LECTURE:-01
Measurement generally involves using an instrument as a physical means of
determining a quantity or variable. The instrument serves as an extension of human faculties
and in many cases enables a person to determine the value of an unknown quantity which his
unaided human faculties could not measure.
An instrument, then, may be defined as a device for determining the value or
magnitude of a quantity or variable. The electronic instrument, as its name implies, is based
on electrical and electronic principles for its measurement function. An electronic instrument
may be a relatively uncomplicated device of simple construction such as a basic dc current
meter. As technology expands, however, the demand for more elaborate and more accurate
instrument increases and produces new developments in instrument design and application.
To use these instruments intelligently, one needs to understand their operating principles and
to appraise their suitability for the intended application. Measurement work employs a
number of terms which should be defined here. Instrument a device for determining the value
or magnitude of a quantity or variable.
Basically there are three types of measuring instruments and they are
(a) Electrical measuring instruments
(b) Mechanical measuring instruments.
(c) Electronic measuring instruments.
Here we are interested in electrical measuring instruments so we will discuss about
them in detail. Electrical instruments measure the various electrical quantities like electrical
power factor, power, voltage and electric current etc. All analog electrical instruments use
mechanical system for the measurement of various electrical quantities but as we know the all
mechanical system has some inertia therefore electrical instruments have a limited time
response.
Now there are various ways of classifying the instruments. On broad scale we can
categorize them as:
Absolute Measuring Instruments
These instruments give output in terms of physical constant of the instruments. For example
Rayleigh’s current balance and Tangent galvanometer are absolute instruments.
Secondary Measuring Instruments
These instruments are constructed with the help of absolute instruments. Secondary
instruments are calibrated by comparison with an absolute instrument. These are more
frequently used in measurement of the quantities as compared to absolute instruments, as
working with absolute instruments is time consuming.
Another way of classifying the electrical measuring instruments depends on the way they
produce the result of measurements. On this basis they can be of two types:
Deflection Type Instruments
In these types of instruments, pointer of the electrical measuring instrument
deflects to measure the quantity. The value of the quantity can be measured by measuring the
net deflection of the pointer from its initial position. In order to understand these types of
instruments let us take an example of deflection type permanent magnet moving coil ammeter
which is shown below:
Deflection type Permanent Magnet Moving Coil Ammeter
The diagram shown above has two permanent magnets which are called the stationary part of
the instrument and the moving part which is between the two permanent magnets that
consists of pointer. The deflection of the moving coil is directly proportion to the current.
Thus the torque is proportional to the current which is given by the expression Td = K.I,
where Td is the deflecting torque. K is proportionality constant which depends upon
the strength of the magnetic field and the number of turns in the coil. The pointer deflects
between the two opposite forces produced by the spring and the magnets. And the resulting
direction of the pointer is in the direction of the resultant force. The value of current is
measured by the deflection angle θ, and the value of K.
Null Type Instruments
In opposite to deflection type of instruments, the null or zero type electrical measuring
instruments tend to maintain the position of pointer stationary. They maintain the position of
the pointer stationary by producing opposing effect. Thus for the operation of null type
instruments following steps are required:
(1) Value of opposite effect should be known in order to calculate the value of unknown
quantity.
(2) Detector shows accurately the balance and the unbalance condition accurately.
The detector should also have the means for restoring force.
Advantages and disadvantages of deflection and null type of measuring instruments:
(1) Deflection type of instruments is less accurate than the null type of instruments. It is
because, in the null deflecting instruments the opposing effect is calibrated with the high
degree of accuracy while the calibration of the deflection type instruments depends on the
value of instrument constant hence usually not having high degree of accuracy.
(2) Null point type instruments are more sensitive than the Deflection type instruments.
(3) Deflection type instruments are more suitable under dynamic conditions than null type of
instruments as the intrinsic responses of the null type instruments are slower than deflection
type instruments.
Following are the important three functions of the electrical measuring instruments.
Indicating Function
These instruments provide information regarding the variable quantity under measurement
and most of the time this information are provided by the deflection of the pointer. This kind
of function is known as the indicating function of the instruments.
Recording Function
These instruments usually use the paper in order to record the output. This type of function is
known as the recording function of the instruments.
Controlling Function
This is function is widely used in industrial world. In this these instruments controls the
processes. Now there are two characteristics of electrical measuring instruments and
measurement systems. They are written below:
Static Characteristics
In these type of characteristics measurement of quantities are either constant or vary slowly
with the time. Few main static characteristics are written below:
Accuracy closeness with which an instrument reading approaches the true value of the
variable being measured.
Precision a measure of the reproducibility of the measurements; i.e., given a fixed value of a
variable, precision is a measure of the degree to which successive measurements differ from
one another.
Sensitivity the ratio of output signal or response of the instrument to a change of input or
measured variable. Resolution the smallest change in measured value to which the instrument
will respond.Error deviation from true value of the measured value.
Several techniques may be used to minimize the effects of errors. For example, in
making precision measurements, it is advisable to record a series of observations rather than
rely on one observation. Alternate methods of measurement, as well as the use of different
instruments to perform the same experiment, provide a good technique for increasing
accuracy. Although these techniques tend to increase the precision of measurement by
reducing environmental or random error, they cannot account for instrumental error.
In order to understand the concept of errors in measurement, we should know the
two terms that defines the error and these two terms are written below:
True Value
It is not possible to determine the true of quantity by experiment means. True value
may be defined as the average value of an infinite number of measured values when average
deviation due to various contributing factor will approach to zero.
Measured Value
It may be defined as the approximated value of true value. It can be found out by taking
means of several measured readings during an experiment, by applying suitable
approximations on physical conditions.
Now we are in a position to define static error. Static error is defined as the difference of the
measured value and the true value of the quantity. Mathematically we can write an expression
of error as, dA = Am - At where dA is the static error Am is measured value and At is true
value.
It may be noted that the absolute value of error cannot be determined as due to the fact that
the true value of quantity cannot be determined accurately.
Let us consider few terms related to errors.
Limiting Errors or Guarantee Errors
The concept of guarantee errors can better clear if we study this kind of error by considering
one example. Suppose there is a manufacturer who manufacture an ammeter, now he should
promises that the error in the ammeter he is selling not greater the limit he sets. This limit of
error is known as limiting errors or guarantee error.
Relative Error or Fractional Error
It is defined as the ratio of the error and the specified magnitude of the quantity.
Mathematically we write as,
𝑑𝐴
Relative Error = 𝐴
Where dA is the error and A is the magnitude.
LECTURE:-02
Accuracy and Precision
Accuracy refers to the degree of closeness or conformity to the true value of the quantity
under measurement. Precision refers to the degree of agreement within a group of
measurements or instruments.
To illustrate the distinction between accuracy and precision, two voltmeters of the same make
and model may be compared. Both meters have knife-edged pointers and mirror-backed
scales to avoid parallax, and they have carefully calibrated scales. They may therefore be read
to the same precision. If the value of the series resistance in one meter changes considerably,
its readings may be in error by a fairly large amount. Therefore the accuracy of the two
meters may be quite different. (To determine which meter is in error, a comparison
measurement with a standard meter should be made.)
Precision is composed of two characteristics: conformity and the number of significant
figures to which a measurement can be made. Consider, for example, that a resistor, whose
true resistance is 1,384,572Ω , is measured by an ohmmeter which consistently and
repeatedly indicates 1.4 MΩ. But can the observer “read” the true value from the scale? His
estimates from the scale reading consistently yield a value of 1.4 MΩ. This is as close to the
true value as he can read the scale by estimation. Although there are no deviations from the
observed value, the error created by the limitation of the scale reading is a precision error.
The example illustrates that conformity is a necessary, but not sufficient condition for
precision because of the lack of significant figures obtained. Similarly, precision is a
necessary, but not sufficient condition for accuracy. Too often the beginning student is
inclined to accept instrument readings at face value. He is not aware that the accuracy of a
reading is not necessarily guaranteed by its precision. In fact, good measurement techniques
demands continuous skepticism as to the accuracy of the results. In critical work, good
practice dictates that the observer make an independent set of measurements, using different
instruments or different measurement techniques, not subject to the same systematic errors.
He must also make sure that the instruments function properly and are calibrated against a
known standard, and that no outside influence affects the accuracy of his measurements.
Significant Figures
An indication of the precision of the measurement is obtained from the number of
significant figures in which the result is expressed. Significant figures convey actual
information regarding the magnitude and the measurement precision of a quantity.The more
significant figures, the greater the precision of measurement.
For example, if a resistor is specified as having a resistance of 68 , its resistance should be
closer to 68Ω than to 67Ω or 69 Ω. If the value of the resistor is described as 68.0 Ω, it
means that its resistance is closer to 68.0Ω than it is to 67.9Ω or 68.1Ω. In 68Ω there are two
significant figures; in 68.0Ω there are three. The latter, with more significant figures,
expresses a measurement of greater precision than the former.
Often, however, the total number of digits may not represent measurement precision.
Frequently, large numbers with zeros before a decimal point are used for approximate
populations or amounts of money.
For example, the population of a city is reported in six figures as 380,000. This may imply
that the true value of the population lies between 379,999 and 380,001, which is six
significant figures. What is meant, however, is that the population is closer to 380,000 than
370,000 or 390,000. Since in this case the population can be reported only to two significant
figures, how can large numbers are expressed? A more technically correct notation uses
powers of ten, 38 × 104 or 3.8 × 105. This indicates that the population figure is only
accurate to two significant figures. Uncertainty caused by zeros to the left of the decimal
point is therefore usually resolved by scientific notation using powers of ten. Reference to the
velocity of light as 186,000 mi/s, for example, would cause no misunderstanding to anyone
with a technical background. But 1.86 × 105 mi/s leaves no confusion. It is customary to
record a measurement with all the digits of which we are sure nearest to the true value. For
example, in reading a voltmeter, the voltage may be read as 117.1 V. This simply indicates
that the voltage, read by the observer to best estimation, is closer to 117.1 V than to 117.0 V
or 117.2 V.
Another way of expressing this result indicates the range of possible error. The voltage may
be expressed as 117.1 ± 0.05 V, indicating that the value of the voltage lies between 117.05 V
and 117.15 V. When a number of independent measurements are taken in an effort to obtain
the best possible answer (closest to the true value), the result is usually expressed as the
arithmetic mean of all the readings, with the range of possible error as the largest deviation
from that mean. 3
Numericals
Example 1
A set of independent voltage measurements taken by four observers was recorded as 117.02
V, 117.11 V, 117.08 V, and 117.03 V. Calculate
1. the average voltage,
2. the range of error.
Solution
1. Average Voltage
Eav =
=
𝐸1+𝐸2+𝐸3+𝐸4
𝑁
117.02+117.11+117.08+117.03
4
=117.06 V
2. Range
Range = Emax − Eav = 117.11 − 117.06 = 0.05 V
but also Eav − Emin = 117.06 − 117.02 = 0.04 V
The average range of error therefore equals (0.05 + 0.04)/2= ±0.045 = ±0.05V
Example 2
Two resistors R1 and R2, are connected in series. Individual resistance measurements, using
a Wheatstone bridge, give R1 = 18.7 Ω and R2 = 3.624 Ω. Calculate the total resistance to the
appropriate number of significant figures.
Solution
R1 = 18.7 Ω (three significant figures)
R2 = 3.624 Ω (four significant figures)
RT = R1 + R2 = 22.324 Ω (five significant figures) = 22.3 Ω
The doubtful figures are written in italics to indicate that in the addition of R1 and R2 the last
three digits of the sum are doubtful figures. There is no value whatsoever in retaining the last
two digits (the 2 and the 4) because one of the resistances is accurate only to three significant
figures or tenths of an ohm. The result should therefore also be reduced to three significant
figures or the nearest tenth, i.e. 22.3 Ω .
Example 3
Add 826 ± 5 to 628 ± 3
Solution
N1 = 826 ± 5 (= ±0.605%)
N2 = 628 ± 3 (= ±0.477%)
Sum = 1454 ± 8 (= ±0.55%)
Example 4
Subtract 628 ± 3 from 826 ± 5 and express the range of doubt in the answer as a percentage.
Solution
N1 = 826 ± 5 (= ±0.605%)
N2 = 628 ± 3 (= ±0.477%)
Difference = 198 ± 8 (= ±4.04%)
Example 5
Subtract 437 ± 4 from 462 ± 4 and express the range of doubt in the answer as a percentage.
Solution
N1 = 462 ± 4 (= ±0.87%)
N2 = 437 ± 4 (= ±0.92%)
Difference = 25 ± 8 (= ±32%)
Types of Error
No measurement can be made with perfect accuracy, but it is important to find out what the
accuracy actually is and how different errors have entered into the measurement. A study of
errors is a first step in finding ways to reduce them. Such a study also allows us to determine
the accuracy of the final test result.
Errors may come from different sources and are usually classified under three main headings:
Gross Errors: Largely human errors, among them misreading of instruments, incorrect
adjustment and improper application of instruments, and computational mistakes.
Systematic Errors: Shortcomings of the instruments, such as defective or worn parts, and
effects of the environment on the equipment or the user.
Random Errors: Those due to causes that cannot be directly established because of random
variations in the parameter or the system of measurement. Each of these classes of errors will
be discussed briefly and some methods will be suggested for their reduction or elimination.
Gross Errors
This class of errors mainly covers human mistakes in reading or using instruments and in
recording and calculating measurement results. As long as human beings are involved, some
gross errors will inevitably be committed. Although complete elimination of gross errors is
probably impossible, one should try to anticipate and correct them. Some gross errors are
easily detected; others may be very elusive. One common gross error, frequently committed
by beginners in measurement work, involves the improper use of an instrument. In general,
indicating instruments change conditions to some extent when connected into a complete
circuit, so that the measured quantity is altered by the method employed. For example, a wellcalibrated voltmeter may give a misleading reading when connected across two points in a
highresistance circuit .The same voltmeter, when connected in a low-resistance circuit, may
give a more dependable reading .These examples illustrate that the voltmeter has a “loading
effect” on the circuit, altering the original situation by the measurement process.
Systematic Errors
This type of errors is usually divided into two different categories:
1. Instrumental errors, defined as shortcomings of the instrument;
2. Environmental errors, due to external conditions affecting the measurement.
Instrumental errors are errors inherent in measuring instruments because of their
mechanical structure.
For example, in the d’Arsonval movement, friction in bearings of various moving
components may cause incorrect readings. Irregular spring tension, stretching of the spring,
or reduction in tension due to improper handling or overloading of the instrument will result
in errors. Other instrumental errors are calibration errors, causing the instrument to read high
or low along its entire scale. (Failure to set the instrument to zero before making a
measurement has a similar effect.) There are many kinds of instrumental errors, depending on
the type of instrument used. The experimenter should always take precautions to insure that
the instrument he is using is operating properly and does not contribute excessive errors for
the purpose at hand. Faults in instruments may be detected by checking for erratic behavior,
and stability and reproducibility of results. A quick and easy way to check an instrument is to
compare it to another with the same characteristics or to one that is known to be more
accurate.
Instrumental errors may be avoided by:
1. Selecting a suitable instrument for a particular measurement application;
2. Applying correction factors after determining the amount of instrumental error;
3. Calibrating the instrument against a standard.
Environmental errors are due to conditions external to the measuring device,
including conditions in the area surrounding the instrument, such as the effects of changes in
temperature, humidity, barometric pressure, or of magnetic or electrostatic fields. Thus a
change in ambient temperature at which the instrument is used causes a change in the elastic
properties of the spring in a moving-coil mechanism and so affects the reading of the
instrument. Corrective measures to reduce these effects include air conditioning, hermetically
sealing certain components in the instrument, use of magnetic shields, and the like.
Systematic errors can also be subdivided into static or dynamic errors. Static errors
are caused by limitations of the measuring device or the physical laws governing its behavior.
A static error is introduced in a micrometer when excessive pressure is applied in torquing
the shaft. Dynamic errors are caused by the instrument’s not responding fast enough to follow
the changes in a measured variable.
Random Errors
These errors are due to unknown causes and occur even when all systematic errors
have been accounted for. In well-designed experiments, few random errors usually occur, but
they become important in high-accuracy work. Suppose a voltage is being monitored by a
voltmeter which is read at half-hour intervals. Although the instrument is operated under
ideal environmental conditions and has been accurately calibrated before the measurement, it
will be found that the readings vary slightly over the period of observation. This variation
cannot be corrected by any method of calibration or other known method of control and it
cannot be explained without minute investigation. The only way to offset these errors is by
increasing the number of readings and using statistical means to obtain the best
approximation of the true value of the quantity under measurement.
LECTURE:-03
STANDARDS OF MEASUREMENTS
The standards of measurements are very useful for calibration of measuring
instruments. They help in minimizing the error in the measurement systems. On the basis of
the accuracy of measurement the standards can be classified as primary standards and
secondary standards.
Primary Standard
A primary standard quantity will have only one value and it is fixed. An instrument
which is used to measure the value of primary standard quantity is called primary standard
instrument. It gives the accurate value of the quantity being measured. No pre-calibration is
required for this instrument. It is used to calibrate the instruments having less accuracy. By
comparing the readings of the two instruments, the accuracy of the second instrument can be
determined.
Secondary Standard
The value of the secondary standard quantity is less accurate than primary standard
one. It is obtained by comparing with primary standard. For measurement of a quantity using
secondary standard instrument, pre-calibration is required. Without calibration, the result
given by this instrument is meaningless. Calibration of a secondary standard is made by
comparing the results with a primary standard instrument or with an instrument having high
accuracy or with a known input source. In practical fields, secondary standard instruments
and devices are widely used. Using calibration charts, the error in the measurement of these
devices can be reduced.
STANDARD UNIT OF LENGTH
The meter is considered as one of the fundamental unit upon which, through
appropriate conversion factors, the English system of length is based. The SI unit of length in
metre.
The standard meter is defined as the length of a platinum-iridium bar maintained at very
accurate conditions at the International Bureau of Weights and Measures at Sevres, near
Paris, France. All other meters had to be calibrated against the meter. The conversion factor
for length for English and Metric systems in the United States is fixed by law as 1 meter =
39.37 inches
Secondary standard of length is maintained at the National Bureau of Standards for
calibration purposes. In 1960, the general conference on weights and measures defined the
standard meter in terms of the wavelength of the orange-red light of a krypton-86 lamp. The
standard meter is thus
1 meter = 1,650,763.73 wavelengths of orange-red light of Krypton-86
In 1982, the definition of the meter was changed to the distance light travels in
1/299,792,458ths of a second. For the measurement, light from a helium-neon laser
illuminates iodine which fluorescence at a highly stable frequency.
In CGS system, the fundamental unit of length is centimeter. Its conversion factors for
other system are already mentioned above. The derived units for length are as follows:
1 m = 100 cm
1 km = 105 cm = 1000 m
1 mm = 10 -3 m = 10 -1 cm
1 centimeter = 10 2 m
1 decimeter = 10 -1 m
1 decameter = 10 m
1 hectometer = 102 m.
We also have some other units, which are frequently used for short and large lengths.
STANDARD UNIT OF WEIGHT
The kilogram is considered as fundamental unit upon which, through appropriate
conversion factors, the English system of mass is based. The SI unit of mass is kilogram. The
standard kilogram is defined in terms of platinum-iridium mass maintained at very accurate
conditions at the International Bureau of Weights and Measures in Sevres, France.
The conversion factors for the English and Metric systems in the United States are fixed by
law is 1 pound-mass = 453.59237 grams = 0.45359237 kilogram
Secondary standard of mass is maintained at the National Bureau of Standards for
calibration purpose. In MKS and SI systems, fundamental unit of mass is kilogram, whereas
in CGS system, the unit for the same is gram. The conversion factors for the above units and
units derived from them are as follows:
1 kilogram = 1000 grams; 1 gram = 10– 3 kilogram
1 hectogram = 100 grams = 10– 1 kilogram
1 decagram = 10 grams = 10– 2 kilogram
1 milligram = 0.001 gram = 10– 6 kilogram
STANDARD UNIT OF TIME
The standard units of time are established in terms of known frequencies of oscillation
of certain devices. One of the simplest devices is a pendulum. A torsional vibration system
may also be used as a standard of frequency. The torsional system is widely used in clocks
and watches. Ordinary 50 HZ line voltage may be used as a frequency standard under certain
circumstances. An electric clock uses this frequency as a standard because it operates from a
synchronous electric motor whose speed depends on line frequency. A turning fork is a
suitable frequency source, as are piezo-electric crystals. Electronic oscillator may also be
designed to serve as very precise frequency sources. The SI unit of time is second.
The fundamental unit of time, the second, has been defined in the past as of a mean
solar day. The solar day is measured as the time interval between successive transits of the
sun across a meridian of the earth. The time interval varies with location of the earth and time
of the year, however, the mean solar day for one year is constant. The solar year is the time
required for the earth to make one revolution around the sun. The mean solar year is 365 days
5 hr 48 min 48 s .
STANDARD UNIT OF TEMPERATURE
An absolute temperature scale was proposed by Lord Kelvin in 1854 and forms the
basis for thermodynamic calculations. This absolute scale is so defined that particular
meaning is given to the second law of thermodynamics when this temperature scale is used.
Derived Units
The units of all other physical quantities can be expressed in terms of these base units.
For example, we can express the unit of speed in meter per second, the unit of density in
kilogram per cubic meter. Let us consider another physical quantity like force. From
Newton’s second law of motion, force can be defined as the product of mass and
acceleration. We can therefore take the unit of force as 1 kilogram x 1 meter/second2. We call
this by the name, Newton for convenience. The unit of energy is Newton-meter. We call this
by the name Joule. The unit of power is Joule per second. We call it Watt.
The conversion factor for various units is
1 H.P = 746 watt (J/s)
1 H.P = 550 ft-1b/sec.
1 H.P = 75 kg-m/sec.
STANDARD UNIT OF LUMINOUS INTENSITY OF A SOURCE OF LIGHT
Candela is the SI unit of luminous intensity of a source of light in a specified
direction. The candela is the luminous intensity of a black body of surface area 1/60,000 m 2
placed at the temperature of freezing platinum and at a pressure of 101, 325 N/m2, in the
direction perpendicular to its surface. Now candela is redefined as the luminous intensity in a
given direction of a source that emits monochromatic radiation of frequency 540 x 10
12
Hz
and that has a radiant intensity in that direction of 1/683 watt per steradian. (SI unit of solid
angle).
STANDARD UNIT OF AMOUNT OF SUBSTANCE
The mole (mol) is the SI unit of amount of substance.
One mole is the amount of substance of a system that contains as many elementary entities as
there are atoms in 0.012 kg of carbon – 12.
LECTURE:-04
STANDARD UNITS OF ELECTRICAL QUANTITIES
The International conference on electrical units in London in 1908 confirmed the
absolute system units adopted by the British Association Committee on Electrical
Measurement in 1863.
This conference decided to specify some material standard
which can be produced in isolated laboratories and used as International standards. The
desired properties of International standards are that they should have a definite value, be
permanent, and be readily set up anywhere in the world, also that their magnitude should be
within the range at which the most accurate measurements can be done.
The four units – ohm, ampere, volt and watt – established by above specifications
were known as International units. The ohm and ampere are primary standards. Definitions of
International unit are given below.
International Ohm
The international ohm is the resistance offered to the passage of an unvarying electric
current at the temperature of melting ice by a column of mercury of uniform cross-section,
106.300 cm long and having mass of 14.4521 gm (i.e., about 1 sq. mm in cross-section).
International Ampere
The international ampere is the unvarying current which when passed through a
solution of silver nitrate in water deposits at the rate of 0.0001118 gm per second.
The International Volt and Watt
The international volt and watt defined in terms of International ohm and ampere. As
constructing standards, which did not vary appreciably with time, was difficult and also as,
by 1930, it was clear that the absolute ohm and ampere could be determined as accurately as
the international units. The International committee on Weights and Measures decided in
October, 1946 to abandon the international units and choose January 1, 1948 as the date for
putting new units into effect. The change was made at appropriate time and the absolute
system of electrical units is now in use as the system on which electrical measurements are
based.
IEEE Standards
The Institute of Electrical and Electronics Engineers (IEEE) is a professional
association with its corporate office in New York City and its operations center in
Piscataway, New Jersey. It was formed in 1963 from the amalgamation of the American
Institute of Electrical Engineers and the Institute of Radio Engineers. Today it is the world's
largest association of technical professionals with more than 400,000 members in chapters
around the world. Its objectives are the educational and technical advancement of electrical
and electronic engineering, telecommunications, computer engineering and allied disciplines.
These standards are not physical items that are available for comparison and checking
of secondary standards but are standard procedure, nomenclature, definitions etc. These
standards have been kept updated. Many of the IEEE standards have been adopted by other
agency and societies as- standards form their organization such as the America National
Standards Institute.
LECTURE:-05
A resistance is a parameter which opposes the flow of current in a closed electrical
network. It is expressed in ohms, milliohms, kilo-ohms, etc. as per the ohmic principle, it is
given by;
R = V/I; with temperature remaining constant.
If temperature is not a constant entity, then the resistance, R2 at t2 0C is given by;
R2 = R1 [1+ α (t2-t1)]
Where t= t1-t2, the rise in temperature from t1 0C to t2 0C, α is the temperature coefficient of
resistance and R1 is the temperature at t1 0C.
Resistance can also be expressed in terms of its physical dimensions as under:
R = ρl/A
Where, l is the length, A is the cross sectional area and ρ is the specific resistance or
resistivity of the material of resistor under measurement.
To realize a good resistor, its material should have the following properties:

Permanency of its value with time.

Low temperature coefficient of resistance

High resistivity so that the size is smaller

Resistance to oxidation, corrosion, moisture effects, etc.

Low thermo electric emf against copper, etc.
CLASSIFICATION OF RESISTANCES
For the purposes of measurements, the resistances are classified into three major
groups based on their numerical range of values as under:

Low resistance (0 to 1 ohm)

Medium resistance (1 to 100 kilo-ohm) and

High resistance (>100 kilo-ohm)
Accordingly, the resistances can be measured by various ways, depending on their range of
values, as under:
1. Low resistance (0 to 1 ohm): AV Method, Kelvin Double Bridge, potentiometer, etc.
2. Medium resistance (1 to 100 kilo-ohms): AV method, wheat stone’s bridge, substitution
method, etc.
3. High resistance (>100 kilo-ohms): AV method, fall of potential method, Megger, loss of
charge method, substitution method, bridge method, etc.
Kelvin Double Bridge Method of Measurement of Low Resistance
Kelvin Bridge, a modification of Wheatstone bridge, method increases the accuracy in
measurement of low resistance and remove the effect of connecting leads and contact
resistance. As shown in figure , r represents the resistance of lead that connects the unknown
resistance R and standard resistance S . The galvanometer is connected at point d that divides
the resistance r into r1 and r2 such that,
𝑟1
𝑟2
𝑃
=𝑄
From the above equation we have
𝑟1
𝑃
𝑟1+𝑟2
𝑟1+𝑟2
𝑟2
𝑃
=𝑃+𝑄
or r1= 𝑃+𝑄r
𝑃+𝑄
=
𝑄
or r2= 𝑃+𝑄r
𝑄
From the figure on balanced condition
𝑅+𝑟1
𝑆+𝑟2
𝑃
=𝑄
𝑃
R+r1= 𝑄 (S+r2)
Substituting the values of r1 &r2 we get
𝑃
R= 𝑄 S
So, connecting the galvanometer at point d, the resistance of leads does not affect the result.
But, the problems with the above method are
_ the method is not practical
_ difficult to find correct galvanometer null point
To solve the above problems, two actual resistance unit of correct ratio is connected between
points m and n as shown in figure (1.6) which is the original Kelvin Double bridge. The ratio
arm of p and q is connected at d to eliminate the effect of connecting leads between R and S.
The value of P, Q, p and q are like that p/q = P/Q.
Under balance condition there is no current through galvanometer, which means
Eab = Eamd. Where, Eab =
𝑃
𝑃+𝑄
Eac
(𝑝+𝑞)𝑟
And Eac = I[ R+S+ 𝑝+𝑞+𝑟 ]
𝑟
And Eamd = I[ R+ 𝑝+𝑞+𝑟 p]
At balanced condition Eab = Eamd
𝑃
𝑃+𝑄
𝑟
𝑃
Eac = = I[ R+ 𝑝+𝑞+𝑟 p],on solving this equation we get R= 𝑄S
The above equation shows that, the resistance of connecting leads has no effect but error may
be introduced in the ratio arms, i.e. p/q=P/Q may not equal. Thermoelectric effect can be
removed by reversing the battery connection, and true value of R will be the mean of two
readings.
LECTURE:-06
Method of Measurement of Medium Resistance
i. Ammeter-Voltmeter method
ii. Substitution method
iii. Wheatstone bridge method and
iv. Carey Foster bridge method
Ammeter Voltmeter (AV) Method
In AV method the measured resistance is given by Rm = V=I, where V and I are the
voltage and current reading of voltmeter and ammeter respectively. The available connection
methods are shown in figure
𝑉
VA+VR
For figure (a) Rm1 = =
=RA+R
𝐼
𝐼
Therefore, the true value of resistance,
R=Rm1 – RA= Rm (1-RA/Rm1)
Relative error E = (Rm1 –R)/R=RA/R
For figure (b)
V
V
Rm 2  
=
I IV  I R
R
1
R
RV
Therefore, the true value of resistance R 
Rm 2 RV
RV  Rm 2


1
= Rm 2 

Rm 2
1
RV









1
If Rv >> Rm2 then, 
 Rm2
 1 R
V







1

= 1 

Rm 2 
  .............
RV 
 R 
Neglecting higher order term, the true value of resistance become, R  Rm 2 1  m 2 
RV 

R2
R R
Relative error,   m 2
=  m2
RRV
R
Since, the value of Rm2 _ R, relative error
The magnitude of error in both cases will be same if
Ra
R
= R  Ra  RV

R RV
Substitution method
The connection diagram for substitution method is shown in fig. below. R is the unknown
resistance to be measured, S is the standard variable resistance, ‘r’ is the regulating resistance
and ‘A’ is an ammeter. There is a switch for putting S and R in a circuit.
Firstly switch is at position 1 and R is connected in a circuit. The regulating resistance ‘r’ is
adjusted till ammeter pointer is at chosen scale. Now switch is thrown to position ‘2’ and now
‘S’ is in a circuit. The value of standard variable resistance ‘S’ is varied till the same
deflection as was obtained with R in the circuit is obtained. When the same deflection
obtained it means same current flow for both the resistances . It means resistances must be
equal . Thus we can measure the value of unknown resistance ‘R’ by substituting another
standard variable resistance ‘S’. Therefore this method is called Substitution method.
This is more accurate method than ammeter-voltmeter method. The accuracy of this method
is greatly affected if the emf of the battery is changes during the time of readings. thus in
order to avoid errors on this account, a battery of ample capacity should be used so that the
emf remains constant. The accuracy of the measurement naturally depends upon the
constancy of the battery emf and of the resistance of the circuit excluding R and S, upon the
sensitivity of the instrument, and upon the accuracy with which standard resistance S is
known.
This method is not widely used for simple resistance measurements and is used in a modified
form for the measurement of high resistances. The substitution principle, however, is very
important and finds many applications in bridge methods and in high frequency a.c.
measurements.
Wheatstone Bridge Method
The method of measuring medium resistance by using Wheatstone bridge is shown in
figure . The bridge is said to be balanced if there is no current flow through
the galvanometer or the potential difference across the galvanometer is zero.
At balance condition, I1 P  I 2 R
The galvanometer current will be zero if I 1  I 3 
And I 2  I 4 
E
RS
E
PQ
Combining the equations we get
P
R

PQ RS
P
S
Q
P and Q are known standard resistors and by varying standard variable resistor S the null
R
point of the galvanometer is obtained and the value of unknown resistor R is calculated.
Carey Foster Slide Wire Bridge
This bridge is suitable for comparing two nearly equal resistances. Resistance P and Q
are adjusted so that the ratio P=Q is approximately equal to the ratio R=S .
Let, balanced point d is obtained at a distance l1 as shown in figure. Therefore
at balance condition,
R  l1r
P

Q S  L  l1 r
R  l1r  S  L  l1 r
P
R  SLr
1 

Q
S  L  l1 r
S  L  l1 r
where, r is the resistance per unit length of the slide wire. Then R and S are interchanged and
balanced obtained again at a distance l2. Similarly for second balance point,
S  l2 r
P

Q R  L  l 2 r
S  l 2 r  R  L  l 2 r
P
R  S  Lr
1 

Q
R  L  l 2 r
R  L  l 2 r
From the equations S  L  l1 r  R  L  l2 r
S  R  l1  l 2 r
Thus the difference between S and R is obtained from the resistance per unit length of the
slide wire together with the difference l1  l 2  between the two slide wire lengths at balance.
The slide wire is calibrated; .i.e. r is obtained by shunting either S or R by a known resistance
and again determining the difference in length( l1'  l 2' ). Suppose, S is known and S 0 is its
value when shunted by known resistance. After shunting S equation becomes


S '  R  l1'  l 2' r ..
Hence from the above two equations we have
R

S  R S'  R
=
l1  l 2 l1'  l 2'

S l1'  l 2'  S ' l1  l 2 
l1'  l 2'  l1  l 2
The equation shows that this method gives the direct comparison between R and S in terms of
length only and the resistances of P and Q contact resistance, and the resistances of
connecting leads are eliminated.
Limitations of Wheatstone bridge:
 few to several M
 upper limit is set by reducing the sensitivity to unbalance caused by resistance
values
 upper limit can be extended by increasing emf that causes heat
 inaccuracy due to leakage out of insulation
 contact resistance presents a source of uncertainty that is difficult to overcome
LECTURE:-07
Methods of Measurement of High Resistance
i. Direct deflection method
ii. Loss of Charge method
iii. Megohm bridge
iv. Meggar
Direct deflection method
The figure shows the measurement of high resistance using direct deflection method.
For measurement of high resistance such as insulation resistance of cables, a sensitive
galvanometer of d’Arsonval type is used in place of the microammeter. In fact many sensitive
type of galvanometers can detect currents from 0.1-1nA.therefore, with an applied voltage of
1kV, resistance as high as 10^12 to 10*10^12Ω can be measured.
The first figure shows the direct deflection method for measurement of high resistance
having metallic sheath. The galvanometer G shows the current between the conductor and the
metallic sheath. The leakage current is carried by the guard wire wound on the insulation and
therefore does not flow through the galvanometer as shown in figure.
Cables without metal sheaths can be tested in a similar way if the cable, except the
ends or ends on which connections are made, is immersed in water in a tank. the water and a
tank then forms the return path for the current .the cable is immersed in slightly saline water
for about 24 hours and the temperature is kept constant at about 20 degree Celsius and then
the measurement is taken as shown in second figure.The insulation resistance of the cable is
given by,
In some cases, the deflection of the galvanometer is observed and its scale is
afterwards calibrated by replacing the insulation by a standard high resistance (usually 1MΩ),
the galvanometer shunt being varied, as required to give a deflection on the same order as
before. In tests on cable the galvanometer should be short-circuited before applying the
voltage. The short-circuiting connection is removed only after sufficient time is elapsed so
that charging and absorption currents cases to flow. The galvanometer should be well shunted
during the early stages of measurement, and it is normally desirable to influence a protective
series resistance (of several megaohm) in the galvanometer circuit. The value of this
resistance should be subtracted from the observed resistance value in order to determine the
true resistance. A high voltage battery of 500V emf is required and its emf should remain
constant throughout the test
Loss of Charge Method
In this method the insulation resistance R to be measured is connected in parallel with
a capacitor C and a electrostatic voltmeter. The capacitor is charged to some suitable voltage
by means of supply voltage V and then allowed to discharge through the resistance.
Circuit for Loss of Charge Method
Graph for Loss of Charge Method
The voltage across the capacitor v at any instant t after application of supply voltage
V as shown in figure is given by v  Ve
t
RC
Therefore, the insulation resistance, R 
t
V 
C log e  
v

0.4343t
V 
C log 10  
v
This method is suitable for high resistance measurement but it requires a capacitor having
very high leakage resistance as high as the resistance being measured. This method is also
time consuming. Actually, in this method the e_ect of the resistance of electrostatic voltmeter
is ignored and the leakage resistance of the capacitor is assumed infinite. In practical,
correction must be applied. In the below figure , R1 represents the resistance of voltmeter and
capacitor.
The measured resistances R ' 
0.4343t
0.4343t
and R1 
V 
V 
C log 10  
C log 10  
v
v
R '  RR1 / R  R1
where, R’ represents the resistance when two resistances are in operation, test is repeated
disconnecting the resistance R.
Methods of Measurement of Earth Resistance
The earth resistance should be as minimum as possible used to: protect various
parts of insulations, high voltage discharge and for stabilizing 3 Φ circuit.
The methods of measuring earth resistance:
i.
Fall of Potential Method and
ii.
ii. Earth Tester
Fall of Potential Method
As shown in figure a current is passed through earth electrode E to another electrode
B. The lines of first electrode current diverge and those of second electrode current converge.
As a result the current density is much greater in the vicinity of the electrodes than at a
distance from them. The potential distribution between the electrodes is shown in figure. It is
obvious from the curve that the potential rises in the proximity of electrodes E and B and is
constant along the middle section. The resistance of earth therefore, RE = V/I
LECTURE:-08
Megger
Insulation resistance quality of an electrical system degrades with time, environment
condition i.e. temperature, humidity, moisture & dust particles. It also get impacted
negatively due to the presence of electrical & mechanical stress, so it’s become very
necessary to check the IR (Insulation resistance) of equipment at a constant regular interval to
avoid any measure fatal or electrical shock.
Uses of Megger
The device enable us to measure electrical leakage in wire, results are very reliable as
we shall be passing electric current through device while we are testing. The equipment
basically use for verifying the electrical insulation level of any device such as motor, cable,
generator winding, etc. This is a very poplar test being carried out since very long back. Not
necessary it shows us exact area of electrical puncture but shows the amount of leakage
current & level of moisture within electrical equipment/winding/system
Types of Megger
This can be separated into mainly two categories:-
1. Electronic Type ( Battery Operated)
2. Manual Type (Hand Operated)
But there are another types of megger which is motor operated type which does not use
battery to produce voltage it requires external source to rotate a electrical motor which in turn
rotates the
generator of the megger.
Advantages of Electronic Type Megger
1. Level of accuracy is very high.
2. IR value is digital type, easy to read.
3. One person can operate very easily.
4. Works perfectly even at very congested space.
5. Very handy & safe to use
Disadvantages of Electronic Type Megger
1. Require an external source of energy to energies i.e. Dry cell.
2. Costlier in market
(Hand operated Megger)
Important parts:Analog display: – Analog display provided on front face of tester for IR value recording.
Hand Crank:- Hand crank used to rotate helps to achieve desired RPM required generate
voltage which runs through electrical system.
Wire Leads :- Used same as in electronic tester i.e. For connecting tester with electrical
system.
Adavantages of Hand operated Megger
1. Still keeps important in such high-tech world as it’s an oldest method for IR value
determination
2. No external source required to operate.
3. Cheaper available in market
Disadavantages of Hand operated Megger
1. At least 2 person required to operate i.e. one for rotation of crank other to connect
megger with electrical system to be tested.
2. Accuracy is not up to the level as it’s varies with rotation of crank.
3. Require very stable placement for operation which is a little hard to find at working
sites.
4. Unstable placement of tester may impact the result of tester.
5. Provides an analog display result.
6. Require very high care & safety during use of the same.
Costruction of Megger
Circuit Construction features:-
1) Deflecting & Control coil: Connected parallel to the generator, mounted at right
angle to
each other and maintain polarities in such a way to produced torque in opposite
direction.
2) Permanent Magnets: Produce magnetic field to deflect pointer with North-South
pole magnet
3) Pointer : One end of the pointer connected with coil another end deflects on scale
from infinity to zero
4) Scale : A scale is provided in front-top of the megger from range ‘zero’ to ‘infinity’,
enable us to read the value
5) D.C generator or Battery connection : Testing voltage is produced by hand
operated D.C generator for manual operated Megger. Battery / electronic voltage
charger is provided for automatic type Megger for same purpose
6) Pressure coil resistance and Current coil resistance : Protect instrument from any
damage because of low external electrical resistance under test
Working Principle of Megger

Voltage for testing produced by hand operated megger by rotation of crank in case of
hand operated type, a battery is used for electronic tester.

500 Volt DC is sufficient for performing test on equipment range up to 440 Volts.

1000V to 5000V is used for testing for high voltage electrical systems.

Deflecting coil or current coil connected in series and allows flowing the electric
current taken by the circuit being tested

The control coil also known as pressure coil is connected across the circuit

Current limiting resistor (CCR & PCR ) connected in series with control & deflecting
coil to protect damage in case of very low resistance in external circuit

In hand operated megger electromagnetic induction effect is used to produce the test
voltage i.e. armature arranges to move in permanent magnetic field or vice versa

Where as in electronic type megger battery are used to produce the testing voltage.

As the voltage increases in external circuit the deflection of pointer increases and
deflection of pointer decreases with a increases of current

Hence, resultant torque is directly proportional to voltage & inversely proportional to
current

When electrical circuit being tested is open, torque due to voltage coil will be
maximum & pointer shows ‘infinity’ means no shorting throughout the circuit and has
maximum resistance within the circuit under test

If there is short circuit pointer shows ‘zero’, which means ‘NO’ resistance within
circuit being tested.
Torque of the megger varies in ration with V/I, (Ohm’s Law :- V=IR or R=V/I).
Electrical resistance to be measured is connected across the generator & in series with
deflecting coil.
Produced torque shall be in opposite direction if current supplied to the coil.

High resistance = No current :- No current shall flow through deflecting coil, if
resistance is very high i.e. infinity position of pointer

Small resistance = High current :- If circuit measures small resistance allows a high
electric current to pass through deflecting coil, i.e. produced torque make the pointer
to set at ‘ZERO’

Intermediate resistance = varied current :- If measured resistance is intermediate,
produced torque align or set the pointer between the range of ‘ZERO to INIFINITY’
Connection Diagram of Megger for testing
LECTURE-10
Methods of Measurement of Earth Resistance
The earth resistance should be as minimum as possible used to: protect various
parts of insulations, high voltage discharge and for stabilizing 3 Φ circuit.
The methods of measuring earth resistance:
i.
Fall of Potential Method and
ii.
ii. Earth Tester
Fall of Potential Method
As shown in figure a current is passed through earth electrode E to another electrode
B. The lines of first electrode current diverge and those of second electrode current converge.
As a result the current density is much greater in the vicinity of the electrodes than at a
distance from them. The potential distribution between the electrodes is shown in figure. It is
obvious from the curve that the potential rises in the proximity of electrodes E and B and is
constant along the middle section. The resistance of earth therefore, RE = V/I
LECTURE:-11
AC Bridges consist of a source, balance detector and four arms. In AC bridges, all the
four arms consists of impedance. The AC bridges are formed by replacing the
DC battery with an AC source and galvanometer by detector of Wheatstone bridge. They are
highly useful to find out inductance, capacitance, storage factor, dissipation factor etc.
Now let us derive general expression for an AC bridge balance.Figure given below shows AC
bridge network.
Here Z1, Z2, Z3 and Z4 are the arms of the bridge.
Now at the balance condition, the potential difference between b and d must be zero. From
this, when the voltage drop from from a to d equals to drop from a to b both in magnitude and
phase.
Thus, we have from figure e1 = e2
From equation 1, 2 and 3 we have Z1.Z4 = Z2.Z3 and when impedance are replaced by
admittance, we have Y1.Y4 = Y2.Y3.
Now consider the basic form of an AC bridge. Suppose we have bridge circuit as shown
below,
In this circuit R3 and R4 are pure electrical resistances. Putting the value of Z1, Z2, Z3 and
Z4 in the equation that we have derived above for AC bridge.
Now equating the real and imaginary parts we get
Following are the important conclusions that can be drawn from the above equations:
(a) We get two balanced equations that are obtained by equating real and imaginary parts this
means that for an ac bridge both the relation (i.e.magnitude and phase) must be satisfied at
the same time. Both the equations are said to be independent if and only if both equation
contain single variable element. This variable can be inductor or resistor.
(b) The above equations are independent of frequency that means we do not require exact
frequency of the source voltage and also the applied source voltage waveform need not to be
perfectlysinusoidal.
Maxwell's Bridge
Under this we going to study about the following
(a) Maxwell's inductance bridge
(b) Maxwell's inductance capacitance bridge
Maxwell's Inductance Bridge
Let us now discuss Maxwell's inductance bridge. The figure shows the circuit diagram of
Maxwell's inductance bridge.
Maxwell Induction Bridge
In this bridge the arms bc and cd are purely resistive while the phase balance depends on the
arms ab and ad.
Here l1 = unknown inductance of r1.
l2 = variable inductance of resistance R2.
r2 = variable electrical resistance.
As we have discussed in ac bridge according to balance condition, we have at balance point
We can vary R3 and R4 from 10 ohms to 10,000 ohms with the help of resistance box.
Maxwell's Inductance Capacitance Bridge
In this Maxwell Bridge, the unknown inductance is measured by the standard
variable capacitor.
Circuit of this bridge is given below,
Maxwell's Inductance Capacitance Bridge
Here, l1 is unknown inductance, C4 is standard capacitor.
Now under balance conditions we have from ac bridge that Z1.Z4 = Z2.Z3
Let us separate the real and imaginary parts, the we have,
Now the quality factor is given by,
Advantages of Maxwell's Bridge
(1) The frequency does not appear in the final expression of both equations, hence it is
independent of frequency.
(2) Maxwell's inductance capacitance bridge is very useful for the wide range of
measurement of inductance at audio frequencies.
Disadvantages of Maxwell's Bridge
(1) The variable standard capacitor is very expensive.
(2) 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.
The above all limitations are overcome by the modified bridge which is known as Hey's
bridge which does not use an electrical resistance in parallel with the capacitor
LECTURE-12
Anderson’s Bridge
Let us understand why there is need of Anderson's bridge though we have Maxwell
bridge and Hay's bridge to measure quality factor of the circuit. The main disadvantage of
using Hay's bridge and Maxwell bridge is that, they are unsuitable of measuring the low
quality factor. However Hay's bridge and Maxwell bridge are suitable for measuring
accurately high and medium quality factor respectively. So, there is need of bridge which can
measure low quality factor and this bridge is modified Maxwell's bridge and known
as Anderson's bridge.
Actually this bridge is the modified Maxwell inductance capacitance bridge. In this bridge
double balance can obtained by fixing the value of capacitance and changing the value
of electrical resistance only. It is well known for its accuracy of measuring inductance from
few micro Henry to several Henry. The unknown value of self inductance is measured by
method of comparison of known value of electrical resistance and capacitance. Let us
consider the actual circuit diagram of Anderson's bridge.
Anderson's Bridge
In this circuit the unknown inductance is connected between the point a and b with electrical
resistance r1 (which is pure resistive). The arms bc, cd and da consist of resistances r3, r4 and
r2 respectively which are purely resistive. A standard capacitor is connected in series with
variable electrical resistance r and this combination is connected in parallel with cd. A supply
is connected between b and e.
Now let us derive the expression for l1 and r1:
At balance point, we have the following relations that holds good and they are:
i1 = i3 and i2 = ic + i4
Now equating voltages drops we get,
Putting the value of ic in above equations, we get
The above equation (7) obtained is more complex that we have obtained in Maxwell bridge.
On observing the above equations we can easily say that to obtain convergence of balance
more easily, one should make alternate adjustments of r1and r in Anderson’s bridge.
Now let us look how we can obtain the value of unknown inductance experimentally. At first
set
the signal generator frequency at audible range. Now adjust r1 and r such that phones gives a
minimum sound. Measure the values of r1 and r (obtained after these adjustments) with the
help of multimeter. Use the formula that we have derived above in order to find out the value
of unknown inductance. The experiment can be repeated with the different value of
standard capacitor.
Phasor Diagram of Anderson's Bridge
Let us mark the voltage drops across ab ,bc, cd and ad as e1, e2, e3 and e4 as shown in
figure
above.
Here in the phasor diagram of Anderson's bridge, we have taken i1 as reference axis. Now
ic is perpendicular to i1 as capacitive load is connected at ec, i4 and i2 are lead by some angle
as shown in figure. Now the sum of all the resultant voltage drops i.e. e1, e2, e3 and e4 is equal
to e, which is shown in phasor diagram. As shown in the phasor diagram of Anderson's
bridge the resultant of voltages drop i1(R1 + r1) and i1.ω.l1 (which is shown perpendicular to
i1) is e1. e2 is given by i2.r2 which makes angle 'A' with the reference axis. Similarly, e4 can be
obtained by voltage drop i4.r4 which is making angle 'B' with reference axis.
Advantages of Anderson's Bridge
(1) It is very easy to obtain the balance point in Anderson's bridge as compared to Maxwell
bridge in case of low quality factor coils.
(2) There is no need of variable standard capacitor is required instead of thin a fixed
value capacitor is used.
(3) This bridge also gives accurate result for determination of capacitance in terms of
inductance.
Disadvantages of Anderson's Bridge
(1) The equations obtained for inductance in this bridge is more complex as complex as
compared to Maxwell's bridge.
(2) The addition of capacitor junction increases complexity as well as difficulty of
shielding the bridge.
Considering above all the advantages and disadvantages, Maxwell bridge is preferred over
Anderson's bridge whenever use of variable capacitor is permissible.
Owen’s Bridge Circuit and Advantages
An Owen's bridge circuit is given below.
The ac supply is connected at a and c point. The arm ab is having inductor having some finite
resistance let us mark them r1and l1. The arm bc consists of pure electrical resistance marked
by r3 as shown in the figure given below and carrying the electric current i1 at balance point
which is same as the electric current carried by arm ab. The arm cd consists of pure
capacitor having no electrical resistance.The arm ad is having variable resistance as well as
variable capacitor and the detector is connected between b and d. Now how this bridge
works? This bridge measures the inductance in terms of capacitance. Let us derive an
expression for inductance for this bridge.
Here l1 is unknown inductance. And c2 is variable standard capacitor.
Now at balance point we have the relation from ac bridge theory that must hold good i.e.
Putting the value of z1, z2, z3 and in above equation we get,
Equating and then separating the real and the imaginary parts we get the expression for l1 and
r1 as written below:
Let us mark drop across arm ab, bc, cd and ad as e1, e3, e4 and e2 respectively as shown in the
above figure. This will help us to understand the phasor daigram well.
In general the most lagging current (i.e. i1) is chosen as reference in order to draw phasor
diagram. Current i2 is perpendicular to electric current i1 as shown and drop
across inductor l1 is perpendicular to i1 as it is an inductive drop while the drop
across capacitor c2 is perpendicular to i2. At balance point e1 = e2 which is shown in the
figure, now resultant of all these voltage drops e1, e2, e3, e4 will give e.
Advantages of Owen's Bridge
(1) The for inductor l1 that we have derived above is quite simple and is independent of
frequency component.
(2) This bridge is useful for the measurement of inductance over wide range.
Disadvantages of Owen's Bridge
(1) In this bridge we have used variable standard capacitor which is quite expensive item and
also the accuracy of this is about only one percent.
(2) As the measuring quality factor increases the value of standard capacitor required
increases thus expenditure in making this bridge increases.
Measurement of Capacitance using Schering Bridge
Schering Bridge Theory
This bridge is used to measure to the capacitance of the capacitor, dissipation factor and
measurement of relative permittivity. Let us consider the circuit of Schering bridge as shown
below:
Here, c1 is the unknown capacitance whose value is to be determined with series
electrical resistance r1.
c2 is a standard capacitor.
c4 is a variable capacitor.
r3 is a pure resistor (i.e. non inductive in nature).
And r4 is a variable non inductive resistor connected in parallel with variable
capacitor c4. Now the supply is given to the bridge between the points a and c. The detector is
connected between b and d. From the theory of ac bridges we have at balance condition,
Substituting the values of z1, z2, z3 and z4 in the above equation, we get
Equating the real and imaginary parts and the separating we get,
Let us consider the phasor diagram of the above Shering bridge circuit and mark the voltage
drops across ab,bc,cd and ad as e1, e3,e4 and e2respectively. From the above Schering bridge
phasor diagram, we can calculate the value of tanδ which is also called the dissipation factor.
The equation that we have derived above is quite simple and the dissipation factor can be
calculated easily. Now we are going to discuss highvoltage Schering bride in detail. As we
have discussed that simple schering bridge (which uses low voltages) is used for measuring
dissipation factor, capacitance and measurement of other properties of insulating materials
like insulating oil etc. What is the need of high voltage schering bridge? The answer to this
question is very simple, for the measurement of small capacitance we need to apply high
voltage and high frequency as compare to low voltage which suffers many disadvantages. Let
us discuss more features of this high voltage Schering bridge.
High Voltage Schering Bridge
(a) The bridge arms ab and ad consists of only capacitors as shown the bridge given
below and impedances of these two arms are quite large as compared to the impedances of bc
and cd. The arms bc and cd contains resistor r3 and parallel combination of capacitor
c4 andresistor r4 respectively. As impedances of bc and cd are quite small therefore drop
across bc and cd is small. The point c is earthed, so that the voltage across bc and dc are few
volts above the point c.
(b) The high voltage supply is obtained from a transformer 50 Hz and the detector in
this bridge is a vibration galvanometer.
(c) The impedances of arms ab and ad very are large therefore this circuit draws
low electric current hence power loss is low but due to this low electric current we need a
very sensitive detector to detect this low current.
(d) The fixed standard capacitor c2 has compressed gas which works as dielectric
therefore dissipation factor can be taken as zero for compressed air. Earthed screens are
placed between high and low arms of the bridge to prevent errors caused due to
inter capacitance.
Let us study how Schering bridge measures relative permittivity: In order measure the
relative permittivity, we need to first measurecapacitance of a small capacitor with specimen
as dielectric. And from this measured value of capacitance relative permittivity can calculated
easily by using the very simple relation:
Where r is relative permeability.
c is the capacitance with specimen as dielectric.
d is the spacing between the electrodes.
A is the net area of electrodes.
and ε is permittivity of free space.
Measurement of Mutual Inductance