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Published byMarybeth Booker Modified over 8 years ago
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1 29 Overview why & how to use rms values determine impedance of L & C why & how: phase relationships in ac circuits
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2 sinusoidal current “ac” I ~ sine, cosine variation with time: (I = Io cos(wt + phi)) w = 2pf, e.g. US grid uses 60 cycles/sec, w = 2p(60) = 377 rad/s
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3 basic circuits with:
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4 resistors: V R ~ I
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5 inductors: V L ~ dI/dt voltage “leads” current
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6 capacitors: V C ~ Q current “leads” voltage
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7 impedance Z = “ac R”
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8 Example: 55mH Inductor, r = 0, connected to household 120VAC (60 hertz).
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9 Example: 10 F capacitor: connected to household 120VAC (60 hertz).
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10 Example I(t) = 0.577 I o
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11 Summary sine dependent I has I rms = 0.707 Io other rms values from direct calculation phase relations: R: phi = 0 L: voltage on inductor leads I. C: I to capacitor leads voltage. impedance & resonance in RLC circuit
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12 exponential notation used to replace cosine or sine dependence
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13 exp derivatives
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14 RLC exp application: From dx/dt = I, Z and phase are:
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15 ac LR lab measure: voltages calculate: L & phase angle
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16 Student Data (L ~ 1mH, f ~ 10,000Hz) 15ohm60ohm100ohm V6.76.36.5 V-ind6.64.83.9 V-R1.04.35.4 angle795036
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17 Trig Calculations
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18 Phasor Calculation phase
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19 Phasor Calculation phase
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20 phasor
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21 Exercise Use trig identity & phasor method to show that has amplitude 5.66 and phase 45°.
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22 Resonance in an RLC Circuit min. Z: when XL = XC result: large currents application: radio tuner hi power at tuned freq. low power at other f’s Ex. calc LC for f = 10,000
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23 Transformer
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24 AC Power average
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25 AC Power
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26 An I(t) current source continuously repeats the following pattern: {1 seconds @ 3 ampere, 1 second @ 0 ampere} Calculate average, rms I.
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27 If a sinusoidal generator has a maximum voltage of 170V, what is the root- mean-square voltage of the generator?
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28 R setting Actual R 10 ohm30 ohm60 ohm100 ohm V app (V) V ind (V) V R (V) Table 2: Calculated Data cosf f(degrees) V L = Vsinf V r = Vcosf - V R r = RV r /V R L = RV L /(wV R )
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29 Alternating Current Generators m = NBAcos .
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30 Generators m = NBAcos : ( = t + when rotating ) emf = -d m /dt = -NBA (-sin( t + )) emf = NBA sin( t + ) (emf) peak = NBA .
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31 AC Generator applied to Resistor
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