Lecture 11 Electromagnetic Oscillations andAlternating Current Ch. 31

• Topics– Transformers– LC Circuit Qualitatively– Electrical and Magnetic energy oscillations– Alternating current– Pure R and L circuits– Series RLC circuit– Power and Transformers

• Demos• Elmo• Polling

Quiz 2

• 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

dAnBm

ˆ!=•

!"

AdB!!

!=

dAB !cos=

θ

n̂

B

�

! = "d#

dt= "

d(BAcos$)

dt= "BA

dcos$

dt= BAsin$

d$

dt

= BA% sin$ but $ = %t so d$

dt= %

�

! = BA" sin"t

�

! = !msin"t

Where ω is the rotational angular frequency of the generator

ω= 2πf and f= 60 Hz

Coil of wireWhat is a 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

0.6

-20

10

10

VC

10

20

1

.05

VL

0.2

9.0

.25

.05

VR

Volts

0.037

1

0.075

0.25

I=V/ZAmps

87.7270101627010000

0101065.365.32445

-85.713310160271000

-89.6401016002.7100

φDeg

ZOhms

ROhms

1/6.28fC1uF

6.28fL4.2mH

fHz

! = tan"1(

#L "1

#C

R)

! = tan"1(2.7 "1600

10) = "89.6

P=Irms

2R

Effective Power

Irms=I

2

rms=root-mean-square

Peak value

Low Pass FilterHigh 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 isdischarging at t = 0. What then is ϕ?

Chapter 31 Problem 21 In an oscillating LC circuit with C = 62.0 µF, the current as afunction of time is given by I = (1.10) sin(2500t + 0.670), where t isin 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?