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Alternating Current

. I.  t. i(t)=I cos  t. Alternating Current. Voltage Source : v(t) = V cos  t Current Source : i(t) = I cos  t. Phasors: a graphical method for (combinations) of trigonometric functions. Full Wave Rectifier. G. I rav = (2/  I. i. t. RMS values. i 2 (t).

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Alternating Current

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  1. I t i(t)=I cost Alternating Current Voltage Source : v(t) = V cos t Current Source : i(t) = I cos t Phasors: a graphical method for (combinations) of trigonometric functions

  2. Full Wave Rectifier G Irav = (2/I i t

  3. RMS values i2(t) Root-Mean-Square: i(t)

  4. R v(t)= Vcos(t)   Current is in phase with Voltage I V=IR t i(t)=I cost v(t)=V cost

  5. L i(t)= Icos(t)   I V=IXL t Current lags Voltage Voltage leads Current i(t)=I cost v(t)=V cos (t+90°)

  6. q C i(t)= Icos(t) q   I t V=IXL i(t)=I cost v(t)=V cost Current leads Voltage Voltage lags Current

  7. XC XL R 

  8. L-R-C Circuit i = I cos(t) vL(t)=IXLcos(t+) L • i(t)=Icos(t) • v(t)=Vcos(t+) • = IXLcos(t+) • + IRcos(t) • + IXCcos(t) R vR(t)=IRcos(t) vC(t)=IXCcos(t) C

  9. VC=IXC VL=IXL VL- VC =IX I V=IZ  VR=IR VL=IXL VC=IXC V=IZ VL- VC =IX  I VR=IR • v(t)=Vcos(t+) • = IXLcos(t+) • + IRcos(t) • + IXCcos(t) • Z2 = R2+ X2 • =R2+ (XLXC)2 • tan() = X/R

  10. LRC series circuit example

  11. Power

  12. Series Resonance log() I = V/Z log()

  13. I o  HW: add Q,  calculations to all rlc series HW problems

  14. LRC series circuit example (more)

  15. LRC series circuit example (and more)

  16. Parallel L-R-C Circuit iL(t)= ILcos(t-90° ) iC(t)= ICcos(t ) iR(t)= IRcos(t) R C L v(t)= Vcos(t) • i = I cos(t+f) • = IL cos(t-90° ) • + IR cos(t) • + IC cos(t) • = V/XLcos(t-90° ) • + V/R cos(t) • + V/XC cos(t)

  17. IL • i = I cos(t+f) • = IL cos(t-90° ) • + IR cos(t) • + IC cos(t) IC IC- IL V I=V/Z  IR IC I2 = IR2+ (ICIL)2 tan() = (ICIL)/IR IL I=V/Z IC- IL  V IR

  18. LRC parallel circuit example

  19. Parallel “Resonance” log() log()

  21. B N2 V2,I2 Secondary N1 V1,I1 Primary Transformers: Ferromagnetic Materials Strengthen Flux

  22. Transformers B N1 V1,I1 Primary N2 V2,I2 Secondary N2 >N1 => V2 > V1 Step-Up Transformer N2 <N1 => V2 < V1 Step-Down Transformer

  23. A coffee maker from Europe is designed to operate on a 240-V line (rms) to obtain 960W of power. • (a) Determine what characteristics are needed by a transformer so that the proper delivery voltage be obtained from the US standard voltage of 120 V (rms)? • (b) What current is drawn at the secondary? • (c) What is the resistance of the coffee maker? • (d) What current is drawn from the 120 V outlet by the primary? • (e) What is the power delivered by the 120 V source?

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