E1C06 09/14/2010
11:55:5 Page 224
Consider the case when all of the resistances in the bridge are initially equal to R, and subsequently
R 1 changes by an amount dR. The current through the meter is given by
I g ¼ E i
dR=R
4 R þ R g
À
Á
ð6:24Þ
and the output voltage is given by E o ¼ I g R g ,
E o ¼ E i
dR=R
4 1 þ R=R g
À
Á
ð6:25Þ
The bridge impedance can affect the output from a constant voltage source having an internal
resistance R s . The effective bridge resistance, based on a Th evenin equivalent circuit analysis, is
given by
R B ¼
R 1 R 3
R 1 þ R 3
þ
R 2 R 4
R 2 þ R 4
ð6:26Þ
such that for a power supply of voltage E s
E i ¼
E s R B
R s þ R B
ð6:27Þ
In a similar manner, the bridge impedance can affect the voltage indicated by the voltagemeasuring device. For a voltage-measuring device of internal impedance R g , the actual bridge
deflection voltage, relative to the indicated voltage, E m , is
E o ¼
E m
R g
R 1 R 2
R 1 þ R 2
þ
R 3 R 4
R 3 þ R 4
þ R g
ð6:28Þ
The difference between the measured voltage E m and the actual voltage E o is a loading error, in
this case due to the bridge impedance load. Loading errors are discussed next.
Example 6.3
A certain temperature sensor experiences a change in electrical resistance with temperature
according to the equation
R ¼ R o 1 þ a T À T o
ð
Þ
½
ð 6:29Þ
where
R ¼ sensor resistance (V)
R o ¼ sensor resistance at the reference temperature, T o (V)
T ¼ temperature (
C)
T o ¼ reference temperature (0
C)
a ¼ the constant 0.00395
C
À1
This temperature sensor is connected in a Wheatstone bridge like the one shown in Figure 6.13,
where the sensor occupies the R 1 location, and R 2 is a calibrated variable resistance. The bridge
is operated using the null method. The fixed resistances R 3 and R 4 are each equal to 500 V. If the
224 Chapter 6 Analog Electrical Devices and Measurements
11:55:5 Page 224
Consider the case when all of the resistances in the bridge are initially equal to R, and subsequently
R 1 changes by an amount dR. The current through the meter is given by
I g ¼ E i
dR=R
4 R þ R g
À
Á
ð6:24Þ
and the output voltage is given by E o ¼ I g R g ,
E o ¼ E i
dR=R
4 1 þ R=R g
À
Á
ð6:25Þ
The bridge impedance can affect the output from a constant voltage source having an internal
resistance R s . The effective bridge resistance, based on a Th evenin equivalent circuit analysis, is
given by
R B ¼
R 1 R 3
R 1 þ R 3
þ
R 2 R 4
R 2 þ R 4
ð6:26Þ
such that for a power supply of voltage E s
E i ¼
E s R B
R s þ R B
ð6:27Þ
In a similar manner, the bridge impedance can affect the voltage indicated by the voltagemeasuring device. For a voltage-measuring device of internal impedance R g , the actual bridge
deflection voltage, relative to the indicated voltage, E m , is
E o ¼
E m
R g
R 1 R 2
R 1 þ R 2
þ
R 3 R 4
R 3 þ R 4
þ R g
ð6:28Þ
The difference between the measured voltage E m and the actual voltage E o is a loading error, in
this case due to the bridge impedance load. Loading errors are discussed next.
Example 6.3
A certain temperature sensor experiences a change in electrical resistance with temperature
according to the equation
R ¼ R o 1 þ a T À T o
ð
Þ
½
ð 6:29Þ
where
R ¼ sensor resistance (V)
R o ¼ sensor resistance at the reference temperature, T o (V)
T ¼ temperature (
C)
T o ¼ reference temperature (0
C)
a ¼ the constant 0.00395
C
À1
This temperature sensor is connected in a Wheatstone bridge like the one shown in Figure 6.13,
where the sensor occupies the R 1 location, and R 2 is a calibrated variable resistance. The bridge
is operated using the null method. The fixed resistances R 3 and R 4 are each equal to 500 V. If the
224 Chapter 6 Analog Electrical Devices and Measurements