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Electrical Measuring Instruments and Measurements
LEARNING OBJECTIVES
After completing this lesson, you will be able to:
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❑
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Recognize the importance of testing and measurements in electric circuits.
Appreciate the essential devices comprising an analogue instrument.
Explain the operation of an attraction and a repulsion type of moving-iron instrument.
Explain the operation of a moving-coil rectifier instrument.
Compare moving-coil, moving-iron and moving coil rectifier instruments.
Calculate values of shunts for ammeters and multipliers for voltmeters.
Understand the advantages of electronic instruments.
Understand the operation of an ohmmeter/megger.
Appreciate the operation of multimeters/AVOmeters.
Understand the operation of a wattmeter.
Appreciate instrument ‘loading’ effect.
Appreciate calibration accuracy of instruments.
INTRODUCTION
Electrical testing and commissioning are the processes of verifying that electrical equipment and systems are installed,
operated, and maintained according to the design specifications and standards. They are essential for ensuring the
quality, reliability, safety, and efficiency of electrical power generation and distribution.
Here are some common electrical tests that are performed during the testing and commissioning of electrical systems:
❑ Insulation Resistance Test (Megger Test):
Purpose: To check the integrity of insulation materials in cables, motors, transformers, and other electrical equipment.
Procedure: A high voltage is applied between conductors and ground, and the resulting current leakage is measured.
Acceptance Criteria: The insulation resistance should be above a specified minimum value (usually in megaohms).
❑ Continuity Test:
Purpose: To verify the continuity of conductors, connections, and bonding.
Procedure: A low voltage is applied, and the resistance is measured.
Acceptance Criteria: The resistance should be very low (close to zero) for proper continuity.
❑ Polarity Test:
Purpose: To ensure correct polarity in electrical circuits.
Procedure: The correct connection of phase, neutral, and ground conductors is verified.
Acceptance Criteria: All connections should match the specified polarity.
❑ Earth Resistance Test:
Purpose: To measure the resistance between the grounding system and the earth.
Procedure: A known current is injected into the grounding system, and the voltage drop is measured.
Acceptance Criteria: The earth resistance should be within acceptable limits.
❑ Functional Tests:
Purpose: To verify the proper functioning of electrical equipment.
Procedure: Equipment (such as switches, relays, circuit breakers) is operated under normal conditions.
Acceptance Criteria: Equipment should perform its intended function correctly.
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❑ High-Potential (Hi-Pot) Test:
Purpose: To test the dielectric strength of insulation.
Procedure: A high voltage (usually higher than the rated voltage) is applied between conductors and ground.
Acceptance Criteria: No breakdown or excessive current flow should occur.
❑ Voltage Drop Test:
Purpose: To assess voltage drop across conductors.
Procedure: Voltage is measured at different points along a circuit during load conditions.
Acceptance Criteria: Voltage drop should not exceed specified limits.
❑ Protection Relay Testing:
Purpose: To verify the correct operation of protection relays.
Procedure: Simulate fault conditions and check if the relay responds appropriately.
Acceptance Criteria: Relays should trip or operate as expected.
Tests and measurements are important in designing, evaluating, maintaining and servicing electrical circuits and
equipment. In order to detect electrical quantities such as current, voltage, resistance or power, it is necessary to
transform an electrical quantity or condition into a visible indication. This is done with the aid of instruments (or
meters) that indicate the magnitude of quantities either by the position of a pointer moving over a graduated scale
(called an analogue instrument) or in the form of a decimal number (called a digital instrument).
Measurement Standards
All instruments, whether electrical or electronic, are calibrated at the time of manufacture against a measurement
standard.
❑ International Standards
These are defined by international agreement and are maintained at the international Bureau of Weights and
Measurements in Paris.
❑ Primary Standards
These are maintained at national standards laboratories in each country. They are not available for use outside
these laboratories. Their principal function is to calibrate and verify the secondary standards used in industry.
❑ Secondary Standards
These are the basic reference standards used by industrial laboratories and are maintained by the particular industry
to which they belong. They are periodically sent to national laboratory for calibration and verification against
primary standards.
❑ Working Standards
These are the main tools of a measurement laboratory and are used to check and calibrate the instrument used in
the laboratory.
The Basic Meter Movement
It is also called D'Arsonval meter movement or a permanent-magnet moving-coil (PMMC) meter movement. Since it
is widely used in electronic instruments, it is worthwhile to discuss its construction and principle of operation.
1. Construction
As shown in figure below, it consists of a permanent horse-shoe magnet with soft iron pole pieces attached to it.
Between the two pole-pieces is situated a cylinder-shaped soft iron core around which moves a coil of fine wire wound
on a light metal frame. The metal frame is mounted in jewel bearings so that it can rotate freely. A light pointer attached
to the moving coil moves up-scale as the coil rotates when current is passed through it. The rotating coil is prevented
from continuous rotation by a spring which provides restoring torque.
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The moving coil movement described above is being increasingly replaced by taut-band movement in which the
moving coil and the pointer are suspended between bands of spring metal so that the restoring force is torsional. The
bands perform two functions (i) they support the coil and (ii) they provide restoring torque thereby eliminating the
pivots and jewels used with coil spring movement.
As compared to pivoted movement, the taut-band has the advantages of:
a. Greater sensitivity i.e. small full-scale deflection current
b. Ruggedness,
c. Minimal friction,
d. Easy to manufacture.
2. Principle of Operation
This meter movement works on the motor principle and is a current-responding device. The deflection of the pointer
is directly proportional to the amount of current passing through the coil. When direct current flows through the coil,
the magnetic field so produced reacts with the field of the permanent magnet. The resultant force turns the coil along
with its pointer. The amount of deflection is directly proportional to the amount of current in the coil. Hence, their
scale is linear. With correct polarity, the pointer reads up-scale to the right whereas incorrect polarity forces the pointer
off-scale to the left.
Analogue Instruments
All analogue electrical indicating instruments require three essential devices:
a. A deflecting or operating device. A mechanical force is produced by the current or voltage which causes the
pointer to deflect from its zero position.
b. A controlling device. The controlling force acts in opposition to the deflecting force and ensures that the
deflection shown on the meter is always the same for a given measured quantity. It also prevents the pointer
always going to the maximum deflection. There are two main types of controlling device – spring control and
gravity control.
c. A damping device. The damping force ensures that the pointer comes to rest in its final position quickly and
without undue oscillation. There are three main types of damping used – eddy current damping, air-friction
damping and fluid friction damping.
There are basically two types of scale – linear and non-linear. A linear scale is shown in figure a, where the divisions
or graduations are evenly spaced. The voltmeter shown has a range 0–100 V, i.e. a full-scale deflection (f.s.d.) of 100
V. A non-linear scale is shown in figure b where the scale is cramped at the beginning and the graduations are uneven
throughout the range. The ammeter shown has a f.s.d. of 10 A.
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Moving-iron Instrument
a. An attraction type of moving-iron instrument is shown diagrammatically in figure a. When current flows in
the solenoid, a pivoted soft-iron disc is attracted towards the solenoid and the movement causes a pointer to
move across a scale.
b. In the repulsion type moving-iron instrument shown diagrammatically in figure b, two pieces of iron are
placed inside the solenoid, one being fixed, and the other attached to the spindle carrying the pointer. When
current passes through the solenoid, the two pieces of iron are magnetized in the same direction and therefore
repel each other. The pointer thus moves across the scale. The force moving the pointer is, in each type,
proportional to I2 and because of this the direction of current does not matter. The moving-iron instrument can
be used on DC or AC; the scale, however, is non-linear.
Characteristics of Moving Coil Meter Movement
We will discuss the following three characteristics:
1. Full-scale deflection current (Im) – It is the current needed to deflect the pointer all the way to the right to the last
mark on the calibrated scale. Typical values of Im for D' Arsonval movement vary from 2 A to 30 mA. It should
be noted that for smaller currents, the number of turns in the moving coil has to be more so that the magnetic field
produced by the coil is strong enough to react with the field of the permanent magnet for producing reasonable
deflection of the pointer. Fine wire has to be used for reducing the weight of the moving coil but it increases its
resistance. Heavy currents need thick wire but lesser number of turns so that resistance of the moving coil is
comparatively less.
2. Internal resistance of the coil (Rm) – It is the DC ohmic resistance of the wire of the moving coil. A movement
with smaller Im has higher Rm and vice versa. Typical values of Rm, range from 1.2  for a 30 mA movement to
2k for a 50 A movement.
3. Sensitivity (S) – It is also known as current sensitivity or sensitivity factor. It is given by the reciprocal of fullscale deflection current Im.
𝟏
S = 𝐈 ohm/volt
𝐦
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Variations of Basic Meter Movement
The basic moving-coil system can be converted into an instrument to measure DC as well as AC quantities like current,
voltage and resistance etc. Without any modification, it can carry a maximum current of Im can withstand a maximum
dc voltage V = ImRm.
1. DC Instruments
a. It can be made into a DC ammeter, milliammeter or micrometer by adding a suitable shunt resistor, Rsh, in
parallel with it as shown in figure a.
b. It can be changed into a DC voltmeter by connecting a multiplier resistor, Rmult, in series with it as shown in
figure b.
c. It can be converted into an ohmmeter with the help of a battery and series resistor, R,as shown in figure c.
2. AC Instruments
a. It can be changed into an AC audio-frequency ammeter or voltmeter by simply adding an extra rectifier as
shown in figure a.
b. It can be converted into a radio frequency ammeter or voltmeter by adding a thermocouple as figure b.
The above modifications of the basic meter movement have been tabulated below:
The moving-coil rectifier instrument
A moving-coil instrument, which measures only DC may be used in
conjunction with a bridge rectifier circuit as shown below to provide an
indication of alternating currents and voltages. The average value of the full
wave rectified current is 0.637 Im. However, a meter being used to measure
AC is usually calibrated in r.m.s. values. For sinusoidal quantities the
indication is (0.707Im)/(0.637Im) i.e. 1.11 times the mean value. Rectifier
instruments have scales calibrated in r.m.s. quantities and it is assumed by the
manufacturer that the AC is sinusoidal.
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Comparison of Moving-coil, Moving-iron and Moving-coil Rectifier Instruments
Digital Instruments
Digital instruments are those which use logic circuits and techniques to obtain a measurement and then display it in
numerical-reading (digital) form. The digital readouts employ either LED displays or liquid crystal displays (LCD).
Some of the advantages of digital instruments over analog instruments are:
1. Easy readability.
2. Greater accuracy.
3. Better resolution.
4. Automatic polarity and zeroing.
Functions of Instruments
Functionally, different instruments may be divided into the following three categories:
❑ Indicating instruments – These are the instruments which indicate the instantaneous value of quantity being
measured, at the time it is being measured. The indication is in the form of pointer deflection (analog instruments)
or digital readout (digital instruments). Ammeters and voltmeters are examples of such instruments.
❑ Recording instruments – Such instruments provide a graphic record of the variations in the quantity being
measured over a selected period of time. Many of these instruments are electromechanical devices which use paper
charts and mechanical writing instruments such as an inked pen or stylus. Electronic recording instruments are of
two types: null type – which operate on a comparison basis; galvanometer type – which operate on deflection type.
❑ Controlling instrument
These are widely used in industrial processes. Their function is to control the quantity being measured with the help
of information feed back to them by monitoring devices. This class forms the basis of automatic control systems
(automation) which are extensively employed in science and industry.
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Electronic Versus Electrical Instruments
Both electrical and electronic instruments measure electrical quantities like voltage and current etc. Purely electrical
instruments do not have any built-in amplifying device to increase the amplitude of the quantity being measured. The
common dc voltmeter based on moving-coil meter movement is clearly an electrical instrument.
The electronic instruments always include in their make-up some active electron device such as vacuum tube,
semiconductor diode or an integrated circuit etc.
As seen, the main distinguishing factor between the two types of instruments is the presence of an electron device in
the electronic instruments. Of course, movement of electrons is common to both types, their main difference being that
control of electron movement is more effective in electronic instruments than in electrical instruments.
Although electronic instruments are usually more expensive than their electrical counterparts, they offer following
advantages for measurements purposes:
1. Since electronic instruments can amplify the input signal, they possess very high sensitivity i.e. they are
capable of measuring extremely small (low-amplitude) signals.
2. Because of high sensitivity, their input impedance is increased which means less loading effect when making
measurements.
3. They have greater speed i.e. faster response and flexibility.
4. They can monitor remote signals.
Essentials of an Electronic Instrument
An electronic instrument is made up of the following three elements:
❑ Transducer
It is the first sensing element and is required only when measuring a non-electrical quantity, say, temperature or
pressure. Its function is to convert the non-electrical physical quantity into an electrical signal.
❑ Signal Modifier
It is the second element and its function is to make the incoming signal suitable for application to the indicating
device. For example, the signal may need amplification before it can be properly displayed. Other types of signal
modifiers are: voltage dividers for reducing the amount of signal applied to the indicating device or wave shaping
circuits such as filters, rectifiers or chopper etc.
❑ Indicating Device
For general purpose instruments like voltmeters, ammeters or ohmmeters, the indicating device is usually a
deflection type meter. In digital readout instruments, the indicating device is of digital design.
1. Ammeter (Shunts and Multipliers)
Ammeter, instrument for measuring either direct current (DC) or alternating current (AC) electric current, in
amperes. An ammeter can measure a wide range of current values because at high values only a small portion of the
current is directed through the meter mechanism; a shunt in parallel with the meter carries the major portion. In circuit
diagrams, the symbol for an ammeter is a circle with a capital A inside. Ammeters vary in their operating principles
and accuracies. The D’Arsonval-movement ammeter measures direct current flowing through a coil suspended
between the poles of a magnet with accuracies of from 0.1% to 2.0%. The electrodynamic ammeter uses a moving
coil rotating in the field produced by a fixed coil. It measures direct and alternating current (by using a rectifier to
convert the AC to DC) with accuracies of 0.1% to 0.25%. In the thermal ammeter (hot-wire), used primarily to
measure AC with accuracies of 0.5% to 3%, the measured current heats a piece of wire, and the current is indicated by
how much the wire expands. Digital ammeters, with no moving parts, use a circuit such as the dual slope integrator to
convert a measured analog (continuous) current to its digital equivalent. Many digital ammeters have accuracies better
than 0.1%.
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An ammeter, which measures current, has a low resistance (ideally zero) and must be connected in series with the
circuit. A voltmeter, which measures potential difference, has a high resistance (ideally infinite) and must be
connected in parallel with the part of the circuit whose potential difference is required.
There is no difference between the basic instrument used to measure current and voltage since both use a milliammeter
as their basic part. This is a sensitive instrument which gives f.s.d. for currents of only a few milliamperes. When an
ammeter is required to measure currents of larger magnitude, a proportion of the current is diverted through a lowvalue resistance connected in parallel with the meter. Such a diverting resistor is called a shunt.
Ammeter shunt (shunt resistance) – used to increase the range of an ammeter. This is used for the measurement of
heavy current using an Ammeter. Ammeter Shunt is basically a low resistance connected in parallel with the moving
coil so that most of the current is bypassed by the Shunt and hence only a small current flow through the moving coil.
The basic requirement for Ammeter Shunt can be summarized as:
1. The resistance of shunt should not vary with time.
2. They should carry current without an excessive rise in temperature.
3. They should have a low thermal electromotive force with copper.
Well, Manganin is generally used for Shunt of DC Instruments as it gives low value of thermal emf with copper
although it is liable to corrosion and difficult to solder. Constantan is used for AC circuit.
Calculation of Ammeter Shunt
Let us assume that we want to measure a current of I while moving coil of Ammeter is only designed to carry a current
of Ia (full-scale deflection current), therefore we need to use ammeter shunt. We will calculate the value of suitable
shunt. The figure shows the basic circuit of an ammeter.
where:
I = maximum current that the meter can measure (ampere)
Ia = full scale current of the ammeter (ampere)
Is = current flowing in the shunt resistance (ampere)
ra = resistance of the ammeter (ohm)
Rs = shunt resistance (ohm)
Rs =
𝐈𝐚 𝐫𝐚
𝐈𝐬
ohm
The milliammeter is converted into a voltmeter by connecting a high value resistance (called a multiplier) in series
with it as shown in figure b.
RM =
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𝐕−𝐈𝐫𝐚
𝐈
ohm
𝐈
𝐫𝐚 +𝐑 𝐬
𝐬
𝐑𝐬
m=𝐈 =
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Sample Problems for Ammeter
Problem 1. A DC ammeter has an internal resistance of 0.1 ohm. A shunt of 1.01x10-3 ohm in connected to the
ammeter. What is the multiplier of the set up?
Solution:
Multiplier =
ra +Rs
Rs
=
(0.1+0.00101) 
0.00101 
= 100
Problem 2. A 1% D’Arsonval meter movement has coil and swamping resistance adding
to 200 ohms. The full-scale voltage is 50 mV. Determine the shunt resistance required
producing a 1 A full scale current meter.
Solution:
using Ohm’s Law, V=IR
E
0.050 V
Ia = Rfs = 200  = 0.250
a
mA
using KCL
Is = I – Ia = 1A – 0.25 mA = 0.99975 A
therefore,
Rs =
Efs
Is
0.050 V
= 0.99975  = 50.01 m
Problem 3. A moving-coil instrument having a resistance of 10 ohms, gives a f.s.d.
when the current is 8 mA. Calculate the value of the multiplier to be connected in
series with the instrument so that it can be used as a voltmeter for measuring p.d.s.
up to 100 V.
where:
ra = resistance of instrument = 10 
I = total permissible instrument current = 8 mA = 0.008 A
V = total potential difference required to give f.s.d. = 100 V
RM = resistance of multiplier = ?
Solution:
Using KCL
V = Va + VM = Ira + IRM
100 = (0.008 A)(10 ) + (0.008 A)(RM)
100 – 0.08 = 0.008 RM
Thus,
RM = (99.92) / (0.008) = 12490  or 12.49 k
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Problem 4. A 20 ohm shunt is joined with an ammeter with 200 ohm resistance. It is joined to
a 10v battery having a resistance of 4 ohm. What will the observation of the ammeter be?
Solution:
Using series and parallel total resistance
r xR
200 x 20
RT = rin + (ra + Rs) = 4  + (200 + 20)
a
s
 = 22.18 
Using Ohm’s Law, V=IR
I = 10 V / 22.18  = 0.45 A
Using Current Divider Theorem (CDT)
IxR
0.45 A x 20 
IT = (r + Rs ) = ( 200  + 20 ) = 0.0409
a
s
A or 40.9 mA
Problem 5. A galvanometer with a 20-ohm coil resistance has a full-scale deflection
current of a 10 mA. If a 0.02 ohm is placed across the meter to increase its capacity,
what is the approximate new full-scale current of the meter?
Solution:
Using Ohm’s Law, V=IR
V = (0.01 A) (20 ) = 0.2 V
using Ohm’s Law, V=IR
V
0.2 V
Is = R = 0.02  = 10
s
A
using KCL
Inew = Ia – Is = 0.010 A + 10 A = 10.01 A
2. Voltmeter
Voltmeter, instrument that measures voltages of either direct or alternating electric current on a scale usually
graduated in volts, millivolts (0.001 volt), or kilovolts (1,000 volts). Many voltmeters are digital, giving readings as
numerical displays. The instruments just described can also provide readings in analogue form, by moving a pointer
that indicates voltage on a scale, but digital voltmeters generally have a higher order of accuracy than analogue
instruments. For example, a common analogue voltmeter is likely to employ an electromechanical mechanism in
which current flowing through turns of wire is translated into a reading of voltage. Other types of voltmeters include
the electrostatic voltmeter, which uses electrostatic forces and, thus, is the only voltmeter to measure voltage directly
rather than by the effect of current. The potentiometer operates by comparing the voltage to be measured with known
voltage; it is used to measure very low voltages. The electronic voltmeter uses amplification or rectification (or both)
to measure either alternating- or direct-current voltages. The current needed to actuate the meter movement is not
taken from the circuit being measured; hence, this type of instrument does not introduce errors of circuit loading.
A permanent magnet moving coil (PMMC) Instrument can be used as voltmeter by just connecting a series resistance
with the moving coil. This series resistance is called Voltmeter Multiplier. This combination of moving coil and
multiplier is connected across the point whose voltage is to be measured.
There are two main functions of voltmeter multiplier:
1. It limits the current through the PMMC moving coil to a value less than full scale deflection current and thus
prevents moving coil from being damaged.
2. It minimizes the flow of current through the voltmeter and thus do not alter the circuit current whose voltage
is to be measured. Ideally the resistance of voltmeter should be infinite.
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The essential requirements of voltmeter multiplier to fulfill are:
❑ Their resistance should not change with time.
❑ Change in their resistance with temperature should be small.
The resistance material used for multipliers is Manganin and Constantan (copper nickel alloy).
Composition of Manganin, Cu (84%) + Mn (12%) + Ni (4%)
From the simplified voltmeter circuit given below:
(V - Vm)
where:
Im = Ifs = Full scale deflection current of meter (ampere)
Rm = Internal resistance of meter (ohm)
Rs = Multiplier resistance or Series resistance (ohm)
Vm = Voltage across the moving coil (volt)
V = Full range voltage of meter (volt)
Vm
)
Note: Potential divider (series resistance) is used to increase the range of a voltmeter.
Calculation of Voltmeter
The basic meter movement can measure a maximum voltage of ImRm which is very small. However, its voltage range
can be extended to any value by connecting a large resistance in series with it as shown in the figure. The series
resistance is also called multiplier resistance because it multiplies the voltage reading capability of the meter many
times. It is usually connected inside the voltmeter case.
V = Im(Rm+Rs) volt
Suppose, it is desired to extend the voltage range of the meter from v to V. The ratio V/v is known as the voltage
multiplication. As seen in the figure, voltage drop across Rse is (V–v) and current through it is the same as meter
current i.e. Im.
The voltage multiplication (m) can be found from first
equation,
Dividing both sides by v, we get
(V-v)
v
 ImRse = (V – v)
 Rse =
V−𝑣
Im
=
V−Im Rm
Im
=
V
Im
– Rm
It is seen that for a given meter, higher the series resistance, greater the voltage range extension.
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Sample Problems for Voltmeter
Problem 1. A voltmeter with an internal resistance of 5kilo-ohms is calibrated to read 10 volts at full scale. How
much series resistance is needed in order to measure 150 volts at full scale?
Solve the Im
Using,
V = Im(Rm+Rse)
Im =
V
Rm
=
10 V
5000 
V
Rse = I – Rm
= 2 mA
m
150 V
 Rse = 0.002 A – 5000  = 70 k
Problem 2. A 1000 ohms per volt (sensitivity), 2% meter movement has a coil resistance of 200 ohms. Determine the
external resistance necessary to provide a full-scale reading of 5 V.
Using,
V
1
m
m

Rse = I – Rm = (v)(I ) – Rm = (5 V)(1000 V ) – 200  = 4.8 k
Problem 3. An ammeter rated 5 A, having resistance of 0.5 ohm, is to be converted into a 200-V voltmeter by
connecting a resistor in series with the ammeter. Calculate the value of this resistance.
Using,
V
Rse = I – Rm = (
m
200 V
)
5A
– 0.5  = 39.5 k
3. Ohmmeter
The ohmmeter is used to measure the quantity of electrical resistance between two points and this value is expressed
in terms of ohms (). The resistance which has to be known can be either in series or parallel connection with that of
the device. In the parallel connection, the device draws high current because resistance is increased. Whereas, in series
connection, the device draws less current because resistance is increased. Micro Ohmmeters are used for knowing the
less resistance values and the mega ohmmeters are used to know high resistance values. For high resistances, the
scale is usually graduated in megohms (106 ohms), and the instrument is called a megohmmeter, or “megger.” This
device provides enhanced convenience to measure the values, but the results are not so accurate.
Resistance is classified into three categories for the sake of Measurement. Different categories of Resistance are
measured by different techniques. That’s why they are classified. They are classified as:
❑ Low Resistance: Resistance having value 1Ω or below are kept under this category.
❑ Medium Resistance: This category includes Resistance from 1Ω to 0.1 MΩ.
❑ High Resistance: Resistance of the order of 0.1 MΩ and above is classified as High resistance.
Ohmmeter Working Principle
Using a battery and a series variable resistor, readings are known through this device. At the terminal end, the resistance
that has to be calculated is connected. With the connection of output resistance, current flows in the device and the
deflection can be measured.
When high resistance values are to be calculated, then the current flow will be less and the output will be maximum
resistance. In the same way, when fewer resistance values are to be calculated such as zero the device reading is
positioned to zero value and this gives less resistance.
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Types of Ohmmeter
With this device, one can know the approximate values of the resistance. Depending upon the application, the
ohmmeters are mainly categorized as three types and they are as follows:
1. Series ohmmeter
The series type ohmmeter consists of a current limiting resistor (R1), Zero
adjusting resistor (R2), EMF source (E), Internal resistance of D’Arsonval
movement (Rm) and the resistance to be measured (R).
When there is no resistance to be measured, the current drawn by the circuit will be
maximum and the meter will show a deflection.
By adjusting R2 the meter is adjusted to a full-scale current value since the resistance will be zero at that time. The
co-responding pointer indication is marked as zero. Again, when the terminal A and B is opened it provides very
high resistance and hence almost zero current will flow through the circuit. In that case, the pointer deflection is
zero which is marked at a very high value for resistance measurement.
So, a resistance between zeros to a very high value is marked and hence can be measured. So, when resistance is
to be measured, the current value will be somewhat less than the maximum and the deflection is recorded and
accordingly, resistance is measured.
2. Shunt ohmmeter
In this type of meters, we have a battery source and an adjustable resistor is connected
in series with the source. We have connected the meter in parallel to the resistance
which is to be measured. There is a switch by the use of which we can on or off the
circuit. The switch is opened when it is not in use. When the resistance to be measured
is zero, the terminals A and F are shorted so the current through the meter will be
zero. The zero position of the meter denotes the resistance to be zero.
When the resistance connected is very high, then a small current will flow the terminal A and F and hence fullscale current is allowed to flow through the meter by adjusting the series resistance connected with the battery.
So, full-scale deflection measures very high resistance. When the resistance to be measured is connected between
A and F, the pointer shows a deflection by which we can measure the resistance values.
3. Multi-range Ohmmeter
This instrument provides the reading up to a very wide range. In this case, we have
to select the range switch according to our requirements. An adjuster is provided
so that we can adjust the initial reading to be zero. The resistance to be measured
is connected in parallel to the meter. The meter is adjusted so that it shows fullscale deflection when the terminals in which the resistance connected is full-scale
range through the range switch.
When the resistance is zero or short circuit, there is no current flow through the
meter and hence no deflection. Suppose we have to measure a resistance under 1
ohm, then the range switch is selected at the 1-ohm range at first. Then that
resistance is connected in parallel and the corresponding meter deflection is noted.
For 1 ohm resistance, it shows full-scale deflection but for the resistance other than 1 ohm it shows a deflection
which is less than the full load value, and hence resistance can be measured. This is the most suitable method of
all the ohmmeters as we can get an accurate reading in this type of meter. So, this meter is most widely used
nowadays.
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Calculation of Voltmeter
For measuring resistance, the ohm-meter leads are connected across the unknown resistance after switching off the
power in the circuit under test. Only in that case, the ohmmeter battery can provide current for the meter movement.
Since the amount of current depends on the amount of external resistance, the meter scale can be calibrated in ohms
(instead of mA). Following points about the ohmmeter are worth noting:
1. The resistance scale is non-linear i.e. it is expanded at the right near zero ohm and crowded at the left near infinite
ohm. This nonlinearity is due to the reciprocal function I = V/R.
2. The ohmmeter reads up-scale regardless of the polarity of the leads because direction of current is determined by
the internal battery.
3. At half-scale deflection, external resistance equals the internal resistance of the ohmmeter.
4. The test leads should be shorted and 'ZERO OHMS' control adjusted to bring the pointer to zero on each range.
where:
RL = current limiting resistor
Rv = resistance used to bring the pointer to the zero reading when Rx = 0
Rx = resistance to be measured
Rg = resistance of the galvanometer coil
E = supply voltage of the meter
Imax = galvanometer current when Rx is zero
Using KVL
RL = (𝐈
𝐄
𝐦𝐚𝐱
) – (Rg + Rv)
for current flowing in the circuit
Imax = (𝐑
𝐄
𝐋 + 𝐑𝐯 + 𝐑𝐠
)
I = (𝐑
𝐄
𝐋 + 𝐑𝐯 + 𝐑𝐠+ 𝐑 𝐱
)
Problem Statement for Ohmmeter
All analog ohmmeters have zero at one end of the scale, and infinity at the other end.
Thus, the various scales available are named for their mid-scale reading. The circuit
below is intended to be a multi-range ohmmeter. The switch is open for one range,
and closed for the other range. The meter indicated is an ammeter. It has a resistance
of 50  and has a full scale current of 1 mA. Remember that an ohmmeter is calibrated
by adjusting Rx to give a full-scale reading when the ohmmeter is short-circuited.
(Full scale on an ohmmeter is zero.)
a. Find the value of the resistor Rx.
b. Find the mid-scale reading of the ohmmeter, when the switch is open. That is, find the reading when the needle
on the scale is in the middle of its range.
c. Find the mid-scale reading of the ohmmeter, when the switch is closed. That is, find the reading when the
needle on the scale is in the middle of its range.
In the first step, we solve this problem by replacing the ammeter with its equivalent resistance. The key idea after that
is that when we short the output, the meter should be full-scale. So, we put a short circuit at the output, and set the
current through the ammeter equal to its full-scale reading, 1 mA. We use this full-scale condition to determine the
value of Rx.
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a. Let’s redraw the circuit, replacing the ammeter with its equivalent resistance, and inserting the short circuit. We
will call this resistor RM. In addition, let’s label the voltages and currents that would occur at full scale. We have
the circuit that follows.
Using this circuit, we can solve for RX, using KVL around the loop. This gives us:
We solve for RX, and we get:
We have solved for this with the switch open. However, even if the switch were closed,
this would not change the answer. The circuit with the switch closed, which still requires a short circuit at the terminals
of the ohmmeter, would result in the circuit that follows. Notice that the equation that we wrote, is unchanged by the
addition of resistor RA.
Thus, our answer remains RX = 1.95 k
b. To solve for the mid-scale value, we need to recognize that the meter is a linear one, so if the needle is in the
middle of the range, the current must be half the full-scale value. Thus, we can redraw our ohmmeter circuit with
a current of 0.5[mA] indicated. The other key is to recognize that when we do this, we are measuring a resistor
value, and we need to insert a resistor at the terminals. Doing so, with the switch open, we have the circuit that
follows.
We have named the resistance across the terminals RHALF, which is the value we
are looking for. Again, we can write KVL, to give:
Simplifying, we get:
We note that as has been noted elsewhere, the half scale reading is equal to the resistance of the ohmmeter. We
have RHALF = 2 k
c. Now, we close the switch, which gives us a new circuit. However, the process is the same; the meter will have
half of its full-scale current through it. We have the circuit that follows.
We can solve this circuit for RHALF2, which is the answer we want for this part. To
get it, though, we will need to solve for the voltage across it and the current through
it, knowing that the ratio of these two quantities is the resistance. Let’s define some
variables, in the circuit that follows.
Now, we can write a KVL, and get:
Solving for vx, we get 1.0 V.
We can also write KVL to get:
From this we can get iRA, by Ohm’s Law,
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Now, using KCL at the upper right-hand node, we get:
We now can solve for RHALF2 by Ohm’s Law,
4. Watthour Meter
A Watthour meter is a device that measures and records over time the electric power flowing through a circuit. Each
consists essentially of a small electric motor and a counter. A precise fraction of the current flowing in the circuit is
diverted to operate the motor. The speed at which the motor turns is proportional to the current in the circuit, and,
therefore, each revolution of the motor’s rotor corresponds to a given amount of current flowing through the circuit.
The counter is connected to the rotor and adds and displays the amount of power the circuit has carried based on the
number of revolutions of the rotor. The counter is usually marked in kilowatt-hours (1,000 watthours).
Mercury-type and commutator-type watthour meters measure power in direct-current circuits. Induction-type meters
measure power in alternating-current circuits and are the type commonly seen on the outside of houses. Specialized
watt-hour meters include totalizing meters, which record the power used in more than one circuit, and highly accurate
portable meters, which are used for testing installed watt-hour meters.
Basic unit of power is watts. One thousand watts is one kilowatt. If we use one kilowatt in one hour, it is considered
as one unit of energy consumed. These meters measure the instantaneous voltage and currents, calculate its product
and gives instantaneous power. This power is integrated over a period which gives the energy utilized over that time
period.
TYPES OF WATTHOUR METER
1. Electromechanical induction
It is the popularly known and most common type of age-old watthour meter. It consists of rotatingaluminum disc mounted on a spindle between two electromagnets. Speed of rotation of disc is
proportional to the power and this power is integrated by the use of counter mechanism and gear
trains. It comprises of two silicon steel laminated electromagnets i.e., series and shunt magnets.
2. Electronic energy meter
These are of accurate, high procession and reliable types of measuring instruments as compared to conventional
mechanical meters. It consumes less power and starts measuring instantaneously when connected to load. These
meters might be analog or digital. In analog meters, power is converted to proportional frequency or pulse rate
and it is integrated by counters placed inside it. In digital electric meter, power is directly measured by high end
processor. The power is integrated by logic circuits to get the energy and also for testing and calibration purpose.
It is then converted to frequency or pulse rate.
a. Analog Electronic Energy Meters
In analog type meters, voltage and current values of each phase are obtained by voltage
divider and current transformers respectively which are directly connected to the load
as shown in figure. Analog to digital converter converts these analog values to digitized
samples and it is then converted to corresponding frequency signals by frequency
converter. These frequency pulses then drive a counter mechanism where these samples
are integrated over a time to produce the electricity consumption.
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b. Digital Electronic Energy Meters
Digital signal processor or high-performance microprocessors are used in digital electric
meters. Similar to the analog meters, voltage and current transducers are connected to a
high-resolution analog-to-digital converter (ADC). Once it converts analog signals to
digital samples, voltage and current samples are multiplied and integrated by digital
circuits to measure the energy consumed.
3. Smart energy meters
It is an advanced metering technology involving placing intelligent meters to read, process and
feedback the data to customers. It measures energy consumption, remotely switches the supply
to customers and remotely controls the maximum electricity consumption. Smart metering
system uses the advanced metering infrastructure system technology for better performance.
These meters reduce the need to visit while taking or reading monthly bill. Another advantage
of smart metering is complete avoidance of tampering of energy meter where there is scope of
using power in an illegal way.
Calculation of
W = kN = Pt
where:
W = reading of the watt-hour meter (watthour)
P = power drawn (watt)
t = time of usage (hour)
N = number of revolutions made by the disk
k = proportionality constant (meter constant)
Problem 1. The Meralco test of 10-A wattmeter having constant of 0.4, the disk makes 40 revolutions in 53.6
seconds. The average volts and amperes during this period of test are 116 volts and 9.4 A. What is the percent
accuracy of the meter at this load?
The formula for percentage accuracy:
% accuracy
=
𝐖𝐦𝐞𝐚𝐬𝐮𝐫𝐞𝐝
𝐖𝐚𝐜𝐭𝐮𝐚𝐥
for Wmeasured:
W = kN = (0.4)(10) = 16 Watthour
for Wactual:
𝟏 𝐡𝐨𝐮𝐫
W = Pt = (116 V)(9.4 A)(53.6 sec.)(𝟑𝟔𝟎𝟎 𝐬𝐞𝐜.) = 16.23 Watthour
for percentage accuracy:
% accuracy =
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𝟏𝟔 𝐖𝐚𝐭𝐭𝐡𝐨𝐮𝐫
𝟏𝟔.𝟐𝟑 𝐖𝐚𝐭𝐭𝐡𝐨𝐮𝐫
= 98.58%
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Problem 2. A 15 A, 120-V watt hour meter has a disk constant of 2. When tested on a 0.8 power factor load, 24 disk
revolution are counted in a period of 3 minutes. Calculate the current drawn by the load.
from the formula:
W = kN = Pt

kN = Pt, which is P = EI(p.f)

I = (𝐄(𝐩.𝐟.)(𝐭)) = ((120 V)(0.8)(3 min.)) (60 min.) = 10 A
𝐤𝐍
2(24)
1 hour
REFERENCES
http://eestaff.kku.ac.th/~mongkol/Instrument/TextBook/ElectricalMeasurements.pdf
https://www.britannica.com/technology/ammeter
https://electricalvoice.com/ammeter-shunt-constructioncalculation/?fbclid=IwAR1iWApensPL1yLiF0BGDGRhxkNSw3kVyFGudZTIJIcPM6XMlKnsHVKhrRk
https://www.britannica.com/science/voltmeter
https://electricalbaba.com/voltmeter-multiplier-construction-andcalculation/?fbclid=IwAR2w2y4jJwghxjvhqawvJv41jK6yU17LAH018N6DonR29FKAXB0EUozs3YU
https://www.britannica.com/technology/ohmmeter
https://www.watelectrical.com/what-is-an-ohmmeter-working-principle-its-types/
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