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# zhang21 - Alternating Current Circuits and Electromagnetic...

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2/21/2010 1 Alternating Current Circuits and Electromagnetic Waves The current in our household electric circuit alternating between positive and negative values with time AC current The instantaneous voltage across the circuit is related to its maximum value by The frequency f=60 Hz in the US. Lower case for instantaneous value Upper case for maximum value Use radians (Rad.) to calculate trigonometry functions. f T 1 Period ) ( t v max V ) 2 sin( ) sin( ) ( max max ft V t V t v

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2/21/2010 2 Instantaneous voltage: The instantaneous current through the resistor ) ( t v max V ) Law s Ohm' ( ) ( ) ( R t v t i R AC source symbol ) sin( ) sin( max max t I t R V R V I max max ) 2 sin( ) sin( ) ( max max ft V t V t v The current and the voltage are said to be in phase they reach their maximum (and minimum) values at the same time Instantaneous power ( always positive ): What is the averaged power? It is the averaged power that really matters heat, lighting, etc., and your electric bill R v R i t v t i t p 2 2 ) ( ) ( ) ( ) ( ) sin( ) ( ) sin( ) ( max max t I t i t V t v R V I max max
2/21/2010 3 Need to introduce some kind of average value for AC circuit The root-mean-square (rms) current: The rms voltage: The average power is then max max rms 707 . 0 2 I I I max max rms 707 . 0 2 V V V R V R I V I P avg 2 rms 2 rms rms rms ) ( ) ( R I V rms rms : holds always law s Ohm' AC ammeters and voltmeters read rms values The household electricity in the US has a rms voltage of

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zhang21 - Alternating Current Circuits and Electromagnetic...

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