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Inductors and AC Circuits

Physics 102: Lecture 12. Inductors and AC Circuits. Today’s lecture will cover Textbook Sections 20.9, 21.1, 3-4. 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

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Inductors and AC Circuits

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  1. Physics 102: Lecture 12 Inductors and AC Circuits • Today’s lecture will cover Textbook Sections 20.9, 21.1, 3-4 L R C Physics 102: Lecture 12, Slide 1

  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: Physics 102: Lecture 12, Slide 2

  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 • Opposes change in current Physics 102: Lecture 12, Slide 3

  4. Physical Inductor l A (# turns) = (# turns/meter) x (# meters) Energy stored: U = Inductor resists current change! Recall: =BA Recall: B=monI N = nl Physics 102: Lecture 12, Slide 4

  5. Physical Inductor l A (# turns) = (# turns/meter) x (# meters) Energy stored: U = ½ LI2 N = n l Inductor resists current change! Recall: =BA Recall: B=monI Physics 102: Lecture 12, Slide 5

  6. ACT Compare the inductance of two solenoids, which are identical except solenoid 2 has twice as many turns/meter as solenoid 1. 1) L2=L1 2) L2 = 2 L1 3) L2 = 4 L1 Physics 102: Lecture 12, Slide 6

  7. ACT Compare the inductance of two solenoids, which are identical except solenoid 2 has twice as many turns/meter as solenoid 1. 1) L2=L1 2) L2 = 2 L1 3) L2 = 4 L1 One factor of 2 for N in equation, another factor of 2 for doubling B field inside solenoid. (F = B A) Physics 102: Lecture 12, Slide 7

  8. q Vmax -Vmax Review: Generators and EMF Voltage across generator: 1 • = w A B sin(wt) • = Vmax sin(wt) w • v v r 2 x Frequency = How fast its spinning Amplitude = Maximum voltage t Physics 102: Lecture 12, Slide 8

  9. +24 -24 AC Source V(t) = Vmax sin(2pf t) Vmax = maximum voltage f = frequency (cycles/second) V(t) = 24 sin(8p t) Example Find ƒ… 0.25 0.5 RMS: Root Mean Square Vrms=Vmax/sqrt(2) Physics 102: Lecture 12, Slide 9

  10. +24 -24 AC Source V(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 0.25 0.5 RMS: Root Mean Square Vrms=Vmax/sqrt(2) Physics 102: Lecture 12, Slide 10

  11. L R C Preflight 12.1, 12.2 I(t) = 10 sin(377 t) Find Imax Find Irms Physics 102: Lecture 12, Slide 11

  12. 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 of sine is 1. So the maximum current is 10! Imax = 10 A Just like Vrms=Vmax/sqrt(2)… Irms=Imax/sqrt(2) =10/sqrt(2) A = 7.07 A Physics 102: Lecture 12, Slide 12

  13. Voltage across resistor is “__________” with current. • VR goes up and down at the same times as I does. I t VR Resistance (R) t Frequency Resistors in AC circuit R VR = I Ralways true - Ohm’s Law • VR,max = ImaxR Physics 102: Lecture 12, Slide 13

  14. 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 Physics 102: Lecture 12, Slide 14

  15. Capacitors in AC circuit • Voltage across capacitor “_______” current. • VR goes up and down after I does. I t VC Reactance (XC) t Frequency VC = Q/Calways true • VC,max = ImaxXC • Capacitive Reactance: XC = C Physics 102: Lecture 12, Slide 15

  16. Capacitors in AC circuit • Voltage across capacitor “LAGS” current. • VR goes up and down 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 Physics 102: Lecture 12, Slide 16

  17. Inductors in AC circuit • Voltage across inductor “_______” current. • VR goes up and down before I does. I t VL Reactance (XL) t Frequency VL = -L(DI)/(Dt) always true • VL,max = ImaxXL • Inductive Reactance: XL = L Physics 102: Lecture 12, Slide 17

  18. Inductors in AC circuit • Voltage across inductor “LEADS” current. • VR goes up and down 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 Physics 102: Lecture 12, Slide 18

  19. L R C Reactance (Z) Frequency Generators in AC circuit • VG+VL+VR+VC = 0 always true. • Vmax = Imax Z • Total Reactance: Z = • Voltage across generators sometimes leads and sometimes lags current. (It depends on the frequency.) Physics 102: Lecture 12, Slide 19

  20. L R C Generators in AC circuit • VG+VL+VR+VC = 0 always true. • Vmax = Imax Z • Total Reactance: Z = R2+ (XL- XC)2 • Voltage across generators sometimes leads and sometimes lags current. (It depends on the frequency.) Frequency does affect Impedance! Reactance (Z) Frequency

  21. L R C Preflight 12.4, 12.5 The capacitor can be ignored when… frequency is very large frequency is very small The inductor can be ignored when… frequency is very large frequency is very small Physics 102: Lecture 12, Slide 21

  22. L R C XC very large w gives very small XC w XL w very small w gives very small XL Preflight 12.4, 12.5 The capacitor can be ignored when… frequency is very large frequency is very small The inductor can be ignored when… frequency is very large frequency is very small Physics 102: Lecture 12, Slide 22

  23. L R C ACT: 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 = VC,max = Imax XC = VL,max = Imax XL = 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 Physics 102: Lecture 12, Slide 23

  24. L R C ACT: 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 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 Physics 102: Lecture 12, Slide 24

  25. See you later! • Read Section 21.5 Physics 102: Lecture 12, Slide 25

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