E1C08 09/14/2010
14:53:56 Page 321
Suppose the coefficient of resistance for this RTD is 0.003925
C
À1
. A temperature measurement
is made by placing the RTD in the measuring environment and balancing the bridge by adjusting R 1 .
The value of R 1 required to balance the bridge is 37:36 V. Determine the temperature of the RTD.
KNOWN Rð0
CÞ ¼ 25 V
a ¼ 0:003925
C
À1
R 1 ¼ 37:36 V (when bridge is balanced)
FIND The temperature of the RTD.
SOLUTION The resistance of the RTD is measured by balancing the bridge; recall that in a
balanced condition
R RTD ¼ R 1
R 3
R 2
The resistance of the RTD is measured to be 37:36 V. With R 0 ¼ 25 V at T ¼ 0
C and
a ¼ 0:003925
C
À1 , Equation 8.5 becomes
37:36 V ¼ 25 1 þ aT
ð
Þ V
The temperature of the RTD is 126
C.
Example 8.2
Consider the bridge circuit and RTD of Example 8.1. To select or design a bridge circuit for
measuring the resistance of the RTD in this example, the required uncertainty in temperature would
be specified. If the required uncertainty in the measured temperature is 0:5
C, would a 1% total
uncertainty in each of the resistors that make up the bridge be acceptable? Neglect the effects of lead
wire resistances for this example.
KNOWN A required uncertainty in temperature of Æ0.5
C, measured with the RTD and bridge
circuit of Example 8.1.
FIND The uncertainty in the measured temperature for a 1% total uncertainty in each of the
resistors that make up the bridge circuit.
ASSUMPTION All uncertainties are provided and evaluated at the 95% confidence level.
SOLUTION Perform a design-stage uncertainty analysis. Assuming at the design stage that the
total uncertainty in the resistances is 1%, then with initial values of the resistances in the bridge
equal to 25 V, the design-stage uncertainties are set at
u R 1 ¼ u R 2 ¼ u R 3 ¼ 0:01
ð
Þ 25
ð Þ ¼ 0:25 V
The root-sum-squares (RSS) method is used to estimate the propagation of uncertainty in each
resistor to the uncertainty in determining the RTD resistance by
u RTD ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
qR
qR 1
u R 1
! 2
þ
qR
qR 2
u R 2
! 2 qR
qR 3
u R 3
! 2
s
8.4 Electrical Resistance Thermometry 321
14:53:56 Page 321
Suppose the coefficient of resistance for this RTD is 0.003925
C
À1
. A temperature measurement
is made by placing the RTD in the measuring environment and balancing the bridge by adjusting R 1 .
The value of R 1 required to balance the bridge is 37:36 V. Determine the temperature of the RTD.
KNOWN Rð0
CÞ ¼ 25 V
a ¼ 0:003925
C
À1
R 1 ¼ 37:36 V (when bridge is balanced)
FIND The temperature of the RTD.
SOLUTION The resistance of the RTD is measured by balancing the bridge; recall that in a
balanced condition
R RTD ¼ R 1
R 3
R 2
The resistance of the RTD is measured to be 37:36 V. With R 0 ¼ 25 V at T ¼ 0
C and
a ¼ 0:003925
C
À1 , Equation 8.5 becomes
37:36 V ¼ 25 1 þ aT
ð
Þ V
The temperature of the RTD is 126
C.
Example 8.2
Consider the bridge circuit and RTD of Example 8.1. To select or design a bridge circuit for
measuring the resistance of the RTD in this example, the required uncertainty in temperature would
be specified. If the required uncertainty in the measured temperature is 0:5
C, would a 1% total
uncertainty in each of the resistors that make up the bridge be acceptable? Neglect the effects of lead
wire resistances for this example.
KNOWN A required uncertainty in temperature of Æ0.5
C, measured with the RTD and bridge
circuit of Example 8.1.
FIND The uncertainty in the measured temperature for a 1% total uncertainty in each of the
resistors that make up the bridge circuit.
ASSUMPTION All uncertainties are provided and evaluated at the 95% confidence level.
SOLUTION Perform a design-stage uncertainty analysis. Assuming at the design stage that the
total uncertainty in the resistances is 1%, then with initial values of the resistances in the bridge
equal to 25 V, the design-stage uncertainties are set at
u R 1 ¼ u R 2 ¼ u R 3 ¼ 0:01
ð
Þ 25
ð Þ ¼ 0:25 V
The root-sum-squares (RSS) method is used to estimate the propagation of uncertainty in each
resistor to the uncertainty in determining the RTD resistance by
u RTD ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
qR
qR 1
u R 1
! 2
þ
qR
qR 2
u R 2
! 2 qR
qR 3
u R 3
! 2
s
8.4 Electrical Resistance Thermometry 321