# P212c32: 1 Alternating Current Voltage Source : v(t) = V cos  t Current Source : i(t) = I cos  t Phasors: a graphical method for (combinations) of trigonometric.

## Presentation on theme: "P212c32: 1 Alternating Current Voltage Source : v(t) = V cos  t Current Source : i(t) = I cos  t Phasors: a graphical method for (combinations) of trigonometric."— Presentation transcript:

p212c32: 1 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   t I i(t)=I cos  t

p212c32: 2 G Full Wave Rectifier i t I rav = (2/  I

p212c32: 3 RMS values Root-Mean-Square: i(t) i 2 (t)

p212c32: 4   t I i(t)=I cos  t R   v(t)= Vcos(  t) V=I R v(t)=V cos  t Current is in phase with Voltage

p212c32: 5 L   i(t)= Icos(  t)   t I i(t)=I cos  t V=IX L v(t)=V cos (  t+90°) Current lags Voltage Voltage leads Current

p212c32: 6   t I i(t)=I cos  t V=IX L v(t)=V cos  t Current leads Voltage Voltage lags Current i(t)= Icos(  t)   qq  q C

p212c32: 7 R XLXL XCXC 

p212c32: 8 L-R-C Circuit i = I cos(  t) L C R i(t)=Icos(  t) v(t)=Vcos(  t+  ) = IX L cos(  t+  ) + IRcos(  t) + IX C cos(  t  ) v L (t)=IX L cos(  t+  ) v R (t)=IRcos(  t) v C (t)=IX C cos(  t  )

p212c32: 9 v(t)=Vcos(  t+  ) = IX L cos(  t+  ) + IRcos(  t) + IX C cos(  t  )  I V R =IR V L =IX L V C =IX C V L - V C =IX V=I Z  I V R =IR V L =IX L V C =IX C V L - V C =IX V=I Z Z 2 = R 2 + X 2 = R 2 + (X L  X C ) 2 tan(  ) = X/R

p212c32: 10

p212c32: 11 LRC series circuit example

p212c32: 12 Power

p212c32: 13 Series Resonance log(  ) I = V/Z

p212c32: 14 I  oo HW: add Q,  calculations to all rlc series HW problems

p212c32: 15 LRC series circuit example (more)

p212c32: 16 LRC series circuit example (and more)

p212c32: 17 Parallel L-R-C Circuit i L (t)= I L cos(  t-90° ) L CR i = I cos(  t+  ) = I L cos(  t-90° ) + I R cos(  t) + I C cos(  t  ) i R (t)= I R cos(  t) i C (t)= I C cos(  t  ) v(t)= Vcos(  t) = V/X L cos(  t-90° ) + V/R cos(  t) + V/X C cos(  t  )

p212c32: 18  V IRIR ILIL ICIC I C - I L I=V/Z  V IRIR ICIC ILIL I C - I L I=V/Z I 2 = I R 2 + (I C  I L ) 2 tan(  ) = (I C  I L )/I R i = I cos(  t+  ) = I L cos(  t-90° ) + I R cos(  t) + I C cos(  t  )

p212c32: 19

p212c32: 20 LRC parallel circuit example

p212c32: 21 Parallel “Resonance” log(  )

p212c32: 22 

p212c32: 23 Transformers: Ferromagnetic Materials Strengthen Flux N 1 V 1, I 1 Primary N 2 V 2, I 2 Secondary B

p212c32: 24 Transformers N 1 V 1, I 1 Primary N 2 >N 1 => V 2 > V 1 Step-Up Transformer N 2 V 2 < V 1 Step-Down Transformer N 2 V 2, I 2 Secondary B

p212c32: 25 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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