E1C06 09/14/2010
11:55:4 Page 222
flow through the galvanometer yields
u R
R 1
¼
I g R 1 þ R g
À
Á
E i
ð6:12Þ
where R g is the internal resistance of the galvanometer. Alternatively, if a current-sensing digital
voltmeter is used, then the input bias current from this meter remains and a small offset voltage is
present as a loading error.
Equation 6.12 can serve to guide the choice in a galvanometer or digital meter and a battery
voltage for a particular application. Clearly, the range of error is reduced by increased input
voltages. However, the input voltage is limited by the power-dissipating capability of the resistance
device, R 1 . The power that must be dissipated by this resistance is I
2
1 R 1 .
Deflection Method
In an unbalanced condition, the magnitude of the current or voltage drop for the meter portion of the
bridge circuit is a direct indication of the change in resistance of one or more of the arms of the
bridge. Consider first the case where the voltage drop from node B to node C in the basic bridge is
measured by a meter with infinite internal impedance, so that there is no current flow through the
meter, as shown in Figure 6.14. Knowing the conditions for a balanced bridge given in Equation 6.10,
the voltage drop from B to C can be determined, since the current I 1 must equal the current I 2 , as
E o ¼ I 1 R 1 À I 3 R 3
ð6:13Þ
Under these conditions, substituting Equations 6.9 to 6.11 into Equation 6.13 yields
E o ¼ E i
R 1
R 1 þ R 2
À
R 3
R 3 þ R 4
ð6:14Þ
The bridge is usually initially balanced at some reference condition. Any transducer
resistance change, as a result of a change in the measured variable, would then cause a deflection
in the bridge voltage away from the balanced condition. Assume that from an initially balanced
condition where E o ¼ 0, a change in R 1 occurs to some new value, R
0
1 ¼ R 1 þ dR. The output from
B
C
A
D
R 4
R 1
R 3
R 2
I 2
I 3
I 1
I 4
E i
E m
R m
∞
Figure 6.14 Voltage-sensitive Wheatstone bridge.
222 Chapter 6 Analog Electrical Devices and Measurements
11:55:4 Page 222
flow through the galvanometer yields
u R
R 1
¼
I g R 1 þ R g
À
Á
E i
ð6:12Þ
where R g is the internal resistance of the galvanometer. Alternatively, if a current-sensing digital
voltmeter is used, then the input bias current from this meter remains and a small offset voltage is
present as a loading error.
Equation 6.12 can serve to guide the choice in a galvanometer or digital meter and a battery
voltage for a particular application. Clearly, the range of error is reduced by increased input
voltages. However, the input voltage is limited by the power-dissipating capability of the resistance
device, R 1 . The power that must be dissipated by this resistance is I
2
1 R 1 .
Deflection Method
In an unbalanced condition, the magnitude of the current or voltage drop for the meter portion of the
bridge circuit is a direct indication of the change in resistance of one or more of the arms of the
bridge. Consider first the case where the voltage drop from node B to node C in the basic bridge is
measured by a meter with infinite internal impedance, so that there is no current flow through the
meter, as shown in Figure 6.14. Knowing the conditions for a balanced bridge given in Equation 6.10,
the voltage drop from B to C can be determined, since the current I 1 must equal the current I 2 , as
E o ¼ I 1 R 1 À I 3 R 3
ð6:13Þ
Under these conditions, substituting Equations 6.9 to 6.11 into Equation 6.13 yields
E o ¼ E i
R 1
R 1 þ R 2
À
R 3
R 3 þ R 4
ð6:14Þ
The bridge is usually initially balanced at some reference condition. Any transducer
resistance change, as a result of a change in the measured variable, would then cause a deflection
in the bridge voltage away from the balanced condition. Assume that from an initially balanced
condition where E o ¼ 0, a change in R 1 occurs to some new value, R
0
1 ¼ R 1 þ dR. The output from
B
C
A
D
R 4
R 1
R 3
R 2
I 2
I 3
I 1
I 4
E i
E m
R m
∞
Figure 6.14 Voltage-sensitive Wheatstone bridge.
222 Chapter 6 Analog Electrical Devices and Measurements