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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

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

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

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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

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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

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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) qq q C

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p212c32: 7 R XLXL XCXC

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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 )

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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

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p212c32: 10

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p212c32: 11 LRC series circuit example

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p212c32: 12 Power

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

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p212c32: 14 I oo HW: add Q, calculations to all rlc series HW problems

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p212c32: 15 LRC series circuit example (more)

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p212c32: 16 LRC series circuit example (and more)

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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 )

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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 )

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p212c32: 19

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p212c32: 20 LRC parallel circuit example

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p212c32: 21 Parallel “Resonance” log( )

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p212c32: 22

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

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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

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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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