Lab #6: the LRC Circuit and Resonance: part I remember how AC circuits containing caps, inductors,...
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Transcript of Lab #6: the LRC Circuit and Resonance: part I remember how AC circuits containing caps, inductors,...
![Page 1: Lab #6: the LRC Circuit and Resonance: part I remember how AC circuits containing caps, inductors, and resistors behave experience resonance experimentally.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649d435503460f94a1f78d/html5/thumbnails/1.jpg)
Lab #6: the LRC Circuit and Resonance: part I
• remember how AC circuits containing caps, inductors, and resistors behave
• experience resonance experimentally
• two week lab. Only 1 lab report. (so, no lab report due next week. A bigish lab report due the following week)
• this week: pgs 56- 57. next week pg 61
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LRC Circuit
i
C
Phenomena of resonance an important one in physics
Impedance:Resistor:
Capacitor:
Inductor: i L
R (voltage in phase with current)
(voltage lags current by 90o)
(voltage leads current by 90o)
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Current
0
0
0
2 2
( )
1( ( ))
1( )
i t
i t
iV e IR I I i L
CV
I eR i L
CV
I
R LC
I is max when denominator is min: when L=1/C
0
1
LC
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Resonance
Resonance
R max
02
/
1 / (width of resonance, V =V / 2)
L R
LQ
R C
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phases0
( )0
0
2 2
( )
1( ( ))
1( )
1
tan
i t
i t i t
iV e IR I I i L
CV
I e I eR i L
CV
I
R LC
LC
R
Phase of current (and thus voltage across R) with respect to V0
Phase shift between voltage across resistor and input is zero when at resonant frequency
![Page 6: Lab #6: the LRC Circuit and Resonance: part I remember how AC circuits containing caps, inductors, and resistors behave experience resonance experimentally.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649d435503460f94a1f78d/html5/thumbnails/6.jpg)
phases
Note that since VL leads by 90 degrees and Vc lags by 90 degrees, they are always out-of-phase by 180 degrees
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IMPORTANT!!!!!
Replace C-1 with
Vary the input frequency using the following values:
(f=f0x(0.1,0.5,0.9,1.0,1.1,1.5,1.9,2.3)
For each value, record the amplitudes of V0 and VR as well as the frequency f and the phase shift phi (from the time shift of the peaks) between V0 and VR. Calculate XL=L and XC=1/C using the measured values for L and C.
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Hints• part A1. 200 mH: make this by putting 2 100 mH inductors in series
• Part A1. assume the uncertainty on internal resistance of the waveform generator is 2 ohms. (50+-2)
• C-1 at low frequency, wave form can be ugly. Measure to the average over the “features”. So, need to use cursors, not “measure”
• C-1 don’t assume V0 does not change, monitor it and check that it does not change
• C-1 note phase shift changes sign.
![Page 9: Lab #6: the LRC Circuit and Resonance: part I remember how AC circuits containing caps, inductors, and resistors behave experience resonance experimentally.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649d435503460f94a1f78d/html5/thumbnails/9.jpg)
Lab Exam
• Dec 3,4
• The question bank is attached to the web page for this class
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Step-wave input
2 20 2
2
1osc
L
R
Charge on cap rings at resonant frequency while decaying away
Like striking a bell with a hammer
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At large RCritically damped: R is large enough so that no oscillation occurs
22
4 1
1
LR
C
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Hints
• Capture a wave form of the ringing with wavestar
• for part C, only vary R and only give a qualitative answer