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

2. Hour Exam I

3. 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”
Can show two demo’s here. First the two Tesla Coils. Second is the two Helmholtz coils. 1 connected to battery, one to meter.
Induced EMF (voltage) in S
Recall Faraday’s law: 10

4. 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 13

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 16

6. 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
One factor of 2 for N in equation, another factor of 2 for doubling B field inside solenoid. (F = B A) 18

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

8. AC Source Example V(t) = Vmax sin(t)=Vmax sin(2pf 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/cycle
Ave V = 0
Ave V^2: Vmax/2
0.25
0.5
RMS: Root Mean Square Vrms=Vmax/√2 23

9. 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
sine is 1. So the maximum current is 10!
Imax = 10 A
73% correct
85% and 78% correct respectively
Just like Vrms=Vmax/sqrt(2)…
Irms=Imax/sqrt(2)
=10/√2 A = 7.07 A
55% correct 26

10. 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! 29

11. 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 just after I does. I t
Frequency
Reactance (XC)
Frequency does affect Reactance! t VC 33

12. 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 just before I does. I t
Frequency
Reactance (XL)
Frequency does affect Reactance! t VL 36

13. Generators in AC circuitL R C
VG+VL+VR+VC = 0 always true.
Vmax = Imax Z
Total Reactance: Z = sqrt[R2+ (XL- XC)2]
Voltage across generators sometimes leads and sometimes lags current.
Frequency does affect Impedance!
Reactance (Z)
Frequency 40

14. Preflight 12.4, 12.5 The capacitor can be ignored when…
frequency is very large
frequency is very small w XC
61%
39%
very large w gives very small XC
“can be ignored” means “behaves like a wire”…no voltage drop
The inductor can be ignored when…
frequency is very large
frequency is very small w XL
38%
62%
very small w gives very small XL 42

15. 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 50

16. See You Wednesday!