chapter21_updated

chapter21_updated - 2/25/2009 Alternating Current Circuits...

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2/25/2009 1 Alternating Current Circuits and Electromagnetic Waves In a AC circuit, the instantaneous voltage drop across a circuit element is When this voltage is applied to a resistor, the instantaneous current is Lower case for instantaneous variables ) 2 sin( ) sin( ) ( max max ft V t V t v f T 1 Period ) ( t v max V ) Law s Ohm' ( ) ( ) ( R t v t i R AC source symbol ) sin( ) sin(
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2/25/2009 2 The current and the voltage reach their maximum (and minimum) values at the same time The current and the voltage are said to be in phase Instantaneous power ( always positive ): What is the averaged power? It is the averaged power that really matters heat, lighting, etc., and your electric bill ) 2 sin( ) ( ) 2 sin( ) ( max max ft I t i ft V t v R v R i t v t i t p 2 2 ) ( ) ( ) ( ) ( R V I max max The rmscurrent is the direct current that would dissipate the same amount of energy in a resistor as is actually dissipated by the AC current Alternating voltages can also be discussed in terms of rms values max max rms 707 . 0 2 I I I R I P avg 2 rms ) ( max max rms 707 . 0 2 V V V R V V I P avg 2 rms rms rms ) (
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2/25/2009 3 Instantaneous power is proportional to the instantaneous current squared Averaged power is proportional to R i t p 2 ) ( ) 2 sin( ) ( max ft I t i ) 2 ( sin 2 2 max 2 ft I i avg i ) ( 2 AC ammeters and voltmeters read rms values The household electricity has a rms voltage of 110 V. What is the peak voltage? Equations are in same form as in DC circuits R t i t v R I V R I V ) ( ) ( max max rms rms R v R i v i t p R V R I V I P R V R I V I P avg 2 2 2 max 2 max max max max 2 rms 2 rms rms rms ) ( ) ( ) ( ) ( ) ( V 156 2 110 max V
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2/25/2009 4 Initially, no resistance; current is the highest; charging starts Charge on the capacitor increases The voltage across the plates increases Current in the circuit decreases (a-b in figure) The applied instantaneous voltage decreases (d-f in figure) The capacitor starts discharging; Current is negative (b-e in figure) Charging effects impedes current flow Originally, the maximum currents in two circuits are the same. The frequency of the AC source is then doubled; the magnitude remains the same. Which of the following is true? max , max , max , max , max , max , 5 . 0 ) 3 ( 2 ) 2 ( ) 1 ( C R C R C R I I I I I I fC C X c 2 1 1
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2/25/2009 5 The capacitor will limit the current flow i.e., it has certain impedance , called capacitive reactance The voltage across the capacitor lags behind the current by 90° fC C X c 2 1
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chapter21_updated - 2/25/2009 Alternating Current Circuits...

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