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Unformatted text preview: Lecture 31 (April 3, 2009): AC Circuits (conclusion): ► Forced oscillation of a series RLC circuit ► Power in ac circuits ► Transformers Maxwell’s Equations (Chapter 32): ► Gauss’ Law for magnetic fields ► Induced magnetic fields ► Displacement current ► Maxwell’s equations and em radiation Summary of phase and amplitude relations for ac currents and voltages: Note that both X C and X L are functions of ω d , but X C decreases with increasing frequency while X L increases with increasing frequency. Therefore the behavior of an ac circuit containing both X C and X L can vary greatly with frequency. Mnemonic: ELI the ICE man Phasors … are a way to represent geometrically such time varying quantities as v R , v L , v C and i R . Phasors have the following properties: •Angular speed = angular frequency ω d ; direction = ccw • Length = amplitude of the alternating quantity • Projection of each phasor on the vertical axis represents the value of the alternating quantity at time t • Rotation angle = phase of the alternating quantity at time t Series RLC circuit: ( 29 ( 29 Applied emf is: sin R, L, and C all see same current sin m d d t i I ϖ ϖ φ = = E E (a) Phasor representing the current i (b) Phasors representing the voltages across L, R, and C (c) Phasor representing the applied emf that drives the current (d) The emf phasor is the vector sum of the three voltage phasors R C C L L V IZ V IX V IX = = = Series RLC circuit (continued): ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 m 2 2 2 2 2 2 (loop rule) or impedance Z current amplitude 1 phase constant tan R C L R L C L C m m L C L C m d d L C L C R v v v V V V IR IX IX I Z R X X R X X I R L C V V X X V R ϖ ϖ ϕ = + + = + = + = = + = + = +...
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 Spring '08
 Koehler
 Current, Force, Power, Magnetic Field, series rlc circuit

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