Download Lab #1: Ohm`s Law (and not Ohm`s Law)

Lab #3 and Lab 4: RC and RL Circuits
• Remember what capacitors and inductors are
• Remember why circuits containing them can
have currents that change with time
No lab report, just excel spreadsheet
Capacitor
Two conducting plates
with an insulating
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, and will
get smaller as the capacitor charges.
Q  CV0 (1  e  t / RC )
VC  Q / C  V0 (1  e  t / RC )
dQ V0  t / RC
 e
dt
R
VR  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 of the components
• measure the RC time constant (t), which is the time to drop to 37% of
maximum signal
• 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 the
last lab, 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…
Comparing more
5 measurements of the same thing
32  2, 35  2, 31  0.5, 29  2, 34  2,
weighted average:
w=
1
 i2
1
mi

w  i2
in this case
m 
Use the weighted average
as your theory. ndof=#data
points -1
w=
1
4

5
.5 2 2 2
1 32 35
31 29 34
 ( 2  2 

 )  31.3
5 2
2
0.5 2 2 2 2 2
Least Significant Bit and Sqrt(12)
When you have an LSB, what is the random error?
Imagine a digital 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 a circuit, use black wires only for portions of
the 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 the “x1” setting
• Make sure they have the same Volts/Division scale
• When you measure R, L, and C, make sure they are not
embedded 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.