2049_ch31A - Chapter 31: RLC Circuits PHY2049: Chapter 31 1...

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PHY2049: Chapter 31 1 Chapter 31: RLC Circuits
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PHY2049: Chapter 31 2 Topics Î LC Oscillations ± Conservation of energy Î Damped oscillations in RLC circuits ± Energy loss Î AC current ± RMS quantities Î Forced oscillations ± Resistance, reactance, impedance ± Phase shift ± Resonant frequency ± Power Î Transformers ± Impedance matching
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PHY2049: Chapter 31 3 LC Oscillations Î Work out equation for LC circuit (loop rule) Î Rewrite using i = dq/dt ± ω (angular frequency) has dimensions of 1/t Î Identical to equation of mass on spring L C 0 qd i L Cd t −− = 22 2 00 dq q dq Lq C dt dt ω +=⇒ + = 2 dx mk x x dt dt += + = 1 LC ω= k m
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PHY2049: Chapter 31 4 LC Oscillations (2) Î Solution is same as mass on spring oscillations ± q max is the maximum charge on capacitor ± θ is an unknown phase (depends on initial conditions) Î Calculate current: i = dq/dt Î Thus both charge and current oscillate ± Angular frequency ω , frequency f = ω /2 π ± Period: T = 2 π / ω ± Current and charge differ in phase by 90 ° () max cos qq t ω θ
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This note was uploaded on 04/12/2008 for the course PHY 2049 taught by Professor Any during the Fall '08 term at University of Florida.

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2049_ch31A - Chapter 31: RLC Circuits PHY2049: Chapter 31 1...

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