#### Transcript Lab #1: Ohm’s Law (and not Ohm’s Law)

```Lab #6: the LRC Circuit and
Resonance: part I
• remember how AC circuits containing a cap,
an inductor, and a resistor in series 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
LRC Circuit
Phenomena of
resonance an important
one in physics
Impedance:
Resistor:
Capacitor:
Inductor:
R
i
C
i L
(voltage in phase with current)
(voltage lags current by 90o)
Current
i
V0e  IR  I
 I (i L)
C
V0
I
e  it
1
( R  i ( L 
))
C
V0
I 
1 2
2
R  ( L 
)
C
it
I is max when
denominator is min:
when  L=1/ C
0 
1
LC
Resonance
Resonance
  L/R
  1 /  (width of resonance, VR =Vmax / 2)
0
L
Q


R 2C
phases
i
V0e  IR  I
 I (i L )
C
V0
I
e  it  I e  i (t  )
1
( R  i ( L 
))
C
V0
I 
1 2
2
R  ( L 
)
C
1
Phase of current (and thus
L 
voltage across R) with
C
tan  
respect to V0
R
it
Phase shift between voltage across resistor and
input is zero when at resonant frequency
phases
Note that since
degrees and Vc
lags by 90
degrees, they
are always outof-phase by 180
degrees
IMPORTANT!!!!!
• Replace C-1 with
Vary the input frequency using the following values:
(f=f0x(0.1,0.5,0.6,0.75,0.9,1.0,1.1,1.25,1.4,1.5,1.9,2.3)
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.
• Also, in C-3, only do the first sentence.
Hints
• part A1.
200 mH: make this by putting 2 100 mH inductors in
series. Because the mutual inductance is non-negligible, please be
sure to wire them together, measure the inductance, and then put
them into the circuit wired exactly as when you measured them.
• 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.
Lab Exam
• Dec 1,2
• The question bank is attached to the web
page for this class
Some Derivatives
Q
L
1 L

R 2C R C
Q 1  L 
  2 
L 2  R C 
1/2
Q 1  L 
  2 
C 2  R C 
1/2
1
1 1
 Q
2
RC 2 L
L
1 1

Q
2 2
RC
2 C
Q 1 L
1
 2
 Q
R R C
R
d tan 2 
1

d
cos 2 
Schedule
• next week is makeup (Nov 3,4). I have William scheduled for Lab 3 on
Nov 3 and Justin for Lab 2 on Tuesday. Let me know if you need to make
up a lab and are not on this list.
• Lab 6 Lab report is thus due on our next class, Nov 10, 11
Step-wave input
Charge on cap rings at resonant frequency while
decaying away
Like striking a bell
with a hammer
Tosc 
L
 2
R

2
osc
 
2
0
1
2
2
 osc
At large R
Critically damped: R is large
4 L no1oscillation
2
enoughRso
that

2
C  1
occurs
Hints
• Capture a wave form of the ringing with
wavestar
• for part C, only vary R and only give a