physics 202, lecture 18...physics 202, lecture 18 today’s topics ... qtcl eq. of harmonic...
TRANSCRIPT
![Page 1: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/1.jpg)
Physics 202, Lecture 18Today’s Topics
Reminder RL Circuits RC Circuits LC (RLC) Circuits and Electromagnetic Oscillations
AC Circuits with AC Source Phasors
![Page 2: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/2.jpg)
Physics 202, Lecture 18Today’s Topics
Reminder RL Circuits RC Circuits LC (RLC) Circuits and Electromagnetic Oscillations
AC Circuits with AC Source Phasors
Phaser
![Page 3: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/3.jpg)
Turn on RL Circuit (reminder)
Note: the time constant is τ=L/R
�
I = V0R(1− e
− tL /R )
![Page 4: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/4.jpg)
Turn off RL Circuit (reminder)
Note: the time constant is τ=L/R
�
I = I0e− tL /R
![Page 5: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/5.jpg)
Charging a Capacitor in RC Circuit
Charging
)1()( /RCteCtq −−= ε RCteR
tI /)( −= ε
Note: τ≡RC is called time constant
0)(/)( =−−dttdqRCtqε
![Page 6: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/6.jpg)
Discharging a Capacitor in RC Circuit
discharging
RCtQetq /)( −=
�
I(t) = − QRC
e−t /RC
Note the time constant τ=RC
�
q(t) /C + R dq(t)dt
= 0
![Page 7: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/7.jpg)
Demo: RC Circuit
Light Bulb
r
![Page 8: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/8.jpg)
LC Circuit and Oscillation Exercise: Find the oscillation frequency of a LC circuit
0)(/)( =−−dttdILctq
)sin()cos(
1
0)(1)(
max
max
2
2
2
φωωφω
ω
ω
+−=+=
=
=+
tQItQq
LC
dttqdtq
0)(/)( 2
2
=+dttqdLCtq
eq. of Harmonic Oscillation
Total Energy is conserved
I
![Page 9: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/9.jpg)
AC Power Source ΔV = ΔVmax Sin(ωt+φ0) = ΔVmax Sin(ωt)
Initial phase, usually set φ0=0
T=2π/ω
ω: angular frequencyω=2πf
t=0
![Page 10: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/10.jpg)
AC Circuit Find out current i and voltage difference ΔVR, ΔVL, ΔVC.
Notes: • Kirchhoff’s rules still apply !• A technique called phasor analysis is convenient.
i
ΔVmax Sin(ωt)
![Page 11: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/11.jpg)
Phasor A sinusoidal function y= Asinφ can be represented
graphically as a phasor vector with length A andangle φ (w.r.t. to horizontal)
φ
A
Asi
nφ
![Page 12: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/12.jpg)
Resistors in an AC Circuit
Ohm’s Law: ΔV=IR at any time
i
iR=ΔV/R=Imax sinωt, Imax=ΔVmax/R
The current through an resistor is in phase with the voltage across it Phasor view
Function view
![Page 13: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/13.jpg)
Inductors in an AC Circuit ΔV - Ldi/dt =0
iL=Imax sin(ωt-π/2)Imax=ΔVmax/XL, XL= ωL inductive reactanceThe current through an inductor is 90o behind the voltage across it.
Phasor view
Function viewi
![Page 14: Physics 202, Lecture 18...Physics 202, Lecture 18 Today’s Topics ... qtCL eq. of Harmonic Oscillation Total Energy is conserved I. AC Power Source](https://reader030.vdocuments.us/reader030/viewer/2022040809/5e4eddf912886155d5594a29/html5/thumbnails/14.jpg)
Capacitors in an AC Circuit
ΔV - q/C=0, dq/dt =i
i
iL=Imax sin(ωt+π/2)Imax=ΔVmax/XC, XC= 1/(ωC) capacitive reactanceThe current through a capacitor is 90o ahead of the voltage across it. Phasor view
Function view