# Mar 6 ```Physics 145
Introduction to Experimental Physics I
Instructor: Karine Chesnel
Office: N319 ESC
Tel: 801- 422-5687
[email protected]
Office hours: on appointment
Class website:
http://www.physics.byu.edu/faculty/chesnel/physics145.aspx
1. Prepare by reading the introduction material
2. Answer quiz questions (within the first half hour) and
submit the sheet to your TA
3. Proceed to the experiments
4. Write a report of your findings for each experiment,
in your lab notebook (individual reports)
Lab 7-9
LRC circuits
Impedances (see Lab 6)
Resistor
Capacitor
Inductor
I
I
I
VC
VL
VR
VL  L
V R  RI
In AC mode: I  I 0 e
VR  RI 0e
i t
dI
VC 
dt
Q
C
1

C
 Idt
i t
V R   iL   I 0 e
i t
VR 
I0e
i t
i C
AC Impedances
• Circuit in series: add impedances
Z  Z R Z L  ZC
Z  R  iL  
Z 
1
i C
 Z e
1 

R   L 


C


2
1 

tan    L  
/R
C 

2
i
“Gain” = output / input
AC Gain
• RLC circuit
G 
V out
V in
Vin

R
Z
R

1 

R   L 

C 

2
2
Vout
• RC circuit
• RL circuit
Vin
Vout
G 
V out
V in
Vin
Vout
R

 1 
R 

 C 
2
2
G 
V out
V in

R
R   L 
2
2
Low-pass and high-pass filters
• RC circuit
• RL circuit
Vin
Vout
G 
Vout

V in
Vout
Vin
R
 1 
2
R 

 C 
G 
2
V out

V in
Frequency response
R
R   L 
2
2
Frequency response
High-pass
Cutoff frequency
f0 
Low-pass
1
2 R C
Cutoff frequency
f0 
R
2 L
Time responses
• RL circuit
• RC circuit
Vin
When
When
Vout
Vin  V 0
V0  R I  L
dI
V in  0
0  RI  L
dI
Response time
 RL 
L
R
When
dt
dt
Vout
Vin
When
Vin  V 0
V0  R I 
V in  0
0  RI 
Response time
1
C
1
C
 RC  RC
 Idt
 Idt
Resonator
• RLC circuit
G 
V out
V in
Vin

R
Z
R

1 

R   L 


C


2
Resonance
frequency
Vout
f0 
Behavior of phase
90
width
f 
90
R
2 L
Resonance
Band-pass
filter
1
2
LC
2
AC Impedances
• Circuit in parallel: add inverses of impedances

Z  Z R 1 / Z L
i C 
Notch filter
1
1

 Z e
i
i L
1 

R  1 / C 

L 

tan  
Frequency (Hz)
 ZC
1
Z  R
Z 
1
2
1
1 

R C 


L


2
Lab 7:
AC impedance &amp; high-pass filter
A. Theory and calculation for RC filter
• L7.1: Compute impedance Z, phase  and gain G
• L7.2: Check analytical results (Mathematica)
• L7.3: Design RC filter with f0 ~ 1 - 5kHz
B. Measurements
• L7. 4, 5: set up the RC circuit
• L7.6: measure gain G versus frequency f
• L7.7: Plot G(f) and fit
• L7.8: Behavior of phase 
Lab 8:
Low-pass &amp; high-pass filters
A. Frequency response for RL filter
• L8.1: Design a RL filter
• L8.2: Set up the RL circuit
• L8.3: Measure gain G versus frequency f, plot and fit
• L8.4: compare experiment to theory
B. Time response for RL filter
• L8.5: response on a square-wave, measure tRL
B. Time response for RC filter
• L8.6: response on a square-wave, measure tRC, compare
Lab 9:
RLC resonator
A. Measure &amp; analyze RLC resonator
• L9. 1: Design RLC series circuit for various f0 ~ 100Hz
• L9.2: Set up the RLC circuit
• L9.3: Measure gain G versus frequency f, plot and fit
• L9.4: Compare experiment to theory
• L9.5: Behavior of phase 
• L9.6: Behavior of Z, current I and gain value at resonance
B. Parallel RLC circuit – notch filter
• L9.7: Measure gain G versus frequency f, hole width
C. Rms quantities and power dissipation
• L9.8: measure Vrms, Irms and P, feel heating through resistor
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