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

Lab #4: RC and RL Circuits
• remember what capacitors and inductors are
• remember why circuits containing them can
have currents that change with time
Capacitor
Two plates with a
dielectric in between

d
V  Ed 
d
Q
 0
 A 0
1
V Q
C
RC Circuit: close switch
Charge will flow to the capacitor,
charging it and raising its potential.
The potential will asymptotically
approach V0. The current will be
biggest at the beginning, when DV
is greatest, and will get smaller as
DV decreases (as the cap charges).
Q  CV0 (1  e  t / RC )
DVC  Q / C  V0 (1  e  t / RC )
dQ V0  t / RC
 e
dt
R
DVR  IR  V0e  t / RC
I
Note: Vc+vr= constant!
RC time constant (t): time for cap to charge to .63 of Vo
Current to drop to .37 of max value
RC Circuit: Open Switch
V0  t / RC
I  I 0e
 e
R
V  IR  V0e  t / RC
 t / RC
Discharge with same RC time constant
Experiment
• Be careful with the
grounds! Outer
shield on bnc cable
from scope is at
ground. Make sure it
goes on ground side
of cap when
measuring it
• instrumentation
amplifier: needed
when measuring
voltage across R
• calculate RC from the values in the circuit
•measure the RC time constant (t), which is the time to drop to 0.37%
of maximum signal and compare
Inductor
A coil of wire
SpragueGoodman
dI
V  L
dt
Minus sign means sense of
the voltage will be to oppose
the change in current.
Inductors
Instead of a step function change in voltage, the inductor will
develop a voltage across it due to the change in current which
will partially cancel the voltage in the battery and reduce the
current.
VB
 t /( L / R )
i  (1  e
)
R
L/R time constant
VL  VB e t /( L / R )
VR  VB (1  e t /( L / R ) )
Experiment: similar to first
part, but with L/R circuit
174 refresher
If you have made two measurements of the same
thing, how do you check to see if they agree within
errors -> Is their difference zero within errors?
x1   x1 x2   x2
theory: x1  x2  0
d   x   x
2
1
2
2
 0  x1  x2 
 

d


2
2
Calculate chi2 and
prob of having a
difference that big or
bigger…
Sqrt(12)
When you have an LSB, what is the random error?
Imagine a step with width a centered at zero.
Remember:
RMS  x  x
2
x0
3 a /2
a /2
x2 

 a /2
2
x dx

a
RMS  a / 12
x
3
 a /2
a
a2

12
2
Hints
• When wiring circuit, use black wires only for portions of
circuit at ground.
• When wiring the circuit, first wire everything except the
scope. Add it last.
• Be sure scope is DC coupled (AC coupling adds an extra
capacitor, beyond the one you want to measure)
• make sure ch1 and ch2 are on x1 setting
• Make sure they have the same v/division scale
• When you measure R, L, and C, make sure they are not
still in the circuit. If you put an ohm meter across a resistor
in a circuit, you measure the resistance of the circuit, not of
the resistor, etc.
• Don’t really need an external trigger for this lab. Can
trigger off signal itself.
Hints
• lab starts pg 39
• Only 6 lcr meters in class. They come in two different types. For
systematic errors, see manual on your desk top (be careful to use the
correct one). Only consider systematic errors in L,R and C
measurements, not in scope measurements
• for A-1, replace 2nd sentence with “Capture both waveforms using
wavestar. Then sketch Vin-Vc and show to your instructor.
• capture VR in A-2. Be sure to use the instrumentation amplifier when
measuring VR
• when calculate lifetime, need an error
• for example, in A-3, need to calculate errors and say if they are
consistent within errors
• A-4. don’t try higher frequencies. Just lower ones.
• A-4. How does the time constant change with frequency? Does it agree
with expectations to within errors? (ignore the sentence “consider the
fact…”
Hints
• DO NOT DO SECTION B.3