Lecture 11 Electromagnetic Oscillations and
Alternating Current Ch. 31
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Topics
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Transformers
LC Circuit Qualitatively
Electrical and Magnetic energy oscillations
Alternating current
Pure R and L circuits
Series RLC circuit
Power and Transformers
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Demos
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Elmo
Polling
Quiz 2
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Resistivity and currents
Apply Kirchhoff Laws to circuits
B fields from simple current geometries
Faraday’s and Lenz’s Law. Electric fields from
changing B fields
• Find acceleration and velocity of partikcles in E
and B fields
• RL circuits
What is a Generator?
Coil of wire
!
• " m = B ! nˆ dA
! !
= B ! dA
= B cos!dA
n̂
θ
B
d#
d(BAcos $ )
d cos $
d$
!="
="
= "BA
= BAsin $
dt
dt
dt
dt
d$
= BA% sin $ but $ = %t so
=%
dt
! = BA" sin "t
! = !m sin "t
ω= 2πf and f= 60 Hz
Where ω is the rotational angular
frequency of the generator
Driven RLC Series Circuit
Series RLC
• Show Generator voltage vs time on scope.
•Vary frequency
• Show voltage across resistor compared to signal voltage
•How is signal voltage related to voltage across resistor
•Vary frequency - ELI the ICE man
• Show voltage across inductor compared to resistor.
•Voltage across resistor is in phase with current through resistor
• Does voltage across inductor lead or lag the current
• Show voltage across capacitor compared to resistor.
•Voltage across resistor is in phase with current through resistor
• Does voltage across the capacitor lead or lag the current
• Show phase angle is related to impedance in circuit and is
frequency dependent
• Show resonance by varying frequency.
• Need table of numbers for some frequency and at resonance.
Series LCR circuit
f
Hz
6.28fL
4.2mH
1/6.28fC R
Z
I=V/Z φ
1uF
Ohms Ohms Amps Deg
100
2.7
1600
10
40
0.25
1000
27
160
10
133
2445
65.3
65.3
10
16
10
10000 270
1
#L "
#C )
! = tan "1 (
R
VR
Volts
VL
VC
-89.6 .05
.05
10
0.075
-85.7 .25
1
10
10
1
0
9.0
20
-20
270
0.037
87.7
0.2
10
0.6
2.7 " 1600
! = tan (
) = "89.6
10
"1
Peak value
Effective Power
2
rms
P=I R
I
Irms =
2
rms=root-mean-square
High Pass Filter
Low Pass Filter
Chapter 13 Problem 17
In an oscillating LC circuit, L = 28.0 mH and C = 7.50 µF. At time t
= 0 the current is 9.50 mA, the charge on the capacitor is 3.20 µC,
and the capacitor is charging.
(a) What is the total energy in the circuit?
(b) What is the maximum charge on the capacitor?
(c) What is the maximum current?
(d) If the charge on the capacitor is given by q = Q cos(ωt + ϕ),
what is the phase angle ϕ?
(e) Suppose the data are the same, except that the capacitor is
discharging at t = 0. What then is ϕ?
Chapter 31 Problem 21
In an oscillating LC circuit with C = 62.0 µF, the current as a
function of time is given by I = (1.10) sin(2500t + 0.670), where t is
in seconds, I in amperes, and the phase angle in radians.
(a) How soon after t = 0 will the current reach its maximum value?
(b) What is the inductance L?
(c) What is the total energy?