lecture22

lecture22 - 22 AC current 1 General ideas R C L 2 = 2f = T...

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22. AC current 1) General ideas R L C ( 29 t V t v ϖ cos = ( 29 ( 29 ( 29 ( 29 ? ? ? ? - - - - t v t v t v t i L C R 2) Phasor diagrams t ϖ t V ϖ cos t V ϖ sin V – length of phasor phasor T f π π ϖ 2 2 = =

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23. AC circuits and reactance 1) Resistor ( 29 t I t i ϖ cos = ( 29 ( 29 t V t IR R t i t v ϖ ϖ cos cos = = = 2 I I rms = 2 V V rms = rms rms rms rms V I R V R I R I t R I R i P = = = = = = 2 2 2 2 1 2 2 2 cos ϖ Current & voltage are in phase t 2) Root-mean-square (rms) values 2 i I rms For sin waves: This definition is convenient for any circuit V I t I i ϖ cos = t V v ϖ cos =
2) Inductor ( 29 ) 90 cos( sin + = - = t V t I L t v ϖ ϖ ϖ t I V L rms rms rms L X I I L V IX I L V = = = = ϖ ϖ The current lags the voltage by 90° fL L X L π ϖ 2 inductive reactance: If the frequency is low then the reactance is small! If the frequency is high then the reactance is big! ( 29 = - = 0 cos dt di L v t I t i ϖ V I t ϖ t I i ϖ cos = ( 29 2 / cos π ϖ + = t V v V I t ϖ

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( 29 ( 29 ) 90 cos( sin - = = = t V t C I C t q t v ϖ ϖ ϖ t I V C rms rms rms C X I L I V IX L I V = = = = ϖ ϖ The current leads the voltage by 90° fC C X C π ϖ 2 1 1 capacitive reactance: If the frequency is low then the reactance is big If the frequency is high then the reactance is small! 3) Capacitor
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