30_Lec-20

30_Lec-20 - Physics 241 Lecture 20 Y. E. Kim November 4,...

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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 V i t Z Resistance 1 C X sin( 90 ) ± q Capacitive Reactance ² ³ sin 90 L ´ q Inductive Reactance Summary: Resistance and Reactance ± Time-varying emf ± Time-varying emf with resistor ± Time-varying emf with capacitor ± Time-varying emf with inductor emf max sin
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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 are in phase with each other and the voltage phasor V is in phase with the current phasor I ± Capacitor ± The current C leads the voltage by 90 q so that the voltage phasor will have an angle 90 q less than and ± Inductor ± The current L lags behind the voltage by 90 q so that voltage phasor will have an angle 90 q greater than and
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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) ± .LUFKKRII·V ORRS UXOHV 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 V v ±±± ² ³³ ± The voltage can be thought of as the projection of the vertical axis of the phasor max representing the time- varying emf in the circuit as shown below ± In this figure we have replaced the sum of the two phasors and with the phasor -
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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 ² C ) and R must equal max (= 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 2 22 m ³ ´ ± ² ± ² 2 m m IR IX ³ ´ ± ² m 2 2 I X ³´ Z 2 ³ ´ ± ² 2 1 { {
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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 alternating current circuit depends on the difference (X L - X C ) between the inductive reactance X L and the capacitive reactance X C ± We can express the difference between the inductive
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30_Lec-20 - Physics 241 Lecture 20 Y. E. Kim November 4,...

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