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AC Calculations W12 D2 What s Happening I gave a test with a problem you should have been able to think your way through After the exam I wanted to explain AC circuits to you but you just kept talking among yourselves You lost about 20 30 minutes of explanation Today I will cover the material in a very cursory way You can learn it from the book since listening didn t seem to occur To be sure you DO read the text there is a WebAssign that will be due next week Do the problems Today we will have a brief discussion of AC circuits and how they work I will assume you read the beginning of the chapter What s Happening Exam III Done AC Discussion Probably NO experiment WebAssign You will probably do the experiment on Friday What the heck is RMS Read the first three sections of chapter 23 and do the problems assigned They will be due on Wednesday I am not sure when I will grade the papers Probably over the weekend unless something else pops up Attitude There is a population in the class who doesn t like physics and seems to blame me Not liking physics is NOT an excuse to do poorly but this group seems to be doing exactly this There is another group in this class that works hard and tries to understand the material They are doing fairly well The first group tends to be hostile the other wants to learn and make the best of the situation Last semester nobody failed this course This is NOT true for this class Learning I do not teach you You learn by Doing the Units to the best of your ability Clear and not sloppy Not Copying from your neighbors but written AFTER and independently of your team s completion of the work Show some individual thinking Think your way through problems rather than complain about them This is college and not High School I know that you think I am a poor instructor You are adults Act that way This may be true but learning is totally YOUR responsibility In this format it is your responsibility learn Think about it it isn t too late do well Read that stuff and learn it it WILL be on the final examination Approximate Calendar Novemb er Decemb er Monday Wednesd ay 15 Short Review Unit 15 AC 17 EXAM 3 Unit 15 AC 19 Unit 15 AC 22 Unit 16Optics 24 QUIZ Unit 16Optics 26 29 Unit 1718 Optics 1 Unit 18 Optics 3 QUIZ Unit 18 Optics 6 LAST DAY EXAM 4 Friday Saturday Holida y 11 FINAL The Sine 2 Average Value of Sine sine 0 POWER I2R so average I2 is important Average value of Sin2 sin 2 q cos 2 q 1 sin 2 q cos 2 q 1 1 sin q 2 2 rms sin q 2 sin q 1 2 Power I 2 R I 02 RSin 2wt Power 0 707 I 02 R I 02 R 2 0 707 Your outlet delivers 120 Volts rms 60 Hz What is the peak voltage A B C D 120 V 240V 170V 340V V peak V peak Vrms 2 1 41 120 170V w 2p f 376sec 1 V 170sin 376t f Amplitude Sine Cosine LAST TIME sin t cos t 2 cos t sin t 2 2 f Draw these graphs and convince yourself that this makes sense I was going to discuss this mayerial AC Applied voltages This graph corresponds to an applied voltage of V cos t Because the current and the voltage are together in phase this must apply to a Resistor for which Ohm said that I V the ac phasor i I cos t The resistor again v iR IR cos t VR Phasor diagram Resistor Length Maximum Voltage IR Length Max Current here comes trouble We need the relationship between I the current through and vL the voltage across the inductor From the last chapter Di vL L Dt unless you have taken calculus check it out means change or difference thing thing final thing initial t t final t initial sovL L Di Dt L D I cos wt L I cos wt Dt cos wt Dt Dt cos wt cos wDt sin wt sin wDt cos wt LI cancel vL Dt When t gets very small cos t goes to 1 Let s look at what s left sin t sin t vL LI t r lim 0 sin 1 this leaves v L sin t The resistor voltage looked like a cosine so we would like the inductor voltage to look as similar to this as possible So let s look at the following f t A sin t A Amplitude 1 here f t A sin t 2 A Amplitude 1 here sin t cos t 2 result inductor vL LI sin t sin t cos t 2 I is the MAXIMUM current in the circuit sin t cos t 2 vL LI cos t 2 Resistor comparing v iR IR cos t vR max I R inductor vL LI cos t 2 vL Max I L L looks like a resistance XL L Reactance OHMS For the inductor vL Max I L IX L VL FOR THE RESISTOR vR Max IR VR slightly confusing point We will always use the CURRENT as the basis for calculations and express voltages with respect to the current What that means We describe the current as varying as i I cos t and the voltage as v Vcos t where is the phase shift between the current and the voltage the vL LI cos t phasor 2 vL LI cos t 2 cos t sin t 2 direction t t remember for ac series circuits In the circuit below R 30 and L 30 mH If the angular frequency of the 60 volt AC source is is 3 K Hz WHAT WE WANT TO DO a calculate the maximum current in the circuit b calculate the voltage across the inductor c Does Kirchoff s Law Work R 30 3 KHZ E 60V L 30 mH R 30 R 30 XL L 90 3 KHZ E 60V The instantaneous voltage across each element is the PROJECTION of the MAXIIMUM I voltage onto the horizontal axis L 30 mH VL IX L VR IR t Source voltage leads the current by the angle I V Vmax VL IX L Let V IZ 2 2 2 VR IR t Z Impedance 2 2 2 I Z I R I X L or Z R 2 X L2 VL tan VR R 30 3 KHZ E 60V 1 L 30 mH The drawing is obviously NOT to scale I 3 KHZ R 30 E 60V VL IX L Let V IZ VR IR t L 30 mH Z Impedance I Z I R I X L or R 30 2 2 2 2 Z R 2 X L2 VL tan VR 1 2 2 V 60 I 0 632 A Z 94 9 X L L 90 Z 30 2 90 2 …


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UCF PHY 2054C - AC Calculations

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