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

Lab #1: Ohm’s Law (and not Ohm’s Law)
• Measure
the internal resistance of a battery
• Study the V vs I characteristics of a diode and show
that it does not obey Ohm’s law
• using a diode, verify Kirchoff’s laws are satisfied even
when a non-ohmic device is in the circuit
Current
• Current: amount of charge that passes a
point on the wire each second (amps =
columb/second)
• Determined by number of charges and by
their speed
Basic Electric Concepts
F  qE
U =-  F  ds
V 
U
q
V=-  E  ds
Resulting Motion depends on
material
• conductor
• insulator
• semi-conductor
Basic Electrical Concepts
Conductors
Terminal velocity depends on
voltage, the geometry of the
materials, and the properties
of the material Resistivity
Ohmic materials:
A
I
V
l
Resistance
Material
Insulators
Mica
Glass
Rubber
Semi-conductors
Silicon
Germanium
Conductors
Carbon
Nichrome
Copper
resistivity at room temp (W-m)
2x1015
1012-1013
1013
2200
0.45
3.5x10-5
1.2x10-6
1.7x10-8
Circuit Symbols
Kirchhoff’s Laws
What if we have several circuit elements attached
together in a circuit?
Kirchhoff’s Laws
Label the unknown currents in your circuit
 I=0 at a junction
2)  V=0 around any closed path
1)
(loop) around the circuit
Currents entering junction: +
Currents leaving junction: Loop in direction of current: voltage drops
Loop in direction opposite current: voltage increases
Use rules 1 & 2 until you have as many equations as you have
variables
• voltage has a unique value at a
unique place
Where do these come from?
• current is just electron moving.
Kirchhoff’s Law
3 variables -> need to use
rules 3 times
I1  I 2  I3  0
loop 1: V0 -I 2 R  0
loop 2: I 2 R  I 3 R  0
Internal Resistance of a Battery
V  V0  ir
Internal resistance of the battery
Question:
Why not put the ammeter next to R?
Fitting and syst errors
Suppose you are measuring V using a meter that has infinite
accuracy and that has no random errors, but that always reports a
voltage that is always off by 0.25V?
Chi2 will be zero! Error on slope and intercept will be
zero! What to do?
slope
How can slope be changed? If voltage is
always off by a scale factor, or if current is
always off by a scale factor, slope is off by the
same factor.
xmeasured  x xtrue
ymeasured   y ytrue
  (m    x )  (m    y )
2
m
2
2
intercept
What if the voltage is always off by a fixed,
constant amount?
xmeasured  x xtrue  bx
ymeasured   y ytrue  by
  (b    y )  ( by )  ( m   bx )
2
b
2
2
2
(see “lectures” link of class web site,
kelly_SystematicErrors.pdf, for a more complete,
rigorous derivation of this result.)
Multi-meter syst errors
Fitting and Syst Errors
Combine this error in quad with the error due
to random errors from the linear fitter.
If you don’t understand this (how to calculate the
syst error on slope/intercept and then combine with
the stat error), don’t leave the room today until you
do! It’s important for this and future labs!
Hints
• should we record R (the resistance of the variable resistor in your
circuit)?
• For R, should we use the color-band value or should we measure it?
• big currents! Should we switch to lower scale when using smaller
currents?
• open switch when not in use (try touching the resistors)
• HOW MANY DATA POINTS?
• Some of these batteries drift with temperature. Take A.1 and A.5
seriously to avoid this problem. Also, recheck results for first value of
resistance used occasionally to look for drift.
Lab
Starts on page 11
• when measure V0 and r, need to report errors on these numbers
• take at least 5 data points
• please put text in your spreadsheet, carefully labeling all the data!
• all numbers should have units!
• Take A.1 and A.5 seriously!
• don’t do A.7 (until you take this into account during the linear fit)
• don’t do C.3
• don’t do C.5
• Don’t do section VII
You must upload your spreadsheet before leaving class!
diode
How to chose what voltages?
Start with the volt meter on the power supply.
Slowly dial it from zero volts up, watching the
ammeter
Don’t dial it above 5 V.
Be careful with voltage signs for this one.
Bureaucracy
• Please note lab report is due Feb 8
• No class Feb 8