E1C06 09/14/2010
11:55:5 Page 225
temperature sensor has a resistance of 100 V at 0
C, determine the value of R 2 that would balance
the bridge at 0
C.
KNOWN R 1 ¼ 100 V
R 3 ¼ R 4 ¼ 500 V
FIND
R 2 for null balance condition
SOLUTION From Equation 6.11, a balanced condition for this bridge would be achieved when
R 2 ¼ R 1 R 4 =R 3 or R 2 ¼ 100 V. Notice that to be a useful circuit, R 2 must be adjustable and provide
an indication of its resistance value at any setting.
Example 6.4
Consider a deflection bridge, which initially has all four arms of the bridge equal to 100 V, with the
temperature sensor described in Example 6.3 again as R 1 . The input or supply voltage to the bridge is
10 V. If the temperature of R 1 is changed such that the bridge output is 0.569 V, what is the
temperature of the sensor? How much current flows through the sensor and how much power must it
dissipate?
KNOWN E i ¼ 10 V
Initial (reference) state: R 1 ¼ R 2 ¼ R 3 ¼ R 4 ¼ 100 V
E o ¼ 0 V
Deflection state: E o ¼ 0.569 V
ASSUMPTION Voltmeter has infinite input impedance but source has negligible
impedance (E s ¼ E i ).
FIND T 1 , I 1 , P 1
SOLUTION The change in the sensor resistance can be found from Equation 6.16 as
dE o
E i
¼
dR=R
4 þ 2 dR=R
ð
Þ
)
0:569
10
¼
dR
400 þ 2dR
dR ¼ 25:67 V
This gives a total sensor resistance of R 1 þ dR ¼ 125:7 V, which equates to a sensor temperature of
T 1 ¼ 65
C.
To determine the current flow through the sensor, consider first the balanced case where all the
resistances are equal to 100 V. The equivalent bridge resistance R B is simply 100 V and the total current
flow from the supply, E i /R B ¼ 100 mA. Thus, at the initially balanced condition, the current flow
through each arm of the bridge and through the sensor is 50 mA. If the sensor resistance changes to
125.67 V, the current will be reduced. If the output voltage is measured by a high-impedance device,
such that the current flow to the meter is negligible, the current flow through the sensor is given by
I 1 ¼ E i
1
R 1 þ dR
ð
ÞþR 2
ð6:30Þ
This current flow is then 44.3 mA.
6.4 Analog Devices: Resistance Measurements 225
11:55:5 Page 225
temperature sensor has a resistance of 100 V at 0
C, determine the value of R 2 that would balance
the bridge at 0
C.
KNOWN R 1 ¼ 100 V
R 3 ¼ R 4 ¼ 500 V
FIND
R 2 for null balance condition
SOLUTION From Equation 6.11, a balanced condition for this bridge would be achieved when
R 2 ¼ R 1 R 4 =R 3 or R 2 ¼ 100 V. Notice that to be a useful circuit, R 2 must be adjustable and provide
an indication of its resistance value at any setting.
Example 6.4
Consider a deflection bridge, which initially has all four arms of the bridge equal to 100 V, with the
temperature sensor described in Example 6.3 again as R 1 . The input or supply voltage to the bridge is
10 V. If the temperature of R 1 is changed such that the bridge output is 0.569 V, what is the
temperature of the sensor? How much current flows through the sensor and how much power must it
dissipate?
KNOWN E i ¼ 10 V
Initial (reference) state: R 1 ¼ R 2 ¼ R 3 ¼ R 4 ¼ 100 V
E o ¼ 0 V
Deflection state: E o ¼ 0.569 V
ASSUMPTION Voltmeter has infinite input impedance but source has negligible
impedance (E s ¼ E i ).
FIND T 1 , I 1 , P 1
SOLUTION The change in the sensor resistance can be found from Equation 6.16 as
dE o
E i
¼
dR=R
4 þ 2 dR=R
ð
Þ
)
0:569
10
¼
dR
400 þ 2dR
dR ¼ 25:67 V
This gives a total sensor resistance of R 1 þ dR ¼ 125:7 V, which equates to a sensor temperature of
T 1 ¼ 65
C.
To determine the current flow through the sensor, consider first the balanced case where all the
resistances are equal to 100 V. The equivalent bridge resistance R B is simply 100 V and the total current
flow from the supply, E i /R B ¼ 100 mA. Thus, at the initially balanced condition, the current flow
through each arm of the bridge and through the sensor is 50 mA. If the sensor resistance changes to
125.67 V, the current will be reduced. If the output voltage is measured by a high-impedance device,
such that the current flow to the meter is negligible, the current flow through the sensor is given by
I 1 ¼ E i
1
R 1 þ dR
ð
ÞþR 2
ð6:30Þ
This current flow is then 44.3 mA.
6.4 Analog Devices: Resistance Measurements 225