1. 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
This lecture may still be short. Add some examples? I added a new slide on physical inductors with a derivation. (The final equation is in the same form as one given in the exam equation sheet.) C
Physics 102: Lecture 12, Slide 1 1

2. Mutual Inductance AC Generator Changing current in P
Primary
Coil
Secondary
AC Generator
Changing current in P
Changing B-field thru P
Changing B-field thru S
Changing  thru S
S proportional to IP:
“Mutual Inductance”
Induced EMF (voltage) in S
Recall Faraday’s law:
Can show two demo’s here. First the two Tesla Coils. Second is the two Helmholtz coils. 1 connected to battery, one to meter.
Physics 102: Lecture 12, Slide 2

3. Self Inductance – Single Coil
AC Generator
Changing current
Changing B-field
Changing 
 proportional to I:
“Inductance”
Induced EMF (voltage)
Recall Faraday’s law:
Direction
Opposes change in current
Physics 102: Lecture 12, Slide 3

4. Physical Inductor Inductor resists current change! Energy stored: U =
Recall: =BA A l
Recall: B=monI
Derivation is blank for them to fill in. Energy Eqn. is also blank.
(# turns)
= (# turns/meter) x (# meters)
Energy stored:
U =
N = nl
Physics 102: Lecture 12, Slide 4

5. Physical Inductor Inductor resists current change! Energy stored:
Recall: =BA A l
Recall: B=monI
Derivation is blank for them to fill in. Energy Eqn. is also blank.
(# turns) = (# turns/meter) x (# meters)
N = n l
Energy stored:
U = ½ LI2
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. Review: Generators and EMF
Voltage across generator: 1
= w A B sin(wt)
= Vmax sin(wt) w • q v v r 2 x
Vmax
-Vmax
Frequency = How fast its spinning
Amplitude = Maximum voltage t
Physics 102: Lecture 12, Slide 8

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

10. AC Source Example V(t) = Vmax sin(2pf t) V(t) = 24 sin(8p t)
Vmax = maximum voltage
f = frequency (cycles/second)
V(t) = 24 sin(8p t)
+24
-24
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. Preflight 12.1, 12.2 I(t) = 10 sin(377 t) Find Imax Find Irms L R C
85% and 78% correct respectively
Physics 102: Lecture 12, Slide 11

12. Preflight 12.1, 12.2 I(t) = 10 sin(377 t) Find Imax Find Irms L R C
Well… We know that the maximum value
of sine is 1. So the maximum current is 10!
Imax = 10 A
85% and 78% correct respectively
Just like Vrms=Vmax/sqrt(2)…
Irms=Imax/sqrt(2)
=10/sqrt(2) A = 7.07 A
Physics 102: Lecture 12, Slide 12

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

14. Resistors in AC circuit
VR = I R always true - Ohm’s Law
VR,max = ImaxR R
Voltage across resistor is “IN PHASE” with current.
VR goes up and down at the same times as I does. I t VR
Frequency
Resistance (R)
Frequency does not affect Resistance!
Physics 102: Lecture 12, Slide 14

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

16. Capacitors in AC circuit
VC = Q/C always true
VC,max = ImaxXC
Capacitive Reactance: XC = 1/(2pfC) C
Voltage across capacitor “LAGS” current.
VR goes up and down after I does. I t
Frequency
Reactance (XC)
Frequency does affect Reactance! t VC
Physics 102: Lecture 12, Slide 16

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

18. Inductors in AC circuit
VL = -L(DI)/(Dt) always true
VL,max = ImaxXL
Inductive Reactance: XL = 2pfL L
Voltage across inductor “LEADS” current.
VR goes up and down before I does. I t
Frequency
Reactance (XL)
Frequency does affect Reactance! t VL
Physics 102: Lecture 12, Slide 18

19. Generators in AC circuitL R C
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.)
Frequency
Reactance (Z)
Physics 102: Lecture 12, Slide 19

20. Generators in AC circuitL R C
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. 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
70% on these!
Physics 102: Lecture 12, Slide 21

22. Preflight 12.4, 12.5 The capacitor can be ignored when…
frequency is very large
frequency is very small w XC
very large w gives very small XC
The inductor can be ignored when…
frequency is very large
frequency is very small
70% on these! w XL
very small w gives very small XL
Physics 102: Lecture 12, Slide 22

23. ACT: AC Circuit Voltages
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
Example L R C =
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. ACT: AC Circuit Voltages
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
Example L R C
= 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