1 / 20

Inductors and AC Circuits

Physics 102: Lecture 12. Inductors and AC Circuits. L. R. C. P rimary Coil. S econdary Coil. “Mutual Inductance”. Mutual Inductance. AC Generator Changing current in P Changing B-field thru P Changing B-field thru S Changing  thru S  S proportional to I P :.

bingram
Download Presentation

Inductors and AC Circuits

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Physics 102: Lecture 12 Inductors and AC Circuits L R C

  2. Primary Coil Secondary Coil “Mutual Inductance” Mutual Inductance • AC Generator • Changing current in P • Changing B-field thru P • Changing B-field thru S • Changing  thru S • S proportional to IP: • Induced EMF (voltage) in S • Recall Faraday’s law: Demo 10

  3. Self Inductance – Single Coil “Inductance” • AC Generator • Changing current • Changing B-field • Changing  •  proportional to I: • Induced EMF (voltage) • Recall Faraday’s law: • Direction • Given by Lenz’s Law • Opposes change in current Units: [L] = [] [t] / [I] 1 H = 1V-sec/amp 13

  4. Physical Inductor l A (# turns) = (# turns/meter) x (# meters) Energy stored: U = ½ LI2 N = n l Inductor resists current change! Recall: =NBA Recall: B=monI 16

  5. ACT Compare the inductance of two solenoids, which are identical except solenoid 2 has twice as many turns as solenoid 1. 1) L2=L1 2) L2 = 2 L1 3) L2 = 4 L1 18

  6. q Vmax -Vmax Review: Generators and EMF Voltage across generator: 1 • = w A B sin(q) • = w A B sin(wt) • = Vmax sin(wt) w • v v r 2 x e Frequency = How fast its spinning Amplitude = Maximum voltage t 20

  7. +24 -24 AC Source V(t) = Vmax sin(t)=Vmax sin(2pf t) Vmax = maximum voltage f = frequency (cycles/second) V(t) = 24 sin(8p t) Example 2pf t = 8pt f = 4 Hz T=(1/4)seconds/cycle 0.25 0.5 RMS: Root Mean Square Vrms=Vmax/√2 23

  8. +Vmax -Vmax RMS? V(t) = Vmax sin(2pf t) Mean: Vmax2 Vmax2 / 2 Square: square Root: Vmax/ √2 RMS: Root Mean Square Vrms=Vmax/√2 23

  9. L R C Preflight 12.1, 12.2 I(t) = 10 sin(377 t) Find Imax Find Irms Well… We know that the maximum value sine is 1. So the maximum current is 10! Imax = 10 A 72% correct Just like Vrms=Vmax/sqrt(2)… =10/√2 A = 7.07 A Irms=Imax/sqrt(2) 60% correct 26

  10. Voltage across resistor is “IN PHASE” with current. • VR goes up and down at the same times as I does. I t VR Resistance (R) Frequency does not affect Resistance! t Frequency Resistors in AC circuit R VR = I Ralways true - Ohm’s Law • VR,max = ImaxR 29

  11. Capacitors in AC circuit • Voltage across capacitor “LAGS” current. • VC goes up and down just after I does. I t VC Frequency does affect Reactance! Reactance (XC) t Frequency • VC = Q/Calways true • VC,max = ImaxXC • Capacitive Reactance: XC = 1/(2pfC) C 33

  12. Inductors in AC circuit • Voltage across inductor “LEADS” current. • VL goes up and down just before I does. I t VL Reactance (XL) Frequency does affect Reactance! t Frequency • VL = -L(DI)/(Dt) always true • VL,max = ImaxXL • Inductive Reactance: XL = 2pfL L 36

  13. L R C XC very large w gives very small XC w XL w very small w gives very small XL ACT/Preflight 12.4, 12.5 The capacitor can be ignored when… (a)frequency is very large (b) frequency is very small The inductor can be ignored when… (a)frequency is very large (b) frequency is very small 42

  14. L R C Generators in AC circuit • VG + VL + VR + VC = 0 always true - VG,max = ImaxZ - impedance - Voltage across generators sometimes leads and sometimes lags current…depends on XL – XC …see next week’s discussion of phasors.

  15. L R C Example: AC Circuit Voltages Example An AC circuit with R= 2 W, C = 15 mF, and L = 30 mH has a current I(t) = 0.5 sin(8p t) amps. Calculate the maximum voltage across R, C, and L. VR,max = Imax R = 0.5  2 = 1 Volt VC,max = Imax XC = 0.5  1/(8p0.015) = 1.33 Volts VL,max = Imax XL = 0.5  8p0.03 = 0.38 Volts ACT: Now the frequency is increased so I(t) = 0.5 sin(16p t). Which element’s maximum voltage decreases? 1) VR,max 2) VC,max 3) VL,max Stays same: R doesn’t depend on f Decreases: XC = 1/(2pfC) Increases: XL = 2pf L 50

  16. L R C Summary so far… • I = Imaxsin(2pft) • VR = ImaxR sin(2pft) • VR in phase with I I VR • VC = ImaxXC sin(2pft-p/2) • VC lags I t VL • VL = ImaxXL sin(2pft+p/2) • VL leads I VC

  17. L R C I VR t VL VC Time Dependence in AC Circuits Write down Kirchoff’s Loop Equation: VG + VL + VR + VC = 0 at every instant of time • However … • VG,maxVL,max+VR,max+VC,max • Maximum reached at different times for R,L,C 5

  18. q+p/2 a a q q-p/2 a A reminder about sines and cosines y • Recall: y coordinates of endpoints are • asin(q + p/2) • asin(q) • asin(q - p/2) x

  19. L R C q+p/2 ImaxR ImaxXL q q-p/2 ImaxXC Graphical representation of voltages I = Imaxsin(2pft) (q = 2pft) VL = ImaxXLsin(2pft + p/2) VR = ImaxR sin(2pft) VC = ImaxXC sin(2pft - p/2)

  20. See you next lecture.

More Related