCR AC circuit Today: I, P, and resonance in driven LCR Thursday: EM Waves Chapter 32 Exam #3 (practice exam now on ctools)
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Summary of the (R, C, and L) AC driven circuits V L =I m X L V C =I m X C V R =I m R ωt ω L X and C X L C ϖ = = 1 capacitive and inductive reactance in Ω Phasors
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The AC driven series LCR circuit Stimulus ξ(t) = ξ m cos(ωt+ φ ) (you control ξ m and ω) Response From our Kirchhoff’s loop analysis of the simple R, L and C driven AC circuits: ξ(t) = V R (t) + V L (t) + V C (t) ( the current in each is identical) x C L R x V V V notation Phasor in ) ( ) ( : + + = ξ
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Solution to LCR AC circuit Z X X R I X I X I R I m C L m m C m L m m m ξ = - + = - + = 2 2 2 2 ) ( ) ( ) ( V L =I m X L V C =I m X C =I m R ω L - C ) ( ) ( ) cos( ) ( 2 2 - + = = = impedance X X R Z t Z t i thus Z I C L m m m ϖ R C L R X X C L ϕ 1 ) tan( - = - = We are done! We know the circuit’s impedance Z to current flow and the relative phase angle φ between the driving EMF and the current.
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Lecture 23 preview april1 - Lecture 23 The LCR AC circuit...

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