This document discusses bridge circuits and their use in instrumentation and measurements. It describes how bridge circuits like the Wheatstone bridge use a null detection or null balancing principle to measure unknown components. The key advantages of bridge circuits are their high accuracy due to comparison-based measurements and independence from input voltage or source impedance. The document outlines various types of DC and AC bridges, providing examples like the Wheatstone, Kelvin, and Maxwell bridges. It also discusses bridge measurement techniques, sources of error, applications, and the use of bridges in control systems.

1. INSTRUMENTATION &
MEASUREMENTS
(EE-302)
WEEK 2
UIT SPRING 20161

2. Derived Units
 Units other than fundamental and supplementary are
derived from the fundamental and supplementary units
and are primarily classified into:
 Mechanical Units like mass, velocity, acceleration, force,
weight, torque, work, energy, power etc.
 Electric and Magnetic Units such as power, energy, ohms,
farads, henries, magnetic flux in webers, tesla etc.
 Thermal Units such as latent heat specific heat capacity,
sensible heat, calorific value etc.
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3. Problems
 A set of solved problems related to Units shall be
provided soon.
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4. Bridge Measurements
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5. Bridge Circuits & their importance
 Used not only for measurement of resistance but also
used for the measurement of capacitance and
inductance.
 In simplest form it consists of four arms network.
 They use Comparison measurement technique and null-
indication principle.
 Unknown component’s value is calculated when the
bridge is balanced.
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6. Advantages of Bridge Circuits
 Balance equation independent of the magnitude of the
input voltage or the source impedance.
 High measurement accuracy since measurement is
based upon comparison.
 Accuracy depends upon component values and not on
the characteristics of the null detector.
 Balance equation is independent of the sensitivity of the
null detector.
 Balance condition transparent to the interchange of
source and detector positions.
 Can be used in the control circuits.
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7. Types of Bridges
 DC bridges
 AC bridges
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8. DC bridges
 Wheatstone Bridge
 Kelvin Bridge
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9. AC Bridges
 Capacitance comparison bridge
 Inductance comparison bridge
 Maxwell’s Bridge
 Hay’s Bridge
 Anderson Bridge
 Schering Bridge
 Wien Bridge
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10. Wheatstone Bridge
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11.  R1 and R2 are called the ratio arms.
 R3 is called the standard arm containing the standard
known resistance.
 R4 is the unknown resistance to be measured.
 Battery connected between A and C.
 Galvanometer attached between B and D.
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Wheatstone Bridge

12.  The balanced condition is defined by a condition when
the galvanometer shows ZERO current through it.
 This bridge works on the principle of null deflection or
null indication.
 For zero current through the galvanometer, B and D
must be at the same potential.
 Thus potential AB should be equal to the potential AD.
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Wheatstone Bridge

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Wheatstone Bridge

14.  Thus R4=R3 R1/R2, and this is the required balanced
condition of this bridge.
 Depends upon the ratio of R1 and R2, hence the arms are
called ratio arms.
 Based upon Null indication, hence results are not
dependant upon the calibration characteristics of the
galvanometer.
 R3 could be varied to get the required resistance.
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Wheatstone Bridge

15. Industrial Form of the
Wheatstone Bridge
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16. 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, where ‘e’ is the voltage across the
galvanometer and ‘θ’ is the deflection of the galvanometer.
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17.  The bridge sensitivity can also be defined as the
deflection of the galvanometer per unit fractional change
in the unknown resistance. This is called SB defined by:
SB = θ/(
∆𝑅
𝑅
)
Here ∆𝑅/𝑅is unit fractional change in unknown resistance.
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Sensitivity of Wheatstone bridge

18. Wheatstone bridge under small
Unbalance
 At the balance condition, 𝑅4 = 𝑅3
𝑅1
𝑅2
, this means
 𝑅4/𝑅3 = 𝑅1/𝑅2.
 Under the unbalanced condition the bridge would look
like:
 Here ∆𝑅 is creating
The unbalance.
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19. UIT SPRING 201619
Wheatstone bridge under small
Unbalance

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Wheatstone bridge under small
Unbalance

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Wheatstone bridge under small
Unbalance

22. Thevenin’s Equivalent &
Galvanometer Current
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23. UIT SPRING 201623
Thevenin’s Equivalent &
Galvanometer Current

24. Galvanometer current under
Unbalanced Condition
 For such a case, various relationships are given below:
 VTH = ERΔR/4R2 = EΔR/4R
 Req = R2/2R + R2/2R = R
 and subsequently
 Ig = EΔR/4R/R+Rg = E (ΔR/4R)/R+Rg
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25. 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.
 Contact/Leads resistances exterior to the bridge might
cause errors.
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26. 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.
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27. Advantages of the Wheatstone
bridge
 Null Detection mechanism ensures accurate results.
 Source fluctuations do not hamper readings.
 Accuracy and sensitivity higher than direct reflection
meters.
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28. Limitations of the Wheatstone
bridge
 Effect of lead and contact resistance becomes significant
while measuring small resistances.
 Cannot be used to measure resistances in the mega
ohms range, this happens because of the high resistance
presented by the bridge and the inability of the
galvanometer to show any imbalance.
 Heating effect as a result of current may permanently
damage the resistors.
 Used resistances must be very precise with 1% or 0.1%
that costs high.
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29. Example
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30. Example 2
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31. UIT SPRING 201631
Example 2-Solution

32. Kelvin bridge
 Low resistances can not be accurately measured by the
Wheatstone bridge due inaccuracies caused by the lead
and contact resistances.
 For low resistance measurement (below 1Ω) Kelvin
bridge is used.
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33. UIT SPRING 201633
Kelvin bridge

34.  Ry represents the resistance of the connecting leads
from R3 to Rx.
 Rx is the unknown resistance to be measured.
 Galvanometer could be connected either at ‘a’, ‘b’ or ‘c’
positions.
 If the galvanometer is connected to ‘a’ , the lead
resistance Ry added to Rx. If the galvanometer is
connected to ‘c’, then Ry gets added to R3.
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Kelvin bridge

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Kelvin bridge

36. Kelvin bridge
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37. Double Kelvin’s bridge
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38. Kelvin Double bridge
 Contains a second arm with resistances ‘a’ and ‘b’. With
these resistances the galvanometer is connected to point
3.
 Galvanometer gives null deflection when the potential of
the terminal 3 is the same as that of the potential of the
terminal 4.
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39.  The equivalent circuit when the galvanometer is carrying
zero current i.e the balanced condition is shown below:
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Then balance equation for the bridge is:
Rx = R1 R3/R2

40. Bridge in Control Circuits
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41.  Parameter sensitive resistance generates the error signal
which could be used for the control purposes. This
mechanism is the same for a number of bridge based
error generation scenarios.
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42. AC Bridges
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43. Sources & Detectors
 At very low frequencies, the power line itself can act as
source of supply.
 For high frequencies, electronic oscillators are used as
supply.
 A typical oscillator has a range of 50 Hz to 125kHz with
a power output of around 7 W.
 Common detectors for AC bridges are Headphones,
Vibration galvanometers and Tunable amplifier
detectors.
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44.  Headphones: from 250 Hz upto 4kHz.
 Vibration Galvanometers: low audio frequencies 5 Hz to
1000 Hz.
 Tunable amplifier detectors: 10 Hz to 100 kHz.
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45. Bridge balance equations
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46. UIT SPRING 201646

47. The summary….
 THE PRODUCTS OF THE MAGNITUDES OF THE OPPOSITE
ARMS MUST BE EQUAL WHILE SUM OF THE PHASE
ANGLES OF THE OPPOSITE ARMS MUST BE EQUAL.
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