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
Internal Resistance of a Battery
V  V0  ir
Internal resistance of the battery
Question:
Why not put the ammeter next to R?
Estimating Errors: Review
•Systematic errors : sources of error that have the same size
effect on every measurement that is made (or a correlated effect)
• a ruler that was not manufactured correctly
• a consistently delayed reaction when using a stop watch
• your inability to perfectly estimate the size of a stray
magnetic field from your computer that leaks into your
experimental area
• Random errors : sources of error whose effect varies with each
measurement
• precision of your measuring device
• when using a stop watch, a reaction time that sometimes
anticipates the event, some times is in retard of the event.
Error on slope and intercept
b  
x
2
j
N  x  ( x j )
2
j
Note error on
intercept
scales with
root(N)
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?
Adding points does not reduce the error. Previous
formula can not work for systematic errors
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
Random and Sys errors
• first, fit to a straight line using only random
errors
• get the error on the fit m and b due to random
errors from the spreadsheet
• calculate the errors on m and b due to
systematic errors as shown on previous 2 slides
• take the error on m due to random errors and
the error on m due to systematic errors and add
them in quad
• ditto for b
Fitting and Syst Errors
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)
• 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.
• If you still have drift, it is important to measure V&I simultaneously. If
you measure one, wait a minute, then measure the other, you’ll get a ba
result. Random error from your ability to read the 2 meters at the same
time. (Drift is biggest when using smallest resistor. Why?
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)
• section C: use the LED
• C.2. only measure current and voltage across diode
• don’t do C.3
• don’t do C.5
• Don’t do section VII
You must upload your spreadsheet before leaving class!
diode
•Start with the volt meter on the power supply.
•First, just qualitatively observe the behavior.
Slowly dial it from zero volts up, watching the
ammeter. Don’t dial it above 5 V.
•After you have a qualitative feel, start taking data.
Take a large number of data points, with both
positive and negative voltages. Take the most
data points where the curve is changing quickly,
fewer where it is changing slowly.
•Be careful with voltage signs for this one.
Bureaucracy
• Please note lab report is due Oct 1/2
• Oct 1/2 Oscilloscope review (in class
spreadsheet due, no lab report)
What are we testing
• Before you leave class, tell professor Eno
what this lab was testing.