241-30_Lec-20 - Physics 241 Lecture 20 Y. E. Kim November...

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November 4, 2010 1 University Physics, Chapter 30 Physics 241 Lecture 20 Y. E. Kim November 4, 2010 Chapter 30, Sections 5, 6, and 7
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Series RLC circuit Energy and Power in AC Circuits Transformers November 4, 2010 Physics for Scientists & Engineers, Chapter 30 2
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November 4, 2010 University Physics, Chapter 30 3 sin R R V it R Resistance R 1 C X C sin( 90 ) C C C V X Capacitive Reactance X C   sin 90 L L L V X L XL Inductive Reactance X L Summary: Resistance and Reactance Time-varying emf Time-varying emf V R with resistor Time-varying emf V C with capacitor Time-varying emf V L with inductor V emf V max sin t
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November 4, 2010 University Physics, Chapter 30 4 Summary: Phase and Phasors
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November 4, 2010 University Physics, Chapter 30 5 Series RLC Circuit (1) We can describe the current flowing in the circuit and the voltage across the various components of series RLC circuit Resistor The voltage v R and current i R are in phase with each other and the voltage phasor V R is in phase with the current phasor I R Capacitor The current i C leads the voltage v C by 90 so that the voltage phasor V C will have an angle 90 less than I C and V R Inductor The current i L lags behind the voltage v L by 90 so that voltage phasor V L will have an angle 90 greater than I L and V R V R V L I L I R V C I C
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November 4, 2010 University Physics, Chapter 30 6 Series RLC Circuit (2) The voltage phasors for an RLC circuit are shown below The instantaneous voltages across each of the components are represented by the projections of the respective phasors on the vertical axis
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November 4, 2010 University Physics, Chapter 30 7 Series RLC Circuit (3) Kirchhoff’s loop rules tells that the voltage drops across all the devices at any given time in the circuit must sum to zero, which gives us 0 R C L R C L V v v v V v v v The voltage can be thought of as the projection of the vertical axis of the phasor V max representing the time- varying emf in the circuit as shown below In this figure we have replaced the sum of the two phasors V L and V C with the phasor V L - V C
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November 4, 2010 University Physics, Chapter 30 8 Series RLC Circuit (4): Impedance The sum of the two phasors ( V L V C ) and V R must equal V max (= V m ) so Now we can put in our expression for the voltage across the components in terms of the current and resistance or reactance We can then solve for the current in the circuit The denominator in the equation is called the impedance The impedance of a circuit depends on the frequency of the time-varying emf   2 22 m R L C V V V V     2 m m m L m C V I R I X I X   m 2 2 m LC V I R X X  Z R 2 X L X C 2 1 C X C L XL
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November 4, 2010 University Physics, Chapter 30 9 Series RLC Circuit (5): Phase The current (projection of the phasor I m ) flowing in an
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This note was uploaded on 11/28/2010 for the course PHY 222 taught by Professor Yu during the Spring '10 term at Beaufort County Community College.

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241-30_Lec-20 - Physics 241 Lecture 20 Y. E. Kim November...

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