1. Unit V
Bridges & Measurement Of
Physical Parameters
-BY
GYNSK SRAVYA
ASST. PROFESSOR
2. Contents
Bridges:
» Wheat stone Bridge,
» Kelvin Bridge, and
» Maxwell Bridge
Measurement of Physical Parameters:
Flow measurement
Displacement meters
Liquid level measurement
Temperature Measurement
Measurement of Humidity and Moisture
Velocity Measurement
Force Measurement
Pressure- High pressure
Vacuum level Measurement
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3. Bridges
> Bridge circuit is an instrument to measure resistance, capacitance,
inductance and impedance.
In simplest form it consists of four arms network.
They use Comparison measurement technique and null- indication
principle.
This means the indication is independent of the calibration of the
indicating device or any characteristics of it.
Unknown components value is calculated when the bridge is
balanced.
4. Advantages of Bridge
Circuits
» Balance equation is independent of the magnitude of the input
voltage or the source impedance.
» High measurement accuracy since measurement is based on
comparison,
Pb Accuracy depends on components values and not on the
characteristics of the null detector.
5. Contd...
» 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.
6. Types of Bridges
» Two types of bridges are used in the measurement based on the
voltage signal with which those can be operated.
+ DC Bridges- Wheatstone Bridge, Kelvin Bridge
+ AC Bridges- Maxwell Bridge
7. DC Bridges
» If the bridge circuit can be operated with only DC voltage signal,
then it is a DC bridge circuit or simply DC bridge.
» DC bridges are used to measure the value of unknown resistance.
» The circuit diagram of DC bridge looks like as shown in below
figure.
8. Contd...
» The DC bridge has four arms and each arm consists of a resistor.
» Among which, two resistors have fixed resistance values, one resistor is a
variable resistor and the other one has an unknown resistance value.
» The above DC bridge circuit can be excited with a DC voltage source by
placing it in one diagonal.
» The galvanometer is placed in other diagonal of DC bridge. It shows some
deflection as long as the bridge is unbalanced.
9. Contd...
» Vary the resistance value of variable resistor until the galvanometer shows
null (zero) deflection.
» Now, the above DC bridge 1s said to be a balanced one. So, we can find the
value of unknown resistance by using nodal equations.
» DC bridges can be operated with only DC voltage signal.
» DC bridges are useful for measuring the value of unknown resistance, which
is present in the bridge.
» Wheatstone’s Bridge & Kelvin Bridge are examples of DC bridge.
10. Wheatstone Bridge
» Wheatstone's bridge is a simple DC bridge, which is mainly having
four arms. These four arms form a rhombus or square shape and
cach arm consists of one resistor.
» To find the value of unknown resistance, we need the galvanometer
and DC voltage source. Hence, one of these two are placed in one
diagonal of Wheatstone’s bridge and the other one is placed in
another diagonal of Wheatstone's bridge.
» It measures resistance from | ohm to lmegaohm.
11. Contd...
» Wheatstone’s bridge is used to measure the value of medium resistance,
The circuit dingram of Wheatstone’s bridge is shown in below figure.
12. Contd...
> R3 is a standard resistor and R4 is unknown resistor which is to be
measured.
» Bridge can be balanced by varying the value of R3 resistor.
» The above bridge circuit is balanced when no current flows through
the diagonal arm, DB. That means, there is no deflection in the
galvanometer, when the bridge is balanced.
13. Contd...
» The bridge will be balanced, when the following two conditions are
satisfied.
Tha voltage across arm AD is equal to the voltage across arm AB. Le.
Vap = Van
= HR = Ly Equation 1
Equation 2
15. Contd...
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16. Sensitivity of Wheatstone
Bridge
» When the bridge is in unbalanced condition, current flows through the
galvanometer causing deflection of the pointer,
» The amount of deflection is the function of sensitivity of the galvanometer.
» The sensitivity can be expressed as amount of deflection per uni
currentimm/pA, radians/pA or degrees/pA).
» Greater the sensitivity ofthe galvanometer, greater its deflection.
17. Unbalanced Wheatstone bridge
» By using Thevenin's theorem, the current through the galvanometer
can be determined.
and at point b,
9-12 Unbalanced wheatstone's bridge
18. Unbalanced Wheatstone bridge
Therefore, the voltage between a and b is the difference between E, and E,,
which represents Thévenin's equivalent voltage,
E ExR
=p = B+ R, =
Ry R,
herefore 3} -
Ry+Ry, Ri+R;)
Fig [IL] Thévenin's reshuance
21. Applications
It is a DC bridge which is used to measure the resistance from lohm to
low mega ohm.
A Wheatstone bridge may be used to measure the de resistance of various
types of wire, either for the purpose of quality control of the wire itself, or
of some assembly in which it is used.
For example, the resistance of motor windings, transformers, solenoids,
and relay coils can be measured.
Wheatstone Bridge Circuit is also used extensively by telephone
companies and others to locate cable faults.
The fault may be two lines shorted together, or a single line shorted to
ground,
22. Limitations
I. For low resistance measurement, the resistance of the leads and contacts
becomes significant and introduces an error. This can be eliminated by
Kelvin’s Double bridge.
2. For high resistance measurements, the resistance presented by the bridge
becomes so large that the galvanometer is insensitive to imbalance.
Therefore, a power supply has to replace the battery and a de VTVM
replaces the galvanometer. In the case of high resistance measurements in
mega ohms, the Wheatstone's bridge cannot be used.
3. Another difficulty in Wheatstone Bridge Circuit is the change in
resistance of the bridge arms due to the heating effect of current through
the resistance. The rise in temperature causes a change in the value ofthe
resistance, and excessive current may cause a permanent change in value.
23. Problems
I. Wheatstone bridge consists of the following parameters,
R1=10K ohm, R2=15K ohm and R3=40K ohm. Find
the unknown resistance Rx.
Solution: RiRr4-R2R3
RIRx=R2R3
Rx= R2R3/R] = (15K X 40K) 10K
= 60K ohms
24. Problems
2; An unbalanced Wheatstone bridge
consists of the following parameters,
R1=1K ohm, R2=25K ohm,
R3=3.5K ohm, R4 = 10K ohm and
Rg=300 ohms and DC source is of
6V. Find the current through the
galvanometer.
26. Kelvin’s Bridge
» When the resistance to be measured is of the order of magnitude of
bridge contact and lead resistance, a modified form of Wheatstone’s
bridge, the Kelvins Bridge theory is employed.
» Kelvins Bridge theory is a modification of Wheatstone's bridge and is
used to measure values of resistance below 1 0.
» In low resistance measurement, the resistance of the leads connecting
the unknown resistance to the terminal of the bridge circuit may affect
the measurement.
28. Contd...
» Ry represents the resistance of the connecting leads from R3 to
Rx (unknown resistance).
» The galvanometer can be connected either to point ¢ or to point a.
» When it is connected to point a, the resistance Ry, of the connecting lead
is added to the unknown resistance Rx, resulting in too high indication
for Rx.
# When the connection is made to point ¢, R3, is added to the bridge arm
R3 and resulting measurement of Rx is lower than the actual value,
because now the actual value of R3 is higher than its nominal value by
the resistance Ry.
29. Contd...
> If the galvanometer is connected to point b, in between points ¢ and a, in
such a way that the ratio of the resistance from c to b and that from a to
b equals the ratio of resistances R1 and R2, then =)
and the usual balance equations for the bridge give the relationship.
33. Contd...
» Equation (11.8) is the usual Wheatstone’s balance equation and it
indicates that the effect of the resistance of the connecting leads
from point a to point ¢ has been eliminated by connecting the
galvanometer to an intermediate position, b.
P The above principle forms the basis of the construction of Kelvin’s
Double Bridge, popularly known as Kelvin's Bridge. It is a Double
bridge because it incorporates a second set of ratio arms. Figure
11.11 shows a schematic diagram of Kelvin’s double bridge.
35. Contd...
» The second set of arms, a and b, connect the galvanometer to a point
c at the appropriate potential between m and n connection, i.e. Ry.
The ratio of the resistances of arms a and b is the same as the ratio of
RI and R2. The galvanometer indication is zero when the potentials
at k and c are equal.
(18.9)
37. Contd... cd
+ Ry+
p— J
Bla+b+ BR) avb+R,
__bRE bR, am + IR,
a+b R,
SL BRR, R,
— aR, — bR,
Ryla+ BAR)
BRR,
Rila+b+R, )
R, hE,
B, Ti
But
Therefore,
38. Contd...
» This is the usual equation for Kelvins Bridge theory. It indicates that
the resistance of the connecting lead has no effect on the
measurement, provided that the ratios of the resistances of the two
sets of ratio arms are equal. In a typical Kelvins Bridge theory the
range of a resistance covered is 1 — 0.00001 € (10 pu ohm) with an
accuracy of + 0.05% to + 0.2%.
39. Advantages
# It can measure the resistance value in the range of 0.1 pohms to 1.0
ohm.
# Power consumption is less
» Simple in construction
» Sensitivity is high.
40. Disadvantages
» For knowing whether the bridge is balanced or not, the sensitive
galvanometer is used.
» To obtain good sensitivity of the device, a high current is required.
» Manual adjustments are to made periodically when required.
41. Problems
# In the figure below the ratio of Ra to Rb is 1000 ohm, R1 is 5 ohm
and R1 is 0.5R2, What is the value of Rx.
43. Problems
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44. Problems
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45. Problems
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46. AC Bridges
# An AC Bridge, In its simplest form consists of 4 arms, a source of
excitation and a balance detector. Each arm consists of impedance.
» The source is an ac supply which supplies ac voltages at required
frequency.
» For low frequencies, powerline itself ean act as source of supply.
» For high frequencies, the electronic oscillators are used as source. A typical
oscillator has a range of 50 Hz to 125kHz with a power output of around 7
W.
# Commonly used balanced detectors are head phones, tunable amplifiers or
vibration galvanometers.
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47. Contd...
» The headphones are used as detectors at frequencies of 250Hz. to 3
to 4KHz.
» For single frequency a tuned detector is most sensitive detector at
frequency range is from [0Hz to 100Hz.
» For low audio frequencies vibration galvanometers are used at 5Hz
to 1000Hz, commonly used below 200Hz.
48. Contd...
» Impedances at AF or RF are commonly determined by means of an
ac Wheatstone bridge.
# This bridge is similar to a de bridge, except that the bridge arms are
impedances.
» The bridge is excited by an ac source rather than dc and
the galvanometer is replaced by a detector, such as a pair of
headphones, for detecting ac.
50. Contd...
» When the bridge is x | where Z1, 22. Z3 and Z4 are
the impedances of the arms, and are vector complex quantities that
possess phase angles.
» It is thus necessary to adjust both the magnitude and phase angles of
the impedance arms to achieve balance, i.e. the bridge must be
balanced for both the reactance and the resistive component.
51. Maxwell’s Bridge a"
» It is an Maxwell Inductance Capacitance bridge developed by
Maxwell,
» It measures an unknown inductance in terms of a known
capacitance.
53. Contd...
» The use of standard arm offers the advantage of compactness and
casy shielding. The capacitor is almost a loss-less component.
# One arm has a resistance RI in parallel with C1, and hence it is
easier to write the balance equation using the admittance of arm |
instead of the impedance.
55. Contd...
From Eq. (11.04)
we have
Equating real terms and imaginary terms we have
LLY nndL, = Cy Ry Ry
WC RR xR =a KR,
RR,
[REELS]
99
56. Contd...
» Maxwell Bridge Theory is limited to the measurement of low Q
values (1 — 10). The measurement is independent of the excitation
frequency. The scale of the resistance can be calibrated to
read inductance directly.
57. Maxwell Bridge Advantages and ”
Disadvantages
Advantages
# The frequency does not appear in the final expression of both
equations, hence it is independent of frequency.
> Maxwell's inductor capacitance bridge is very useful for the wide
range of measurement of inductor at audio frequencies.
58. Contd...
#» The bridge is particularly suited for inductances measurements,
since comparison with a capacitor is more ideal than with
another inductance.
» Commercial bridges measure from 1 — 1000 H, with + 2% error. (If
the Q is very large, Rl becomes excessively large and it is
impractical to obtain a satisfactory variable standard resistance in
the range of values required).
59. Contd...
Disadvantages
I. The variable standard capacitor is very expensive.
2. Inductance cannot be measured over a wide range, since Q is
proportional to inductance.
3. The bridge is limited to measurement of low quality coils (1 <Q <
10) and it is also unsuitable for low value of Q (i.e. Q < 1) from this
we conclude that a Maxwell bridge is used suitable only for medium
Q coils.
60. Problems
» In Maxwell's Bridge, as shown in the figure below, Determine the
values of the resistance R1 and inductance L1 of a coil after the
bridge is balanced with capacitance of 0.5 pF.
62. Contd...
» A maxwell bridge is used to measure inductive impedance. The
bridge constants at balance are C1=0.01 pF, R1=470KQ, R2=51KQ
and R3=100KQ. Find the series equialent of the unknown
impedance.
63. Contd...
R,
- 5k, o JOORXSIK ool
470k
L,= RR, C,
=5.1
kx 100k x 0.0)pf
=51H
The equivalent series circuit is shown in Fig. 11.22
R= 109K Le=81H
Fig. 11.22
63
64. Measurement of Physical Parameters
Flow measurement
Displacement meters
Liquid level measurement
Temperature Measurement
Measurement of Humidity and Moisture
Velocity Measurement
Force Measurement
Pressure- High pressure
Vacuum level Measurement
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65. Flow Measurement
# In many process industries, measurement of flow is an important
aspect,
» Depending on the quantity flowing such as Solid, Liquid and
gaseous appropriate method of flow rate measurement is used.
» Incase of solids, rate of mass flow rate is measured while in case of
liquids and gases flow interms of volume flow rate is measured.
67. Contd...
» The volume flow rate is used for finding flow of materials in liquids,
gases and semi liquid forms.
» Devices used for measurement are of 2 types
I. Mechanical type flow meters
2. Electrical type flow meters
68. Contd...
Different instruments are used for measurement of flow rate.
B
3
4
5.
Head type flowmeters (based on differential pressure measurement)
Variable area meters (Rotameters)
Mechanical Flow meters (Turbine flow meter)
Electromagnetic Flow meter
Anemometer
Ultrasonic Flow meter
Vertex Flow meter
69. Variable Area Flowmeter(Rotameter)
Blt gives visual indication of flow.
Advantages
I. Reliable and inexpensive.
2. It gives direct visual indication on linear scale.
It can measure flow rate in the range of m/sec to 0.1 m/sec.
Accuracy is 0.5 to 3% of full scale range.
Disadvantages
I. It must be mounted vertically.
Bubbles in the Auid results in oscillations of float.
71. Contd...
Advantages
I. Reliable & less rugged.
2. High accuracy.
3. Lighter.
Disadvantages
I. Large permanent pressure losses as bearing wears out.
Applications
I. Used in oil industries, for low viscosity and high flow measurements.
72. Electromagnetic Flowmeter
» Volume flow rates of
electrically conductive fluids
can be measured.
» According to Faraday's law
of electromagnetic induction,
voltage V induced across
length | of flowing fluid with
velocity v in the magnetic
flux density B 1s given by
» V=B.Lv
73. Contd...
Advantages
I. Simple construction & rugged with no moving parts.
2. No obstruction in flow is required.
3. Output is independent of temperature, viscosity
& Pressure.
4 Good accuracy & highly reliable.
5. Bidirectional flow measurements are possible.
6. It can measure flow in any size of tube because magnetic fields can be
generated easily.
74. Contd...
Disadvantages
I. Meter is expensive.
2. Conductivity of the fluid should not be less than 10pm.
3, The output signal is of very low level usually micro volts, therefore,
high amplification is required.
4. The system requires to generate magnetic field, which is bulky and
requires more floor space,
75. Liquid Level Measurement
# In modern manufacturing plants, various methods are used to measure
levels of liquids, solvents chemicals required for processing and
sometimes solids which are in the form of powders or small particles.
» It is used in industries not only for monitoring but also for measuring
liquid contents in tanks, reservoirs etc.,
76. Contd...
» Two methods are used for measurement
a Direct method
+ Dip stick
+ Bob and tape method
+ Hook Gauge
+ Float Gauge
a Indirect method
» Hydraulic method
Mechanical method
Pneumatic method
Electrical method
Ultrasonic method
Nucleonic method
77. Ultrasonic Method for Level
Measurement
B It is used to measure liquid
level in a tank.
» It is based on principle of
sound echo.
» This principle is also used for
measurement of thickness of a
given material.
78. Contd...
Advantages
I. This is a non disturbance technique i.e., it does not involve placing sensor in
the material.
2. Installation is easy.
i. It is used for liquids as well as solids measurements.
Disadvantages
I. System is costly.
2. The electronic circuit required for detection, amplification, synchronization
makes it a complex circuit.
79. Pneumatic Method
» This method Is also called
Bubbler method or Purge
method.
B It is suitable for liquid
measurements and also for
COITOSIVE liquids, liquids
containing solids.
80. Temperature Measurement
Based on the principle of operation of thermal expansion, different
temperature measurement instruments are used.
I. Bimetallic Strip
-
2. Liquid in gas thermometer
3. Pressure thermometer
82. Liquid in gas thermometer
PB It is used to measure temperature from -200 degree centigrade to 1000
degree centigrade range.
83. Velocity Measurement
+ Velocity transducers are used for measurement of Linear velocity as well as Angular
velocity.
Linear Velocity Measurement
» Based on the electromagnetic induction mechanical vibrations are converted in to
alternating voltages. Hence, called electromagnetic transducers.
# There are 2 types of EM transducers
I. Moving Coil type
2. Moving Magnet type
84. Moving Magnet type Velocity of
Transducer
Advantages
I. There are no mechanical surfaces or
contacts, hence the maintenance
required is negligible.
2 Robust and less expensive.
i. Output voltage is linearly
proportional to the velocity.
Disadvantages
—— Air gap I. Limited frequency response.
2 The stray magnetic fields affects the
performance of these transducers.
85. Angular Velocity Measurement
» The main disadvantage of linear velocity measurement is that for large
distance travel it is very difficult to detect with fixed reference.
» In such cases, Angular velocity transducers are used by converting
linear velocity in to angular velocity.
» The measurement of speed can be done with the help of
Tachogenerator.
86. Contd...
» Tachogenerators are of 2 types
I. Electrical type tachogenerator
2. Mechanical type tachogenerator
» Electrical type are preferred over mechanical type.
88. Contd...
Advantages
3
Output voltage is small enough to measure it with DC Voltmeters.
Polarity of output directly indicates direction ofrotation.
Disadvantages
Ba
Because of variation in contact resistances, considerable error is introduced in the output
voltage. Hence, the maintenance of commutator is required.
Non linearity in output occurs because of distortions in permanent magnetic field due to
large armature currents. Hence, input resistor should be very high as compared to output
resistor of generator.
89. AC Tachogenerator
» It is used to measure speed in only one direction.
#» The emf induced in quadrature coil is directly proportional to the rotor
speed and is in phase with applied voltage to the reference coil.
Wom ed 1)
90. Contd...
Advantages
I. Output can be calibrated in terms of amplitude and frequency of
induced voltage.
2. Commutator contact resistance problems are eliminated as the coil is
wounded on the stator.
Disadvantages
I. For low speed rotation, frequency of induced voltage is very low thus
ripples in output increases.
2. At high speeds frequency is very high, coil impedance increases. This
effects linearity of output.
91. Digital methods of measurement of
angular velocity
» Electro mechanical methods are used for angular velocity measurement
effectively for speeds of 10,000rpm or less.
» For higher speeds, electromechanical transducers are not suitable.
» The main advantage of digital method is that there is no physical
contact between shaft whose speed is to be measured and measuring
device, thus loading of shaft is avoided.
92. Contd...
» There are two methods
I. Photo Electric type Tachometer
2. Inductive type Tachometer
93. Photo Electric Tachometer
Advantuges
I. Output is Pulsmed output, i.c., output is in digital form,
So no additional ADC is required.
1 Amplitude of pulses is constant, hence complex
electronic circuit is not required
Disadvantages
I. Life time of light source is drawback, typical life time
of light source is 50,000 10 60,000 hours. Hence
|
Lpalib
ial helss necessary to replace light source.
Accuracy depends on error represented by one pulse
95. Measurement of Moisture
» There are two types of moisture measurement techniques.
I. Laboratory Techniques
2. Industrial Techniques
96. Laboratory Techniques for Moisture ol
Measurement
B It gives better accurate measurement, but requires longer time for
measurement.
» Different methods of Moisture measurement are
I. Water Separation Method
2. Gravimetric Methods
3. Phase Change Method
4. Equilibrium Relative Humidity Measurement
97. Industrial Techniques for Moisture .
Measurement
» These techniques are based on the change of physical property of the
material with moisture.
» Different methods of Moisture measurement are
I. Electrical Methods
2. Neutron Moderation
98. Measurement of Humidity
» The amount of water vapour in surrounding air is called Humidity.
» Three separate terms are used to represent the Humidity.
» Absolute Humidity H, It is defined as mass of water vapour in unit
volume of a moist air.
» Relative Humidity Hy, It is defined as ratio of moisture content of the gas
to the maximum moisture of gas at a temperature 1.¢., saturated gas.
» Generally it is expressed in percentage. The relative humidity of dry air is
zero, while that of air with all moisture is 100%.
99. Contd...
» Specific Humidity H, It is defined as mass of water in a unit mass
of a moist air.
» Dew Point It is defined as the saturation temperature of the mixture
at the corresponding vapour pressure. It is expressed in degree
centigrade.
100. Contd...
Bb The instruments used for measurement of relative humidity are
called HYGROMETERS.
» Some of the important types of Hygrometers are
I. Electrical Hygrometer
2. Psychrometer (Wet and dry bulb Hygrometer)
3. Hair Hygrometer
4. Dew Point Meter
102. Contd...
Advantages
I. Simple in construction.
2. High response time.
i. High sensitivity.
4. Digital readout is possible.
5. 1% variation in relative humidity can be detected.
Disadvantages
I. Consiant temperature environment is necessary.
2. Cannot measure extreme changes in humidity as scale becomes non linear.
i. Hygrometer gets damaged in 100% humid environment.
103. Displacement Measurement
Displacement is classified as
I. Translational Displacement
Rotational Displacement
» Some ofthe translational displacement transducers are
I. Resistive potentiometers
2. Strain gauges
i LVDT
4. Variable inductance transducers
Some of the angular displacement transducers are
I. Capacitive transducers
2. Synchros
106. Force Measurement
» According to Newton's Law, F= m.a
» Different methods are used for the measurement of Force.
I. Force measurement using Accelerometer
[a
Force measurement using Vibrating wire sensor
Les
Force measurement using Load cell
110. Column type load cell
Column type load cell structure
pr — Lode put
111. Pressure Measurement
» Pressure is a non electrical, physical quantity defined as force acting
per unit area measured at a given point over a surface.
» Classification of Pressure
112. Pressure Measurement by U tube
Manometer
> P—Pref=p.g.h
» P- pressure field
PB Pref reference pressure
source
PB g- gravitational constant
» h- difference in heights of
liquid levels in 2 columns
113. Pressure Measurement by Well type
Manometer
# Pressure measurement using well type manometer is given as,
114. High Pressure Measurement
» When the pressure exceeds 10.000 psi high pressure measurement
techniques are used.
» Bulk modulus resistance pressure gauge is used for high pressure
measurement,
117. Contd...
» Different instruments used for vaccum measurement are
I. Mc Leod Gauge
id
Thermal Conductive Gauge
I. Pirani Gauge
2. Thermo couple Gauge
3. lonization Gauge
118. Pirani Gauge
Advantages
I. Easy to operate
2 Simple design
Limitations
I. Scale is non linear
2 Calibration of pirani gauge is
dependent on nature of gas.
119. Data Acquisition Systems (DAS) ws
# The system used for data processing, data conversion, data
transmission, data storage is called DAS.
> DAS can be classified as follows
I. Analog DAS
2. Digital DAS
120. Data Acquisition Systems (DAS) 120
# A schematic block diagram of a General of DAS is shown below.
|
[]
[|]
1
[]
[J]
1
[1
x
]
r
121. AC BRIDGE
An ac bridge consist Gi four ams of impedances, a
source of excilalion @ndi@ balance detector.
»Used for measUEMERMBIRUARAOWN impedances (ke
inductance, cap for sforage factor,
dissipation factor, pRasESsE
» All the ac bridges
are basedon’
