Transcript experiment_V

Lab #5: RC AC Circuits
• remember how AC circuits containing
capacitors and resistors behave.
Caps and AC sources
Voltage across cap is same as
voltage across supply.
When the voltage is changing
quickly, the charge also has to
change quickly -> big current
V  V0 sin( t ) 
1
Q
C
Q  CV0 sin( t )
dQ
i
 CV0 cos( t )  CV0 sin( t   / 2)
dt
i
V0

sin( t  )
1/( C )
2
V
i0 
(1/  C )
Size of the current depends on the frequency
Get biggest currents at high frequencies
AC RC Circuits
As per last
week, be
careful with
the grounds!
• Presence of the capacitor affects the size of the current in the circuit
in a frequency-dependent way.
• “phases” of signals across voltage source, resistor, and capacitor
differ
• math is most easily done by modeling the voltage source as V  V0eit
instead of V  V0 cos(t ) and an imaginary reactive for the
capacitor (to shift its affect on the current by 90 degrees) and then
taking the real part at the end.
The Math
What is the current?
V0eit  i (t )  Z
 i (t )  ( R 
1
i
)  i (t )  ( R 
)
iC
C
Any complex number can be written as a magnitude and an angle in the
complex plane.
Z  R2 
tan  
V0eit  i (t ) R 1 
1
i
e
 2 R 2C 2
V0
i (t ) 
R 1
1
 2 R 2C 2
ei (t  )
1
1

R
1

 2C 2
 2 R 2C 2
1
 RC
Easy to read off mag of current.
Current (and thus voltage across the
resistor) is shifted in phase from the
voltage source by 
V across R and across C
Again, V across C tends to be
large when V source is
changing quickly
hints
• lab starts pg 47
• include syst errors for R and C measurements, but not for t and V
measurements with scope.
•MAKE SURE DUTY CYCLE IS ALL THE WAY COUNTER CLOCKWIZE!
•pay attention to the scale (v/division) on ch1,ch2 VERY IMPORTANT
WHEN DOING PART C!!!
• phase shift can not be greater than pi
• remember “compare” is a mathematical operation involving a chi^2 test
• make sure the wave oscillates around zero (using the offset knob). Make
sure there is no dc offset.
• remember, VR lags VIN by phi
•
changes
• use the 10k resistor and the 0.1mF cap for Part A.
• in part A.1, where it says “between the zero crossings”, I suggest
using the time between the maximums of the waveform instead.
•For part A.1, capture your waveform and paste into lab report.
• A-2. replace “qualitively” with “qualitively and quantitatively”.
• In B, don’t go as low as 10 Hz. Do 50-500 Hz.
• in part C, if your wave form is funny, your amplitude is too big for the
instrumentation amplifier. Make it smaller
Errors
cos  
VR
V0
2
2

 
  
  
 VR   
 V0 
 VR
  V0


1
 VR
from the first: sin 

and sin 
 2
VR V0
V0 V0
2
1
  VR

1
 
  VR    2  V0 
sin   V0
  V0

2
2

 1
 1
   cot( )   VR     V0 
 VR
  V0

2
errors
You measure dt. Calc y=cotan(2*pi*f*dt). What
is error on y?
y  cot( )
1
y
 2
sin ( )
