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Unformatted text preview: Lecture 23 Lecture 23 Physics 2102 Jonathan Dowling AC Circuits: Power AC Circuits: Power Electromagnetic waves Electromagnetic waves Driven RLC Circuits: Driven RLC Circuits: Summary Summary I m = E m Z 2 2 ( ) L C Z R X X = + tan L C X X R  = E = E m sin( d t); I = I m sin( d t  ) X C =1/( d C), X L = d L At resonance: X L =X C ; d 2 =1/LC; =0; Z =R (minimum), E m =E m /R (maximum) Power in AC Circuits Power in AC Circuits E = E m sin( d t) I = I m sin( d t  ) Power dissipated by R: P = I 2 R P = I m 2 R sin 2 ( d t  ) P average = (1/2) I m 2 R = I rms 2 R I rms = E rms Z P average = E rms Z ae I rms R = rms I rms R Z ae = E rms I rms cos f cos = Power Factor Maximum power dissipated when cos = 1. The average of sin 2 over one cycle is : Power in AC Circuits: Example Power in AC Circuits: Example Series RLC Circuit: R = 15 , C = 4.7 F, L = 25mH. The circuit is driven by a source of E rms = 75 V and f = 550 Hz. At what average rate is energy dissipated by the resistor? = + = 29 ) 1 ( 2 2 C L R Z d d w w s rad Hz d / 3457 ) 550 )( 2 ( = = P average = I rms 2 R = E rms Z ae 2 R = 75 V 29W ae 2 (15W) =100.3 W Power in AC circuits Power in AC circuits Whats the average power dissipated in the following circuits? River Bend power plant LSU Transmission lines 735KV Distance~30 miles~50km Resistance 0.22 /km Power capacity 936 MW If the power delivered is constant, we want the highest voltage and the lowest current to make the delivery efficient! At home, however, we dont want high voltages! We use transformers....
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This note was uploaded on 11/18/2011 for the course PHYSICS 2102 taught by Professor Dowling during the Fall '10 term at LSU.
 Fall '10
 DOWLING
 Physics, Power

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