PROBLEM 8.5
KNOWN:
A thermistor has a resistance of 20,000
Ω
at 100
°
C.
β
= 3650
°
C
R
o
= 20,000
Ω
R
= 500
Ω
FIND:
The temperature corresponding to a thermistor resistance of 500
Ω
.
SOLUTION:
From (8.11)
RR
e
o
TT
o
=
−
⎛
⎝
⎜
⎞
⎠
⎟
β
11
Letting
R
o
= 20,000
Ω
3650
373
500
20,000
T
Re
⎛⎞
−
⎜⎟
⎝⎠
==
and
ln500
ln 20,000 3650
373
T
=+
−
Solving for
T
T
= 598.7 K = 325.7
°
C
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View Full DocumentPROBLEM 8.6
KNOWN:
The uncertainty in temperature
0.005
T
uC
=
±°
.
FIND:
Required uncertainty in measured resistance.
ASSUMPTIONS:
Initially assume that we wish to find the required uncertainty in
resistance measurement as if it were the only contributor to the total uncertainty.
In
addition, this problem is openended to some extent, in that some nominal value of
R
o
must be assumed, or a range of values for
R
o
examined.
SOLUTION:
With
()
[]
RR
TT
oo
=+−
1
α
and
α
= 0.003925
°
C
1
, we can express
u
T
R
u
TR
=
∂
Then
1
o
o
R
R
⎛⎞
−
⎜⎟
⎝⎠
=+
∂α
T
o
=
1
Taking R
o
= 100
Ω
(
)
o
1
2.55 C/
0.003925 100
T
R
=
=Ω
and the uncertainty in resistance is
u
R
= ±
000196
.
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 Spring '08
 Miller

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