E1C08 09/14/2010
14:53:57 Page 327
Example 8.5
The material constant b is to be determined for a particular thermistor using the circuit shown in
Figure 8.10a. The thermistor has a resistance of 60 kV at 25
C. The reference resistor in the circuit,
R 1 , has a resistance of 130:5 kV. The dissipation constant d is 0.09 mW/
C. The voltage source used
for the measurement is constant at 1.564 V. The thermistor is to be used at temperatures ranging
from 100 to 150
C. Determine the value of b.
KNOWN The temperature range of interest is from 100
to 150
C.
R 0 ¼ 60; 000 V; T 0 ¼ 25
C
E i ¼ 1:564 V; d ¼ 0:09 mW=
C; R 1 ¼ 130:5 kV
FIND The value of b over the temperature range from 100
to 150
C.
SOLUTION The voltage drop across the fixed resistor is measured for three known values of
thermistor temperature. The thermistor temperature is controlled and determined by placing the
thermistor in a laboratory oven and measuring the temperature of the oven. For each measured
voltage across the reference resistor, the thermistor resistance R T is determined from
R T ¼ R 1
E i
E 1
À 1
The results of these measurements are as follows:
Temperature
R 1 Voltage
R T
(
C)
(V)
(V)
100
1.501
5477.4
125
1.531
2812.9
150
1.545
1604.9
Equation 8.12 can be expressed in the form of a linear equation as
ln
R T
R 0
¼ b
1
T
À
1
T 0
ð8:14Þ
Applying this equation to the measured data, with R 0 ¼ 60; 000 V, the three data points above yield
the following:
ln R T =R 0
ð
Þ
1=T À 1=T 0
ð
ÞK
À1
Â
Ã
b(K)
À2.394
À6:75 Â 10
À4
3546.7
À3.060
À8:43 Â 10
À4
3629.9
À3.621
À9:92 Â 10
À4
3650.2
COMMENT These results are for constant b and are based on the behavior described by
Equation 8.12, over the temperature range from T 0 to the temperature T. The significance of the
measured differences in b is examined further.
8.4 Electrical Resistance Thermometry 327
14:53:57 Page 327
Example 8.5
The material constant b is to be determined for a particular thermistor using the circuit shown in
Figure 8.10a. The thermistor has a resistance of 60 kV at 25
C. The reference resistor in the circuit,
R 1 , has a resistance of 130:5 kV. The dissipation constant d is 0.09 mW/
C. The voltage source used
for the measurement is constant at 1.564 V. The thermistor is to be used at temperatures ranging
from 100 to 150
C. Determine the value of b.
KNOWN The temperature range of interest is from 100
to 150
C.
R 0 ¼ 60; 000 V; T 0 ¼ 25
C
E i ¼ 1:564 V; d ¼ 0:09 mW=
C; R 1 ¼ 130:5 kV
FIND The value of b over the temperature range from 100
to 150
C.
SOLUTION The voltage drop across the fixed resistor is measured for three known values of
thermistor temperature. The thermistor temperature is controlled and determined by placing the
thermistor in a laboratory oven and measuring the temperature of the oven. For each measured
voltage across the reference resistor, the thermistor resistance R T is determined from
R T ¼ R 1
E i
E 1
À 1
The results of these measurements are as follows:
Temperature
R 1 Voltage
R T
(
C)
(V)
(V)
100
1.501
5477.4
125
1.531
2812.9
150
1.545
1604.9
Equation 8.12 can be expressed in the form of a linear equation as
ln
R T
R 0
¼ b
1
T
À
1
T 0
ð8:14Þ
Applying this equation to the measured data, with R 0 ¼ 60; 000 V, the three data points above yield
the following:
ln R T =R 0
ð
Þ
1=T À 1=T 0
ð
ÞK
À1
Â
Ã
b(K)
À2.394
À6:75 Â 10
À4
3546.7
À3.060
À8:43 Â 10
À4
3629.9
À3.621
À9:92 Â 10
À4
3650.2
COMMENT These results are for constant b and are based on the behavior described by
Equation 8.12, over the temperature range from T 0 to the temperature T. The significance of the
measured differences in b is examined further.
8.4 Electrical Resistance Thermometry 327