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Lect13 handout
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2. Peak & RMS values in AC Circuits (REVIEW) When asking about RMS or Maximum values relatively simple expressions V R, max = I max R V C, max = I max X C V L, max = I max X L L R C
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4. I = I max sin(2 ft ) ( = 2 ft ) V L = I max X L sin(2 ft + ) V R = I max R sin(2 ft ) V C = I max X C sin(2 ft – ) Graphical representation of voltages I max X L I max R I max X C L R C
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9. Phase angle I = I max sin(2 ft ) V gen = I max Z sin(2 ft + ) is positive in this particular case. 2 ft I max I max Z 2 ft +
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11. ACTS 13.1, 13.2, 13.3 When does V gen = V R ? When does V gen = 0 ? The phase angle is: (1) positive (2) negative (3) zero? time 1 time 2 time 3 time 4
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13. ACT: Voltage Phasor Diagram At this instant, the voltage across the generator is maximum. What is the voltage across the resistor at this instant? 1) V R = I max R 2) V R = I max R sin( ) 3) V R = I max R cos( ) I max X L I max X C I max R V gen,max
14. Resonance and the Impedance Triangle R (X L -X C ) Z X L and X C point opposite. When adding, they tend to cancel! When X L = X C they completely cancel and Z = R. This is resonance! V max,gen = I max Z I max (X L -X C ) I max X L I max X C I max R V gen,max L R C
15. Resonance R is independent of f R X L increases with f X L X C decreases with f X C Z : X L and X C subtract Z X C = 1/(2 fC ) X L = 2 fL Resonance: X L = X C f 0 Z is minimum at resonance frequency!
16. Resonance R is independent of f X L increases with f X C decreases with f Z : X L and X C subtract Z X C = 1/(2 fC ) X L = 2 fL Resonance: X L = X C Current I max = V gen,max /Z f 0 Current is maximum at resonance frequency!
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Notas do Editor
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Note: VR=IR VL=IXL VC=IXC
Note the lagging and leading. Do demo with phasor board
Have them go back and fill in (4)
demo with RLC and oscilliscope: Note that XL > XC for f>f0 and vice versa.
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