Lab #1: Imperfections in Equipment
• Measure
the internal resistance of a battery
• Measure the input impedance of the oscilloscope
• Measure the output impedance of the signal
generator
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 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
Circuits
You learned in your class how to analyze circuits
using Ohm’s law and Kirchkoff’s laws. However,
most of the time, you neglected to take into account
the fact that the instruments you use to measure
the circuit can themselves alter the performance of
the circuit.
We will study this in the lab, see how big the effect
is, and from that get an idea of when this needs to
be taken into account when comparing results to
predictions.
Internal Resistance of a Battery
V  V0  ir
Internal resistance of the battery
Input/Output Impedences
Likewize, a realistic oscilloscope can be modeled
as an ideal one in series with a resistor and a
realistic signal generator can be modeled as an
ideal one in series with a resistor. We will
measure the internal resistance of each of these
devices. We will also practice error propogation,
and understanding how to
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.
Systematic Errors
Most of the time, you will treat systematic errors
in the same way as random errors. Most of the
time you can use standard error propogation to
get the error in a quantity calculated from
another that has a systematic error.
However, when you are fitting, you have to
handle systematic errors in a different way.
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!
Linearizing
This semester, we will often do a variable
transformation in order to get a linear dependence
that we can easily fit. When we transform
variables, we also need to recalculate the errors.
In this lab:
1
y
x
y 1
 2
x x
y 
x
x
2
Lab
• do not do section A.3 or any of section B.
Do the supplement instead
• do not do systematic error analysis for supplement, only for the part in the manual.
• do not do the second paragraph of section A in the manual
• do not do the first 2 sentances of section III.A in the supplement
• be careful with grounds when measuring the output impedence of the signal generator
• Some of the resistors have values that drift with temperature. It is important to measure V&I
simultaneously. If you measure one, wait a minute, then measure the other, you’ll get a bad result.
Random error from your ability to read the 2 meters at the same time. (Drift is biggest when using
smallest resistor. Why?)
• You need to quote errors on all measured numbers and all numbers calculated from measured
numbers.
• Never use the nominal value of a resistor. Always measure the resistance using an ohm meter.
Always remove the resistor from the circuit before measuring its resistance (why?)
• all numbers should have units and be carefully labeled
• last line of supplement r_load -> r_out
What are we testing
• Before you leave class, tell professor Eno
what this lab was testing.
Bureaucracy
• Please note lab report is due Sept 22,23.
Please upload to elms and bring a paper
copy to my office (slide under my door if I’m
not there)
• No Class Sept 22,23
• See you Sept 29,30
You must upload your spreadsheet before leaving class!