Module 1

Principles of Analog Instruments

Hrs:16
• Errors in Measurement
• Difference between Indicating and Integrating Instruments.
• Moving coil and Moving iron Instruments
• Ammeters Shunts & Voltmeter Multiplier
• Extension of ranges by using shunt Multipliers,
• Dynamometer type Wattmeter &
• Power Factor meters.
• Reed Moving Coil type Frequency Meters.
• Weston type Synchroscope.
• DC Permanent magnet moving coil type Galvanometers.
• Ballistic Galvanometer and AC Vibration Galvanometer
(only the basic working Principle and Applications).
MEASURING INSTRUMENTS
“The device used for comparing the unknown quantity with
the unit of measurement or standard quantity is called a
Measuring Instrument.”
OR
“An instrument may be defined as a machine or system
which is designed to maintain functional relationship
between prescribed properties of physical variables &
could include means of communication to human
observer.”
BASIC CLASSIFICATION OF INSTRUMENTS
1. Absolute instruments,
2. Secondary instruments.

• Absolute instruments gives the quantity to be measured in

term of instrument constant or physical constant (universal
constant) & its deflection.
• Mostly used in standard laboratories and in similar institutions
as standardising.

• In Secondary instruments the deflection gives the

magnitude of electrical quantity to be measured directly.
These instruments are required to be calibrated by
comparing with another standard instrument before
putting into use.
CLASSIFICATION OF INSTRUMENTS
Analog Instruments Classification
Indicating Instrument
• Indicates magnitude of the measured quantity
at the time when it is being measured.
• Uses dial and pointer as an indicator.
• Eg. ammeter and voltmeter
Recording Instrument
• Records the continuous variation of
the magnitude of an electrical quantity for
a particular period.
• Used in a placed where continuous reading of
circuit conditions is required.
• The record is used for future reference or
computational work.
• Voltmeter, Thermoscope, ECG machine
Indicating and Recording Instruments
• Indicating instrument : records a continuous reading, but they require an
observer for continuously observing the variations in readings.

• It is converted into a recording instrument by replacing their pointer with the

light arm ink pen.

• The ink pen is deflected for recording the readings on the graph paper.

• pen is continuously rotated on the drum at the constant speed.

• The path traced by the pen gives a continuous reading of the variant physical
quantity.

• The magnitude of the quantity is read from the traced chart.

• Used in the power stations where continuous reading is required.

Integrating Instruments

• Measures the summation of

electrical quantity over a given
period

• Measure total amount of either

quantity of electricity or electrical
energy supplied over a period of
time

• Ampere hour meters, watt-hour

meters, energy meters
Errors in Measurement
• Through measurement, we try to obtain value of an unknown
parameter.
• However this measured value cannot be the actual or true value.
• If the measured value is very close to the true value, we call it to
be a very accurate measuring system.
• But before using the measured data for further use, one must
have some idea how accurate is the measured data.
• So error analysis is an integral part of measurement.
• We should also have clear idea what are the sources of error,
how they can be reduced by properly designing the
measurement methodology and also by repetitive
measurements.
• Besides, for maintaining the accuracy the readings of the
measuring instrument are frequently to be compared and
adjusted with the reading of another standard instrument.
• This process is known as calibration.
Error Analysis
• Error in a measurement is defined
as difference between the true or actual
value and the measured value.
• The true value is the average of the infinite
number of measurements, and the
measured value is the precise value.

• Error = Instrument reading – true reading.

• Error is often expressed in percentage as:
• Ballistic Galvanometer and
• AC Vibration Galvanometer
Classification of Errors
1. Gross errors
2. Systematic errors
3. Random Errors.
Gross Errors
• Arise due to human mistakes in reading the
instrument, recording and calculating results of
measurement.
• such as:
– reading of the instrument value before it reaches steady
state,
– mistake of recording the measured data in calculating a
derived measured, etc.
– Parallax error in reading on an analog scale

• Avoided by:
– Taking immense care while reading and recording of data
– Taking more no. of readings.
Systematic errors
Observational error
Observational error
• Occurs due to carelessness of operator
• Due to parallax effect
• Wrong recording of data
• Incorrect conversion of units.
Environmental Errors
• Systematic errors can be due to environmental effect
also.
• The sensor characteristics may change with
temperature or other environmental conditions.
• Are due to conditions external to the measuring
device
• Effect of temperature, pressure, humidity, dust,
vibrations, external magnetic and electrostatic field.
• Can be eliminated by:
– Proper electromagnetic or electrostatic shield
– Using instrument in controlled condition of pressure,
temperature and humidity.
Instrumental Errors
• Due to construction, calibration and operation of
equipment
• Zero error, and bias of an instrument are
examples of systematic errors.
• Are due to:
– Mechanical friction and wear
– Poor maintenance of instrument
– Displaced scale
– Non uniform division
– Bent or distorted pointer
Systematic Errors (major feature)
• sources of errors are recognisable
• can be reduced to a great extent by carefully
designing the measuring system and selecting
its components.
• By placing instrument in a controlled environment
also help in reducing systematic errors.
• Also can be further reduced by proper and regular
calibration of the instrument.
Random Errors
• Causes of random errors are not exactly known,
so they cannot be eliminated.
• Are accidental, small and independent
• Vary in unpredictable manner
• They can only be reduced
• If we measure the same input variable a number
of times, keeping all other factors affecting the
measurement same, the same measured value
would not be repeated, the consecutive reading
would rather differ in a random way.
• we may be able to reduce the error by taking a
number of readings and averaging them out.
ESSENTIALS OF INDICATING INSTRUMENTS

• Consist essentially:
– a pointer
– a calibrated scale attached to a moving system pivoted in
bearing.

• Moving system subjected to following three torques:

1. Deflecting ( or operating) torque;
2. Controlling ( or restoring) torque;
3. Damping torque.
DEFLECTING TORQUE (Td)
- Used for producing deflection in pointer

- Can be produced by :
- Magnetic effect,

- Heating effect, chemical effect,

- electrostatic and electromagnetic induction effect of

current or voltage

- Cause moving system of instrument to move from its

zero position.

- https://youtu.be/ZtBKC6WSjD0
DEFLECTING TORQUE (Td)
Instruments with Voltage and Current effects

• Magnetic effect : Moving-iron instruments.

• Electrodynamic effect : (i) Moving coil instruments,
(ii) Dynamometer type.

• Electromagnetic induction effect: Induction type

instruments.
• Thermal effect : Hot-wire instruments.
• Chemical effect : Electrolytic instruments.
• Electrostatic effect : Electrostatic voltmeters
Electrical measuring instruments in which deflecting torque
is produced by utilizing first three effects.
CONTROLLING TORQUE (Tc)
- Opposes deflecting torque
- Increases with deflection of moving system.

- Magnitude of moving system would be

indefinite with only deflecting torque, unless
controlling torque existed to oppose
deflecting torque.

• Pointer comes to rest at a position where two

opposing torques are equal i.e. Td = Tc.
Functions Controlling Torque
• Controlling torque increases with deflection of
moving system so that final position of pointer
on scale will be according to magnitude of
electrical quantity to be measured.

• Controlling torque brings pointer back to zero

when deflecting torque is removed.
– If it were not provided, pointer once deflected
would not return to zero position on removing
deflecting torque.
- Td α I
- Tc α θ
- Td = Tc
- θ α I (to be measured)
Importance of TC
- Under the influence of controlling torque pointer will
return to its zero position on removing source producing
the deflecting torque.

- Without controlling torque pointer will swing at its

maximum position & will not return to zero after removing
the source.
• Controlling torque provided by one of the
following two methods:

– Spring control.
– Gravity control.
Spring Control Method
• Spiral hairspring made of non-magnetic material like phosphor
bronze is attached to moving system of instrument
• also provide current to the moving system (i.e. operating coil).
Spring Control Method

• With deflection of pointer, spring is

twisted in opposite direction.

• This twist in spring provides

controlling torque.
Since torsion torque of a spiral spring
is proportional to angle of twist,
controlling torque (Tc ) is directly
proportional to angle of deflection of
pointer (θ) i.e. Tc α θ.

• Pointer will come to rest at a position

where controlling torque is equal to
deflecting torque i.e.
Td =Tc.
• Small weight is attached to moving system:
provides necessary controlling torque.

• In zero position of pointer, control weight hangs

vertically downward and therefore provides no
controlling torque.
• After deflecting torque acts pointer moves from zero position and
control weight moves in opposite direction.
• Due to gravity ,control weight will try to come in original position
(i.e. vertical) and thus provides an opposing or controlling torque.
• Pointer comes to rest at a position where controlling torque =
deflecting torque.
• In this , controlling torque (Tc) is proportional to sin of angle of
deflection (θ) i.e. Tc α sin θ.
DAMPING TORQUE

• We have seen:
– action of deflecting torque: moving system tend to move
– Control torque: will try to occupy a position of rest when two
torques are equal and opposite.

• Inertia of moving system: pointer will not come to rest

immediately but oscillate about its final deflected position
and takes appreciable time to come to steady state.

• To overcome this difficulty a damping torque is to be

developed by using a damping device attached to moving
system.
Dynamic Torque Equation

• Damping torque is proportional to speed of

rotation of moving system, that is
Dynamic Response of a Measuring System
Depending upon degree of damping introduced in
moving system, instrument may have any one of
the following conditions
 Under damped condition
 Over damped condition
 Critically damped condition
Degree of Damping and Behaviour of
Moving System
• If instrument is Under-damped (If degree of damping is
low): pointer oscillate about final position for some
time before coming to rest.

• If instrument is Over damped (If degree of damping is

too high): pointer will become slow and lethargic: rises
very slowly from its zero position to final position.

• Critically damped (If degree of damping is just

sufficient to enable the pointer to rise quickly to
equilibrium point without overshoot.): pointer comes
up to correct reading quickly without oscillating about
it: response settles quickly without any oscillation
Methods to produced Damping

1.Air Friction Damping

2.Fluid Friction Damping
3.Eddy Current Damping
4.Electromagnetic Damping
Performance Characteristics of
measuring Instruments
• Allows users to select most suitable instrument
for specific measuring jobs.

• Types :
1. Static characteristics: value of measured
variable change slowly.

2.Dynamic characteristics: value of measured

variable change very fast.
STATIC CHARACTERISTICS
• Set of criteria defined for the instruments, which are used to
measure the quantities which are slowly varying with time
– Accuracy
– Precision
– Error
– Resolution
– Sensitivity
– Dead zone
– Dead time
– Threshold
– Range
– Span
– Linearity
– Stability
– Tolerance
Accuracy
• is closeness with which instrument reading approaches
true value of the variable under measurement.
• Determined as the maximum amount by which result
differs from true value.
• Specifications of accuracy given in terms of error (in
terms of inaccuracy)
• Accuracy=100% if Measured value=True value
(True value: almost impossible to determine
experimentally )
• not indicated by any measurement system due to
loading effect and mechanical problems (e.g., wear,
hysteresis, noise, etc.).
Precision
• Measure of reproducibility of the
measurements
• measure of consistency or repeatability, i.e
successive reading do not differ.
• Gives capability of an instrument to show
same reading when used each time
(reproducibility of the instrument).
• An instrument which is precise may not be
necessarily accurate.
Difference between
accuracy and precision:

– Example: a shooter
aiming at the target.

– If all the shots are hit at

the particular point it is
said to have high
precision.
Error
• Algebraic different between the actual value
and measured value.

• Involves comparison of unknown quantity

with standard quantity.

• Different types of error. Gross error,

systematic error, random error, schematic
error.
Resolution (smallest measurable
i/p change)
• Smallest change in a measurement variable to
which an instrument will respond.

• Sometimes referred as sensitivity

• Sensitivity gives relation between input signal

to an instrument and output.
Sensitivity
• Ratio of output signal or response of
instrument to a change in input signal or
quantity under measurement.

• Where,
• ∆θo = Change in output
• ∆θi = Change in input
Dead Zone
• it’s largest change in input quantity for which
there is no output.
Dead time
• Is the time before which instruments starts to
responds after the output has been changed.
• OR
• Time required by a measurement system to
begin to respond to a change in measurand.
Threshold
• If the instrument input is increased very
gradually from zero there will be some
minimum value below which no output
change can be detected.
• This minimum value defines the threshold of
the instrument.
Range
• Specified by minimum and maximum values of
input variable (Xmin to Xmax)

• example: from -10 to +150 oC (for temperature

measuring device).
Span
• Difference between maximum Xmax and
minimum Xmin values of input variables:
• Span=(Xmax - Xmin ).
• Example: for measuring devices with temp.
range from -10 oC to +150 oC,
span is: +150 oC - (-10 oC) = 160 oC.
Linearity

• Ability of an instruments to reproduce its input linearly.

When incremental change in input and output is
constant over the specified range

Graph shows the output reading of an instrument

when a few input readings are entered.
• Stability :- Ability of an instrument to retain its
performance throughout is specified
operating life.

• Tolerance:- Maximum allowable error in the

measurement
Dynamic Characteristics:
Speed of Response
• Is the quickness of an instrument to read the
measurand variable

• Or is time elapsed between start of the

measurement to the reading taken.

• This time depends upon the mechanical

moving system, friction, etc.
TYPES OF AMMETERS & VOLTMETERS
1) Moving Iron Type Meters (AC & DC);
a) Attraction type,
b) Repulsion type.

2) Moving Coil Type Meters (AC & DC);

a) Permanent Magnet Moving Coil (PMMC): DC
b) Electrodynamic or Dynamometer: AC & DC

3) Hot Wire Type (AC & DC);

4) Induction Type (AC & DC);

a) Split phase,
b) Shaded Pole type.

5) Electrostatic Type for Voltmeters Only;

Moving-iron instruments

• Used as Voltmeter and Ammeter only.

• Both can work on AC as well as on DC.

• Movable system : soft iron, pivoted on spindle

with bearings
– Acts upon the magnetic field produced by current
in coil.
Components of a moving-iron instrument

• Moving element: small piece of soft iron in the form of a vane or

rod/plate.

• Stationary Coil acting as electromagnet: when current flows

through it produce magnetic field and also magnetize iron piece.

• Control torque :provided by spring or weight (gravity).

• Damping torque (normally pneumatic): provided by damping device

consisting of an air chamber and a moving vane attached to the
instrument spindle.

• Deflecting torque produces a movement on an aluminum pointer

over a graduated scale.
Types of Moving-Iron instruments
• Attraction (or single-iron) type
• Repulsion (or double iron) type
Attraction Moving Iron Instrument
Construction
• Soft iron plate is used as moving element

• Is so placed that it can freely move in magnetic field of

stationary coil.

• Uses stationary coil acting as electromagnet.

• Electromagnet is temporary magnet whose magnetic

field strength increases or decreases with magnitude of
current passes through it.

• Stationary coil is excited by voltage or current whose

magnitude is used to be measured.
Attraction type Moving Iron Instruments
• Iron plate attracts from weaker field towards the
stronger field
• Whenever a piece of iron is placed nearer to a
magnet it would be attracted by the magnet.
• Force of this attraction depends upon magnetic
field strength.
• Magnetic field strength can easily be increased or
decreased by increasing or decreasing current
through its coil.
• Accordingly attraction force acting on iron plate
would also be increased and decreased.
Attraction Type Moving Iron Instrument
• Thin disc of soft iron is pivoted in front of a coil.
• Iron disc tends to move inward that is from
weaker magnetic field to stronger magnetic field
when current starts flowing through the coil.
• Controlling torque: gravity control used in
vertically mounted instruments.
– spring control in modern instrument.
• By adjusting balance weight null deflection of the
pointer is achieved.
• Damping force: provided by air friction. where
damping is achieved by a moving piston in an air
syringe.
Repulsion Moving Iron Instrument

(a) Radial vane type. (b) Co-axial vane type

Repulsion Moving Iron Instrument
• Consist of Two soft Iron vanes inside the coil
• one fixed and attached to stationary coil and other
movable and mounted on spindle of instrument.
• These are similarly magnetized
• when operating current flows through the coil the two
vanes are magnetised developing similar polarity at the
same ends consequently repulsion takes place
between the vanes and movable vane causes the
pointer to move over the scale.
• Controlling torque: provided by springs.
– Gravity control can also he used in vertically mounted
instruments.
• Damping torque is produced by air friction as in
attraction type instruments.
• Radial Vane Type:
– Vanes are radial strips of iron.
– Fixed vane is attached to the coil and movable one
to the spindle of the instrument.

• Co-axial Vane Type:

– fixed and moving vanes are sections of co axial
cylinders
Advantages of the MI Instruments
• Universal use – used for both AC and DC
– MI instrument is independent of direction of current

• Less Friction Error –has high torque weight ratio

as their current carrying part is stationary and
moving parts are lighter in weight.

• Cheapness – As requires less number of turns

compared to PMMC instrument.

• Robustness – Because of simple construction.

And also because their current carrying part is
stationary.
Disadvantages of Moving Iron Instruments
• Accuracy – Scale of MI instruments is not
uniform, and hence accurate result is not
possible.

• Errors – Some serious error occurs due to

hysteresis, frequency and stray magnetic field.

• Difference between AC and DC calibration

• Two type of error occurs in MI instruments i.e.,

error which occurs on both AC and DC and the
error which only occur on AC.
Torque Equation:
• According to law of conservation of energy,

Electrical energy supplied by source = energy stored in coil

+ mechanical work done for
deflection of needle

• Let I= current flowing in the coil.

• Energy stored in coil in the form of magnetic field = (1/2)LI2.

• As current changes to (I+dI),

deflection in pointer becomes dƟ
resulting into change in inductance of coil from L to (L+dL).

• Let this deflection in pointer is due to deflection torque Td.

• Thus mechanical work done = Td dƟ ………,……..(1)
• Energy stored in Coil = (1/2)(L+dL)(I+dI)2

• Change in stored energy of coil= Final Stored Energy

– Initial Stored Energy

= (1/2)(L+dL)(I+dI)2 – (1/2)LI2
= (1/2)[ (L+dL)(I+dI)2 – I2L]
= (1/2)[ (L+dL)(I2+2IdI+(dI)2 – I2L]
= (1/2)[ LI2+2LI dI+L (dI)2 + dLI2+2IdI dL+dL (dI)2 – I2L]

• Neglecting second order and higher terms of differential quantities

i.e. L(dI)2, 2IdIxdL and dLx(dI)2

= (1/2)[ 2LIdI+dLxI2]
= LIdI +(1/2)dLx I2 ……………………(2)
• when there is change of current from I to
(I+dI), it causes change in emf of coil.

• Thus e = d(LI) / dt
= IdL/dt + LdI/dt

• Electrical energy supplied by the source = e Idt

= (I dL + L dI) I
= I2dL + LI dI
…..3
• Law of conservation of energy:

• Electrical energy supplied by source = energy stored in coil

+ mechanical work done
for deflection of needle

• Hence,
I2dL + LIdI = Change in stored energy + Work done
I2dL + LIdI = LIdI +(1/2)dL I2 + Td dƟ ….[from (1), (2)
and (3)]

• ⇒ Td dƟ = (1/2)dLxI2
• ⇒ Td = (1/2)I2(dL/dƟ)

• deflecting torque dependent on:

– rate of change of inductance with angular position of iron vane and
– square of rms current flowing through the coil.
• In moving iron instruments, controlling torque is provided by spring.

• Controlling torque due to spring is: Tc = KƟ

• Where K = Spring constant

Ɵ = Deflection in the needle

• In equilibrium state,
• Deflecting Torque = Controlling Torque

• ⇒ Td = Tc
• ⇒ (1/2)I2(dL/dƟ) = KƟ
• ⇒ Ɵ = (1/2)(I2/K)(dL/dƟ)

• Angular deflection of needle is proportional to square of rms current

flowing through the coil.
• Therefore, deflection of moving iron instruments is independent of
direction of current.
Moving-Coil instrument

• Permanent Magnet Moving Coil type

– used for DC current, voltage measurements.

• Dynamometer type
– used on ac or dc current, voltage measurements.
Principle:

• When a current carrying conductor is placed

in a magnetic field, it experiences a force

• Fleming left-hand rule:

• Thumb: direction of force on conductor,
• First finger: direction of magnetic field and
• Second finger : direction of current in wire.
Permanent Magnet Moving Coil (PMMC) Meter

• Also known as D’Arsonval meter or Galvanometer

• works on electromagnetic effect.

• Only used for measuring (DC) current.

– With AC current, direction of current will be reversed during
negative half cycle, and hence direction of torque will also be
reversed.
– This results in average value of zero torque
– hence no net movement against the scale.

• Uses permanent magnet to produce magnetic flux and a

coil that carries current to be measured moves in this
field.
• Pointer is connected to coil it gets deflected in proportion
with the current.
5 main components OF PMMC meter
(or D’Arsonval meters)
• Stationary Part or Magnet System

• Moving Coil

• Control System

• Damping System

• Meter
• Stationary Part or Magnet System:
– Made up of materials like alcomax and alnico
(composed of aluminium (Al), nickel (Ni) and cobalt
(Co)) which provide high field strength.

• Moving Coil:
– Wound with many turns of copper wire and placed on
rectangular Aluminium which is pivoted on jeweled
bearings.
– Can freely move between two permanent magnets
– Light rectangular coil wound on an aluminum frame is
pivoted within the air gaps between the two poles of a
permanent magnet and a cylindrical soft iron core.
– The aluminum frame supports the coil as well as
provides eddy current damping.
• Control System
– spring generally acts as control system for PMMC
instruments.
– spring also provides path to lead current in and out of
the coil.

• Damping System
– damping force hence torque is provided by movement
of aluminium former in the magnetic field created by
the permanent magnets.

• Meter
– Consists of light weight pointer to have free
movement and
– Scale which is linear or uniform and varies with angle.
Construction
• Coil of thin wire is mounted on an aluminum frame (spindle)

• positioned between the poles of a U shaped permanent magnet

which is made up of magnetic alloys like alnico.
• This light rectangular coil carries the current to be measured. Soft
iron core provides formation of uniform magnetic field.
• Coil is pivoted on jeweled bearing and thus is free to rotate.

• Current is fed to the coil through spiral springs which are two in
numbers.

• Coil carrying current, to be measured, moves in a strong magnetic

field produced by a permanent magnet and a pointer is attached to
the spindle which shows the measured value.
Working
• When current flow through coil,
generates magnetic field which is
proportional to current.
• Deflecting torque is produced by
electromagnetic action of the current in
coil and magnetic field.
• When torques are balanced moving coil
will stop and its angular deflection
represents amount of electrical current
to be measured.
• If permanent magnet field is uniform
and the spring linear, then pointer
deflection is also linear.
• Controlling torque is provided by two
phosphorous bronze flat coiled helical
springs. These springs serve as a flexible
connection to the coil conductors.
• Damping is caused by the eddy current
set up in the aluminum coil which
prevents the oscillation of the coil.
Deflecting Torque
• Interaction between induced field and field produced by
permanent magnet causes a deflecting torque, results in
rotation.
• force F = NBIL
– where N: no. of turns of coil
– B: magnetic field density in Tesla
– I: current carried by coil
– L: vertical length of coil
– d: horizontal side of coil
– A: area of coil
• Torque (electro-magnetical torque)= force
* perpendicular distance
• Torque = NBIL*NBId = NBIA
• N,B,A=Constant=G
• T=G.I
• Spring Torque (Controlling Torque)

• Tc=kθ

• At eqilibrium, Tc=Td
• GI=k θ

• Θ=GI/k
Advantages of PMMC Instruments
• Scale is uniformly divided as current is directly
proportional to deflection of the pointer.

• Hence it is very easy to measure quantities from these

instruments.

• Power consumption is also very low

• Higher torque is to weight ratio.

• Single instrument can be used for measuring various

quantities by using different values of shunts and
multipliers.
Disadvantages of PMMC Instruments

• Cannot measure ac quantities.

• Cost is high as compared to moving iron
instruments.
Electrodynamic or Dynamometer type
instruments.
• Suitable for measurement of dc-ac current, voltage and power.
• operating field is produced by the fixed coils
• Deflecting torque in dynamometer is produced by interaction
of magnetic field produced by a pair of fixed air cored coils and
a third air cored coil capable of angular movement suspended
within the fixed coil.
• Very important because commonly employed for measuring
power in AC circuits.
Dynamometer type wattmeter principle

• Current carrying conductor placed inside a

magnetic field, experiences a mechanical force
causing deflection in it.
Dynamometer Type Wattmeter
Working Principle
• When current carrying moving coil is
placed in magnetic field produced by
current carrying fixed coil, a force is
exerted on coil sides of the moving coil
and deflection takes place
• OR
• When field produced by current carrying
moving coil (Fr) tries to come in line with
the field produced by current carrying
fixed coil (Fm), a deflecting torque is
exerted on moving system and
deflection takes place
Construction Dynamometer Type Wattmeter
• Consists of two coils called:
– Fixed coil (Current Coil)and
– Moving coil (Pressure Coil)
Fixed coil
• Connected in series with load and carries
circuit current.
• Therefore, called current coil.
• Splitted into two equal parts which are placed
parallel to each other.
• Two fixed coils are air-cored to
avoid hysteresis effects when used on AC.
Moving coil
• Connected in parallel with the load and carries
current proportional to the voltage.
• Therefore, called potential (or pressure)coil.
• Pivoted between two parts of fixed coil and is
mounted on spindle.
• Pointer is attached to the spindle which gives
deflection.
• A high resistance is connected in series with the
moving coil to limit current through it.
• By limiting current, moving coil is made of light
weight which increases sensitivity of instrument.
Controlling Torque
• Only spring controlled systems are used in
these types of wattmeter.

• Gravity controlled system not employed as

produces errors
Damping System
• Uses Air friction damping
Dynamometer Type Wattmeter Working

• Current coil is connected in series with load, carries load

current
• potential coil, connected in parallel with load, carries
current proportional to voltage across load.
• Fixed coil produces a field Fm
• Moving coil produces a field Fr.
• Field Fr tries to come in line with the main field Fm, which
produces a deflecting torque on moving coil.

• Thus, pointer attached to the spindle of moving coil

deflects.
• Deflection is controlled by controlling torque produced by
springs.
Expressions for controlling torque and deflecting torques.
• I1 : instantaneous current in current coil.
• I2 : instantaneous current in pressure coil

• Instantaneous torque in electrodynamic type

instruments is directly proportional to product of
instantaneous values of currents flowing
through both coils and rate of change of flux
linked with the circuit.

• Where, x is the angle.

• Applied voltage across pressure coil:

• Assuming electrical resistance of pressure coil

be very high hence we can neglect reactance
with respect to its resistance.
• So impedance = electrical resistance therefore
it is purely resistive.
• instantaneous current , I2 = v / Rp
• where Rp is the resistance of pressure coil.
• If φ=phase difference between voltage and
current, instantaneous current in current coil

• As current through pressure coil is very small

compared to current through current coil hence
current through current coil = total load current.

• Hence instantaneous value of torque is

• Average deflecting torque = integration of
instantaneous torque from limit 0 to T, time
period of cycle.

• Controlling torque : Tc = K θ , where

– K is spring constant and
– θ is final steady state value of deflection.
• Advantages:

• Can be used both on AC and DC circuits.

• Has uniform scale.
• High degree of accuracy can be obtained by careful
design.

• Disadvantages:

• At low power factors, inductance of potential coil

causes serious errors.
• Reading of instrument may be affected by stray fields
acting on moving coil. To prevent it, magnetic shielding
is provided by enclosing instrument in an iron case.
Power Factor Meters

• In power transmission system and distribution

system we measure power factor at every
station and electrical substation using power
factor meters.

• Power factor measurement:

– provides knowledge of type of loads we are using
– helps in calculation of losses during power
transmission system and distribution.
Electrodynamometer Type Power
Factor Meter
• Two types on the basis of supply voltage
• Single phase
• Three phase.
Construction of Electrodynamometer
Type Power Factor Meter
• Include two coils namely
– pressure coil and
– current coil.

• Pressure coil is connected across load

• Current coil is connected in series with load carries
circuit current
• Pressure coil is splits into two parts namely inductive
and non-inductive part or pure resistive part.
• No requirement of controlling system because at
equilibrium there exist two opposite forces which
balance movement of pointer without requirement of
controlling force.
• By measuring phase difference between voltage and
current power factor obtained on calibrated scale.
• Coil 1 making angle θ with
Reference plane.
• Angle between both coils 1 and 2 is
90o.
• Coil 2 is making angle (90o + θ)
with reference plane.
• Scale of meter is calibrated to
show values of cosine of angle θ.
• Resistance connected to coil 1 = R
and
• Inductor connected to coil 2 = L.
• Values of R and L are adjusted such
that R = wL so both coils carry
equal magnitude of current.
• Therefore current passing through
the coil 2 is lags by 90o with
reference to current in coil 1 as coil
2 path is highly inductive in nature.
Working Principle
• Angle between planes of two coils is exactly 90º
• There will be two deflecting torques produced.
• One acting on coil A and other on coil B
• Coil winding are so arranged that torques due to two
coils are opposite in direction.
• Therefore pointer will take up a position where two
torques are equal.
• And when two torques are equal, θ=φ
• So deflection of instrument is measure of phase angle of
the circuit.
• Scale of instrument is calibrated in terms of power factor.
Expression for Deflecting Torque

• M : mutual inductance between two coils,

θ : angular deflection of plane of reference.
• Deflecting torque for coil 2 is-
• At equilibrium both torque as equal.
– thus on equating T1=T2

• So, deflection angle is measure of phase

angle of given circuit.
Advantages of Electrodynamic Type
Power Factor Meters
• Losses are less because of minimum use of
iron parts
• Give less error over a small range of frequency
Measurement of Frequency
• Reed type
• Moving Iron type
• Electrodynamometer type
Mechanical Resonance Type/ Vibrating Reed
Type Frequency Meter
• Reeds: thin steel strips
• Reeds placed in a row
alongside and close to
an electromagnet.
• Are fixed at bottom end
and free at top end.
• Electromagnet consists
of thin laminations and a
coil is wound around it
• Coil is connected across
the supply whose
frequency is to be
measured.
Mechanical Resonance Type/ Vibrating Reed
Type Frequency Meter
• Approximate dimensions of vibrating reeds = 4 mm wide
and ½ mm thick.
• Reeds are not similar to each other
• They differ either in their dimensions or weight or carry
different flags at their tops.
• This is to vary natural frequency of vibration of each reed.
• Reeds are arranged in ascending order of natural frequency
• Difference in frequency is usually 1Hz.
• Thus natural frequency of first reed may be 45 Hz, second
46 Hz, next 47 Hz and so on of the last may be 55 Hz.
• Flags at top of reeds are -painted white, and frequency is
read directly from the instrument by observing the scale
mark opposite to the reed which is vibrating most.
Frequency Meter Working Principle
• Vibrating reed frequency meter is connected across supply
whose frequency is to be measured.
• Alternating current flows through coil of an electromagnet
which produces a force of attraction on reeds.
• Force of attraction is proportional to the square of current
• therefore it varies at twice the supply frequency.
• Hence a force exerted on reeds at every half cycle.
All the reeds thus tend to vibrate, but only the one whose
natural frequency is double that of supply will vibrate
appreciably.
• Mechanical resonance is obtained in this reed.
• Frequency is determined, by noting the scale reading
opposite the reed that vibrates with maximum amplitude.
Vibrating Reed Type Frequency
Meter

https://www.youtube.com/watch?v=n86f-L-IG1s
• Advantages of Reed Type Frequency:
• Meter Indication is independent of magnitude of
supply voltage (but not too low as vibration will
not be sufficient and reading will not be reliable)

• Disadvantage:
• Can not read frequencies which are much closer
• So cannot be used for precision measurements
• Reliability of reading also depends upon the
accuracy with which meter reeds are tuned
Weston Frequency Meter
(Moving Iron type
Frequency Meter)
Working Principle of Weston Frequency Meter

• Consists one Inductive and one Resistive coil.

• When frequency of measurand signal varies,

distribution of current between inductive and
resistive circuit changes.

• Change in frequency causes change in inductive

impedance of the circuit
– because of which variation occurs in distribution of
current between the parallel paths.
Construction of Weston Frequency Meter
• Consists two coils placed perpendicular
to each other.
• Each coil divided in two sections.
• RA connected in series with coil A
• LB connected in series with coil B.
• LA connected in parallel with coil A and
• RB in parallel with coil B.
• L connected in series with LA and RB:
– reduces harmonics in circuit current.
– reduces error in indication.
• Moving element is soft iron needle
pivoted on spindle which also carries
pointer,
• There is no controlling force
Working of Weston Frequency Meter
• When meter connected across supply coil A and B carries
current.
• These currents set up two magnetic fields which are
Perpendicular to each other.
• Magnitude of field depends on current flowing through the
coils.
• Both these fields act upon soft iron magnetic needle.
• Position of needle depends on relative magnitude of magnetic
field acts on it.
• Meter is so designed that when supply of normal frequency
applied:
– voltage drop of same magnitude occurs across reactance LA and
resistance RB.
– Hence equal current passes through the coil A and coil B.
• So, magnetic needle takes a position at 45° to both the coils
and pointer is at centre of the scale.
• If frequency increases above its normal value:
– Reactance LA and LB increases (XL=2πfL)and
– RA and RB remains same.
• So this increases impedance of coil B.
• So decreasing IB.
• So Field develops because of coil also decreases.
• More current flows through coil A because of parallel
connections with coil B.
• Field of coil A becomes stronger than B.
• Tendency of needle is to deflect towards stronger field
and it tends to set itself in line with axis of coil A
• So Pointer deflects towards left.
• When frequency decrease below normal value,
opposite action takes place, and pointer deflects
towards right.
Electrodynamometer type Frequency Meter
• Consist of fixed coil and moving coil.
• Fixed coil divided in two parts.
• Fixed coil 1 has L1, C1 in series. (inductive)
• Fixed coil 2 has L2, C2 in series.(capacitive)
• Operates on principle of electrical resonance
• At normal frequency XL=XC
• At higher Frequency, XL>XC
• At Lower Frequency, XL<XC
• Torque on pointer is proportional to current in
moving coil.
• Which is sum of two currents
• As One fixed coil is inductive other is capacitive
Torque produced by I1 and I2 act in opposite on
moving coil.
• Resultant torque is function of frequency of
applied voltage.
• Mater scale is calibrated in terms of frequency.
Synchroscope
• Indicates degree to which two systems (generators
or power networks) are synchronized with each other.
• For two electrical systems to be synchronized,
– both systems must operate at same frequency, and
– phase angle between the systems must be zero (and two
polyphase systems must have the same phase sequence).
• Only when these two quantities are zero it is safe to
connect the two systems together.
• Connecting two unsynchronized AC power systems
together: cause high currents to flow, which will severely
damage any equipment not protected.
• Used to determine correct instant of closing the
switch which connects an alternator to power station
busbar.
• Process of connecting at correct instant
(synchronising) is necessary when unloaded
alternator is to be connected to busbar to share load.
• The correct instant of synchronizing is when busbar
and incoming machine voltages.
– Are equal in magnitude
– Are in phase
– Have the same frequency
• For polyphase machines, phase sequence should be
same.
• Synchroscope indicate: Difference in phase and
frequency
• Voltage checked with voltmeter.
Synchroscope
Synchroscope: indicates phase displacement
and frequency of two machines
• Consists of a three limb transformer.
• winding of one outer limb was excited from one
alternator the other by incoming busbar.
• Central limb connected with a lamp
• Resultant flux in central limb=phasor sum of two
alternators.
• If incoming voltages are in phase:
– two fluxes are additive in nature and
– Emf induced in central limb is maximum,
– Causing lamp to glow with full brightness.
• When two voltages are out of phase (180):
– Resultant flux is zero
– No emf induced in central limb winding
– lamp will not glow at all.
• If there is frequency difference between two
machines lamp will be alternately bright and dark or it
flickers.
• Frequency of flicker is difference in frequencies of two
machines.
• Correct instance of synchronizing is when lamp is
flickering at very slow rate and is at its maximum
brightness.
– Maximum brightness: 0 phase difference
– Slow flickering: less difference in frequencies.

• Defect of the system:

– Does not indicate whether incoming machine is too fast or
two low.

• This defect can be corrected by introducing

electrodynamometer type instrument in circuit.
Weston Synchroscope
• Consist of:
– Fixed coil
– Moving coil

• Fixed coil:
– divided in two parts
– Connected in series with
resistor across busbar

• Moving coil:
– Connected across
terminals of incoming
machine in series with
capacitor

• Busbar Voltage= V2
• Incoming Voltage=V1
• When two voltages in phase: V1=V2
– Currents in fixed coil I1 and moving coil I2 in
quadrature with each other.
– No torque on the instrument
– Pointer is at vertical position
– Lamp is at maximum brightness

• If V2 leading to V1 and incoming machine

slightly slow:
– Torque changes and
– Pointer moves to fast
Ballistic Galvanometer
• Is of d’Arsonval type

• Measures quantity of charge passed through it

• Does not show steady deflection as in current

galvanometer due to transitory (momentary) nature of
current passing through it and oscillates with decreasing
amplitude.

• Amplitude of first deflection or swing or throw is

proportional to charge passing.
Construction
• consists coil of copper wire wound on
non-conducting frame of galvanometer.
• Phosphorous bronze wire suspends the
coil between north and south poles of a
magnet.
• For increasing magnetic flux uses iron
core within the coil.
• Lower portion of coil connects with the
spring.
• spring provides restoring torque to coil.
• When charge passes through
galvanometer, coil starts moving and
gets an impulse.
• impulse of coil is proportional to
charges passes through it.
Vibration Galvanometer
• Oscillation frequency of moving element and
measurand current becomes equal

• Used for detecting alternating current

• Working Principle:
• When ac current passes through moving element of
galvanometer, deflecting torque produces because of
which coil vibrates.
• If vibration frequency of moving element is equal to
frequency of measurand current, moving element
vibrates with large amplitude.
Types of Vibration Galvanometer
• Moving Iron Type Vibration Galvanometer
• Moving Magnet Type Vibration Galvanometer
Moving Iron Type
Vibration Galvanometer

• Coil suspends between

the poles of permanent
magnet.

• Measurand AC when
passes through the
moving coil produce the
deflection torque on it.
Construction of
Vibration Galvanometer
• Moving element is suspended between the gap of a
permanent magnet or in the field of an electromagnet.
• Moving element suspends with the help of fine bronze
or platinum wire.
• The wire is attached to the pulley at the top.
• Pulley with the help of the spring keeps the string or
wire tight.
• Wire or string stretches between the two ivory bridges,
the position of the bridges can be adjusted according
to the requirement. The tension on the spring depends
on the position of the ivory bridges.
• Mirror is placed on string or thread between ivory
bridges.
• When measurand current passes through the coil, the
reflected beam through the mirror focus on the scale.
• Natural oscillation frequency of moving
element is tuned to the specified
frequency.
• Tunning is the adjustment of the
natural frequency oscillation so that it
is equal to the frequency of
measurand current passing through it.
• Tuning of the vibration galvanometer
depends on the tension of the
suspension spring.
• The tension on the spring means the
pulling force acts axially on the
spring. The tuning increases the
amplitude of vibration because of
which the wide band of light is
reflected on the screen.
Moving Magnet Type Vibration
Galvanometer
• Operation depends on magnetic field of the resonance
frequency.
• small piece of magnet is suspended between poles of
two permanent magnets along with the mirror.
• Measurand current passes through the coil because of
which the magnetic field develops around them.
• Small magnetic field starts rotating between the poles of
a magnet.
• Electromagnets are also used in place of permanent
magnets.
• Electromagnet energises through the measurand current
passes through the coil.
• In moving magnet type vibration galvanometer, tuning
between moving system and frequency can be done by
adjusting tension or suspension of the spring and
magnetic field between the pole of magnets.
Moving Magnet Type Vibration
Galvanometer
• Weston type Synchroscope.
• DC Permanent magnet moving coil type
Galvanometers.
• Ballistic Galvanometer and AC Vibration
Galvanometer (only the basic working
Principle and Applications).