Transcript experiment_VI

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 big 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
Impedence:
Resistor:
Capacitor:
Inductor:
R
i
C
i L
(voltage in phase with current)
(voltage lags current by 90o)
(voltage leads 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

1
LC
Resonance
Resonance
R
L
Q


R 2C
  L/R
  1/  (width of resonance, VR =Vmax / 2)
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
VL leads by 90
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(0.1,0.5,0.9,1.0,1.1,1.5,1.9,2.3)
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=WL and XC=1/wC using the
measured values for L and C.
Hints
• part A1.
200 mH -> 100mH
• Part A1. assume uncertainty on internal resistanc eof the wave for
is 2 ohms.
• C-1 at low frequency, wave form across inductor is 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.
• C-3. don’t read off plot. Just extrapolate data linearly between the
+ and – shift point.
• ditto for C-4
Step-wave input
Like striking a bell
with a hammer
 2

2
osc
T
L
R
 
2
0
2

1
2
Charge on cap rings at resonant frequency while
decaying away
At large R
Critically damped: R is large
enough so that no oscillation
occurs
Hints: Part b
Capture a wave form of the ringing with
wavestar