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Phys 0175 - Lecture 30

Phys 0175 - Lecture 30 - Lecture 30(April 1 2009 EM...

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Lecture 30 (April 1, 2009): EM Oscillations, AC Circuits (cont’d): Damped oscillations in an R-L-C circuit Alternating current Resistive, capacitive, and inductive load Forced oscillation of a series R-L-C circuit

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R-L-C Series Circuit: Every real inductor actually also has resistance R, so L-C circuits are really R-L-C circuits. The presence of R will cause energy to be dissipated (through i 2 R losses).
R-L-C Series Circuit: The value of R determines how rapidly the energy is dissipated and hence the oscillatory behavior of the R-L-C circuit. 2 2 1 ' 4 R LC L ϖ = - R 2 = 4L/C (a) underdamped (b) critically damped (c) overdamped 2 2 1 0 4 R LC L - f 2 2 1 0 4 R LC L - = 2 2 1 0 4 R LC L - p

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Damped oscillations in an R-L-C circuit: ( 29 ( 29 2 2 2 2 2 2 2 2 2 2 2 Substituting i= and 1 0 This equation has solution cos ' where ' 2 B E Rt L Li q U U U C dU di q dq i R Li dt dt C dt dq di d q yields dt dt dt d q dq L R q dt dt C q Qe t R L ϖ φ ϖ ϖ -
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Phys 0175 - Lecture 30 - Lecture 30(April 1 2009 EM...

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