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1
MP0
Propagation of Errors
PHY 257
I. Objective.
To study the propagation of errors
II. Equipment:
Incandescent light source, component carriers, optical bench, lens (f = 127 mm), screen.
III. Introduction.
In many experiments we wish to determine the quantity z which is connected with a
parameter x through the equation:
)
(
x
f
z
.
First we measure x with an uncertainty
σ
x
and using the expression
)
(
x
f
z
we then determine
z
.
For example, the area
A
of a
square of side
a
is given by the equation:
2
a
A
.
The uncertainty
σ
x
in the parameter x
will propagate through the function f and result in an uncertainty
σ
z
in the parameter
z
.
The general expression for
σ
z
is given by the equation:
x
z
x
f
In a different type of experiments the parameter
z
we wish to determine depends on two
other parameters
x
and
y
through the equation:
)
,
(
y
x
f
z
For example in order to determine the resistance
R
of a resistor we measure the voltage
V
applied across the resistor and the current
I
that passes through it. The resistance
R
is
given by the equation:
I
V
R
.
In the course of such an experiment we measure the
parameters
x
and
y
with uncertainties
σ
x
and
σ
y
, respectively.
These uncertainties
propagate through the function
f
and result in an uncertainty
σ
z
of the parameter
z
.
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This note was uploaded on 11/09/2010 for the course PHY 35345 taught by Professor Aa during the Spring '10 term at SUNY Buffalo.
 Spring '10
 aa

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