29 Overview why how to use rms values
- Slides: 31
29 Overview • why & how to use rms values • determine impedance of L & C • why & how: phase relationships in ac circuits 1
sinusoidal current “ac” • I ~ sine, cosine variation with time: (I = Io cos(wt + phi)) • w = 2 pf, e. g. US grid uses 60 cycles/sec, w = 2 p(60) = 377 rad/s 2
basic circuits with: 3
resistors: VR ~ I 4
inductors: VL ~ d. I/dt voltage “leads” current 5
capacitors: VC ~ Q current “leads” voltage 6
impedance Z = “ac R” 7
Example: 55 m. H Inductor, r = 0, connected to household 120 VAC (60 hertz). 8
Example: 10 m. F capacitor: connected to household 120 VAC (60 hertz). 9
Example I(t) = 0. 577 Io 10
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 11
exponential notation used to replace cosine or sine dependence 12
exp derivatives 13
RLC exp application: From dx/dt = I, Z and phase are: 14
ac LR lab • measure: voltages • calculate: L & phase angle 15
Student Data (L ~ 1 m. H, f ~ 10, 000 Hz) V V-ind V-R 15 ohm 6. 7 6. 6 1. 0 60 ohm 6. 3 4. 8 4. 3 100 ohm 6. 5 3. 9 5. 4 angle 79 50 36 16
Trig Calculations 17
Phasor Calculation e phase e 2 f e 1 18
Phasor Calculation e phase e 2 f e 1 19
phasor 20
Exercise • Use trig identity & phasor method to show that • has amplitude 5. 66 and phase 45°. 21
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 22
Transformer 23
AC Power average 24
AC Power 25
An I(t) current source continuously repeats the following pattern: {1 seconds @ 3 ampere, 1 second @ 0 ampere} Calculate average, rms I. 26
If a sinusoidal generator has a maximum voltage of 170 V, what is the rootmean-square voltage of the generator? 27
R setting Actual R 10 ohm 30 ohm 60 ohm 100 ohm Vapp(V) Vind(V) VR(V) Table 2: Calculated Data cosf f(degrees) VL = Vsinf Vr = Vcosf - VR r = RVr/VR L = RVL/(w. VR) 28
Alternating Current Generators fm = NBAcosq. 29
Generators fm = NBAcosq: ( q = wt + d when rotating ) emf = -dfm/dt = -NBAw(-sin(wt + d)) emf = NBAw sin(wt + d) (emf)peak = NBAw. 30
AC Generator applied to Resistor 31
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