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

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

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 + 

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

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!