Todays lecture will cover Textbook Sections 20'9, 21'1, 21'34

1
Inductors and AC Circuits
Physics 102 Lecture 12

• Todays lecture will cover Textbook Sections
  20.9, 21.1, 21.3-4

L
R
C
2
Hour Exam I
3
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 Faradays law

10
4
Self Inductance Single Coil

• AC Generator
• Changing current
• Changing B-field
• Changing ?
• ? proportional to I

• Induced EMF (voltage)
• Recall Faradays law

• Direction
• Opposes change in current

13
5
Physical Inductor
Inductor resists current change!
Recall ?BA
Recall BmonI
16
6
ACT
Compare the inductance of two solenoids, which
are identical except solenoid 2 has twice as many
turns as solenoid 1.
1) L2L1 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

• w A B sin(q)
• w A B sin(wt)
• Vmax sin(wt)

v
v
r
2
x
e
Frequency How fast its spinning Amplitude
Maximum voltage
t
20
8
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 VrmsVmax/v2
23
9
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
73 correct
Just like VrmsVmax/sqrt(2)
10/v2 A 7.07 A
IrmsImax/sqrt(2)
55 correct
26
10
Resistors in AC circuit

• VR I R always true - Ohms Law
• VR,max ImaxR

R
29
11
Capacitors in AC circuit

• VC Q/C always true
• VC,max ImaxXC
• Capacitive Reactance XC 1/(2pfC)

C
33
12
Inductors in AC circuit

• VL -L(DI)/(Dt) always true
• VL,max ImaxXL
• Inductive Reactance XL 2pfL

L
36
13
Generators in AC circuit

• VGVLVRVC 0 always true.
• Vmax Imax Z
• Total Reactance Z sqrtR2 (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

61 39
The inductor can be ignored when frequency is
very large frequency is very small
38 62
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
0.5 ? 2 1 Volt
0.5 ? 1/(8p?0.015) 1.33 Volts
VC,max Imax XC
0.5 ? 8p?0.03 0.38 Volts
VL,max Imax XL
Now the frequency is increased so I(t) 0.5
sin(16p t). Which elements maximum voltage
decreases? 1) VR,max 2) VC,max 3) VL,max
Stays same R doesnt depend on f Decreases XC
1/(2pfC) Increases XL 2pf L
50
16
See You Wednesday!