EL 302-Instruments & Measurements
Lecture 05
DC Bridges (Continued..)
Wheatstone Bridge
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Thevenin’s Equivalent & Galvanometer Current
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DC Bridge (Wheatstone Bridge)
Upon balance condition
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Example (ii)
• A certain type of pressure transducer, designed to measure
pressures in the range 0–10 bar, consists of a diaphragm with
a strain gauge cemented to it to detect diaphragm deflections.
The strain gauge has a nominal resistance of 120Ω and forms
one arm of a Wheatstone bridge circuit, with the other three
arms each having a resistance of 120Ω. The bridge output is
measured by an instrument whose input impedance can be
assumed infinite. If, in order to limit heating effects, the
maximum permissible gauge current is 30mA, calculate the
maximum permissible bridge excitation voltage. If the
sensitivity of the strain gauge is 338mΩ/bar and the maximum
bridge excitation voltage is used, calculate the bridge output
voltage when measuring a pressure of 10 bar.
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Example (iii)
• Consider a platinum resistance thermometer with a range of 0°to
50°C, whose resistance at 0°C is 500Ω and whose resistance varies
with temperature at the rate of 4Ω/°C.
• Case(i): where R1=R2=R3 =500Ω and Vi =10 V
It would be like:
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Example (iii) (Continues..)
• Case(ii): where R1=500 but R2=R3=5000Ω and let Vi=26V:
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Example (iii) (Continues..)
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Sensitivity of Wheatstone bridge
• When the Wheatstone bridge is not balanced, a certain amount of
current flows through the galvanometer that depends upon the
sensitivity of the galvanometer.
• This is given by:
Sensitivity S=deflection D/current I (mm/µA, radians/µA or
degrees/µA)
• Greater the sensitivity of the galvanometer, greater its deflection.
• Another means of defining sensitivity of the galvanometer is the
amount of deflection per unit voltage across the galvanometer
means:
Sv=θ/e, (mm/mV, radians/mV or degrees/mV)
where ‘e’ is the voltage across the galvanometer and ‘θ’ is the
deflection of the galvanometer.
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Sensitivity of Wheatstone bridge
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Sensitivity of Wheatstone bridge under small unbalance
(in term of Voltage)
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Sensitivity of Wheatstone bridge under small unbalance
(in term of Current)
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Measurement Errors
• Very precise reference resistances are required to
properly balance the Wheatstone bridge
• Insufficient efficiency of the null detector might cause
error
• Resistance variations due to the heating effect
• Low value resistance measurement problems due to the
Thermal emf (A thermal EMF is a very small voltage in
the microvolt range (μV) which is produced due to
temperature variations across the resistor)
• Contact/Leads resistances exterior to the bridge might
cause errors
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Applications of the Wheatstone bridge
• Measurement of various DC resistances of
wires for quality control
• Measurement of motor winding resistance,
relay coils etc
• Used by telephone companies to detect
underground cable faults (line to line short
or line to ground short)
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Bridge in Control Circuits (Error Detectors)
• The unbalanced bridge causes a potential difference
across the galvanometer which causes current to flow
through the galvanometer, can be used as Indicating
Instrument.
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Bridge in Control Circuits (Error Detectors)
• The bridge can also be used in control
circuits (as error detector), the potential
developed due to unbalanced is used to
drive some other control circuit. This
potential is called error voltage (or output
voltage)
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Bridge in Control Circuits (Error Detectors)
Example:
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Limitations of the Wheatstone Bridge
• Effect of lead resistance and contact
resistance is very much significant while
measuring low resistance
• Cannot be used for high resistance
measurement as the galvanometer
becomes insensitive to show an imblance
• Heating effect due to large current
• Resistance tolerance upto 1% or 0.1%,
hence cost is high
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Assignment
1.
The wheatstone bridge shown in figure 3.6. calculate the unknown
resistance, assuming the bridge is in balanced condition. (25KΩ)
2.
In Example(i), calculate the bridge output voltage when measuring
a pressure of 3bar.
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3.
Consider a platinum resistance thermometer with a range of 0°to
50°C, whose resistance at 0°C is 200Ω and whose resistance
varies with temperature at the rate of 4Ω/°C. Draw and compare its
linearity curve for following cases:
Case (i): where R1=R2=R3 =200Ω and Vi =10 V
Case (ii): where R1=200Ω but R2=R3 =2000Ω and Vi =10 V
Case (ii): where R1=200Ω but R2=R3 =2000Ω and Vi =20 V
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