This presentation gives an insight into the various types of voltmeters and transformers that exist. The are both electronic measuring instruments. All the types of voltmeters and transformers have been discussed alogwith numerical examples and their solutions.

1. EMI Presentation
Topics Covered:
1. Voltmeter
2. Transformer
PRESENTED BY:
DIKSHA PRAKASH
140020204002

2. Voltmeter
• Measures: Potential difference between two
nodes
• Connection: Parallel across the node
• Difference between Voltmeter & Ammeter:
Ammeter is connected in series with the circuit
& Voltmeter is connected in parallel across the
node.

3. • Voltmeter as an electronic meter can be characterized by a
three port network:
ELECTRONIC METER
INPUT SIGNAL OUTPUT SIGNAL
POWER SUPPLY

4. Types of VoltmeterBASIS: Voltage
Measurement
Produced
Digital
Voltmeters
VTVMs &
FET-VMs
BASIS:
Measurement
Type produced
AC Voltmeter
DC Voltmeter
BASIS:
Construction
Principle
PMMC
Voltmeter
MI Voltmeter
Electro-
Dynamometer
Type Voltmeter
Rectifier
Voltmeter
Induction Type
Voltmeter

5. 1.1 PMMC Voltmeter
• General arrangement of a voltmeter: coil wound over an iron
core.
• Thus, two possibilities: Either the coil moves or the iron core.
• When the coil moves, its called ‘Permanent Magnet Moving
Coil’ voltmeter & when the iron core moves, its called
‘Moving Iron’ voltmeter.
• Are suitable for DC work only.
• PRINCIPLE :
when a current carrying conductor is placed in a magnetic
field, a mechanical force acts on the conductor.

6. The current carrying coil, placed in magnetic field is
attached to the moving system.
With the movement of the coil, the pointer moves over the
scale to indicate the electrical quantity being measured.
This type of movement is known as D’Arsenoval
movement.
FIGURE: Construction of a PMMC Voltmeter

7. FIGURE: PMMC Voltmeter’s Construction & Working

8. • It consists of a light rectangular coil of many turns of fine
wire wound on an aluminium former inside which is an iron
core .
• The coil is delicately pivoted upon jewel bearings and is
mounted between the poles of a permanent horse shoe
magnet.
• Two soft-iron pole pieces are attached to these poles to
concentrate the magnetic field. The current is led in to and out
of the coils by means of two control hair- springs, one above
and other below the coil.
• These springs also provide the controlling torque. The
damping torque is provided by eddy currents induced in the
aluminium former as the coil moves from one position to
another.

9. WORKING
• Why only DC measurement?
When the current in the coil reverses, the direction of the field of
permanent magnet remains the same & the deflecting torque gets
reversed. Thus, the pointer tries to deflect below zero. This motion
is prevented by a “stop” spring.
Current
flows
through coil
Mechanical
torque acts
on coil
Pointer moves
over a
graduated scale
Coil is placed in
B-field of
Permanent magnet

10. FIGURE: Assembled 3D Arrangement

11. DEFLECTING TORQUE EQUATION
The magnetic field in the air gap is radial due to the presence of soft iron core. Thus, the conductors of the coil will move
at right angles to the field. When the current is passed through the coil, forces act on its both sides which produce the
deflecting torque.
Let, B = flux density, Wb/m2
l = length or depth of coil, m
b = breadth of the coil.
N = no. of turns of the coil.
If a current of ‘I’Amperes flows in the coil, then the force acting on each coil side is given by,
Force on each coil side, F = (BINl) Newton.
Deflecting torque, Td = Force × perpendicular distance
= (BIlN) × b
Td = BINA Newton metre.
Where, A = l × b, the area of the coil in m2.
Thus, Td α I
The instrument is spring controlled so that, Tc α θ
The pointer will comes to rest at a position, where Td =Tc
Therefore, θ α I
Thus, the deflection is directly proportional to the operating current. Hence, such instruments have uniform scale.

12. • Uniform Scale
• High Efficiency
• Little power for operation
• No hysteresis loss
• No effect of stray external magnetic fields
Advantages
• Not applicable for AC measurements
• Expensive
• Variation in working due to temperature change (spring &
the strength of permanent magnet may get affected).
Disadvantages
• Measurement of DC current & voltages
• Used in DC galvanometers to detect small currents
• For measuring change in magnetic flux linkages
Applications

13. EXAMPLE:
A permanent magnet moving coil instrument has a coil dimensions of
15mmX 12 mm. The flux density in the air gap is 1.8X10-3 Web/m2
and the spring constant is 0.14 Nm/rad. Determine the number of
turns required to produce an angular deflection of 90 degrees when
a current of 5 mA is flowing through the coil.
Deflection= Θ = 90°= (П/2) rad
At equilibrium, Tc=Td or (NBldI) =K Θ
=
0.14𝑋10−6 𝑋
𝜋
2
1.8𝑋10−3 𝑋15𝑋10−3 𝑋12𝑋10−3 𝑋12𝑋10−3 𝑋5𝑋10−3
= 136

14. 1.2 MOVING IRON VOLTMETER
• Mainly used for AC measurements & can also be used for DC measurements.
• Two types of MI instruments:
1. Attraction Type
2. Repulsion Type
• General Principle of Working:
I. The iron vane (made up of high permeability steel & forms the moving
element of the system) is situated so as, it can move in a magnetic field
produced by a stationary coil.
II. The coil is excited by the current or voltage under measurement.
When the coil is excited, it becomes an electromagnet and the iron vane
moves in such a way so as to increase the flux of the electromagnet.
III. Thus, the vane tries to occupy a position of minimum reluctance. Thus, the
force produced is always in such a direction so as to increase the inductance of
the coil.

15. 1.2.1 ATTRACTION TYPE
FIGURE: Construction of an Attraction Type MI Voltmeter

16. DEFLECTING TORQUE EQUATION
The force F, pulling the soft -iron piece towards the coil is directly proportional to the
Field strength H, produced by the coil & the pole strength ‘m’ developed in the iron
piece.
Thus, F α mH
F α H2 (Since, m α H )
Thus, the Instantaneous deflecting torque α H2
Also, the field strength H = μi
If the permeability(μ) of the iron is assumed constant,
Then, H α i (Where, ‘i’ is the instantaneous coil current in Ampere)
Instantaneous deflecting torque α i2
Therefore, Average deflecting torque, Td α mean of i2 over a cycle.
Since the instrument is spring controlled,
Tc α θ
In the steady position of deflection, Td = Tc
θ α mean of i2 over a cycle
Thus, θ α I2

17. 1.2.2 REPULSION TYPE
• Two soft iron vanes are used; one fixed and attached the stationary
coil, while the other is movable (moving iron), and mounted on the
spindle of the instrument.
• 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 the
movable vane causes the pointer to move over the scale.
• Two types
1. Radial vane type: - vanes are radial strips of iron.
2. Co-axial vane type:-vanes are sections of coaxial cylinders.

18. IMPORTANT OBSERVATION
The scale of the instrument is non- uniform; being crowded in
the beginning and spread out near the finish end of the scale.
WHY?
The deflection is proportional to the square of the coil current.
(However, the non- linearity of the scale can be corrected to
some extent by the accurate shaping and positioning of the iron
vanes in relation to the operating coil).

19. TABLE: MI Instruments vs. PMMC Instruments

20. Extension of the range of PMMC &
MI Instruments
Shunt Multiplier
A shunt is a small amount of resistor
that tis connected in parallel with
Ammeter to extend its range.
It’s a large amount of resistance connected
in series with the voltmeter to extend the range.
Let the full scale deflection be ‘V’ volts,
the meter resistance be Rm ohms, the load
voltage or new range be ‘

21. 1.3 ELECTRODYNAMOMETER
TYPE VOLTMETER
• It’s a type of ‘Transfer Instrument’ i.e. it has same calibration for
AC & DC sources.
• Overcomes the flaw of PMMC instrument in which magnetic
field in the air gap doesn’t change with the current.
• Instead of a permanent magnet, the electrodynamometer type
instrument uses the current under measurement to produce the
necessary field flux.
• In other words, the magnet of PMMC is replaced by two serially
connected fixed coils that produce the magnetic field when
energized (using the current under measurement).

22. Construction
FIGURE: Electrodynamometer (or Dynamometer) type Voltmeter

23. • Fixed Coil – The magnetic field produced by the fixed coil is
divided into two sections to generate a more uniform field at the
centre.
• Moving Coil – Has an air core & follows light and rigid
construction methods.
• Springs – Provides the controlling torque.
• Dampers – Air friction damping is employed in the instrument &
provided by Aluminium vanes attached to a spindle at the
bottom. The vanes move in sector shaped chamber.
• Shielding – The magnetic fields produced are weaker than in
other type of instruments and thus needs special shielding. The
arrangement is enclosed in laminated hollow cylinder with closed
ends.

24. FIGURE: Simplified circuit of Electrodynamometer Voltmeter

25. Expression for developed Torque
Consider the currents in fixed and moving coil as 𝑖 𝑓 & 𝑖 𝑚 respectively. Let the
fixed and moving coil have self-inductances 𝐿 𝑓 &𝐿 𝑚 respectively. Let ‘M’ be the
mutual inductance between fixed and movable coil.
Total energy stored in the magnetic field of the coils is given by:
𝑊 =
1
2
𝐿 𝑓 𝑖 𝑓
2
+
1
2
𝐿 𝑚 𝑖 𝑚
2
+M𝑖 𝑚 𝑖 𝑓
Thus, the equation for the torque developed can be written as:
𝑇𝑑 =
𝑑𝑊
𝑑𝜃
=𝑖 𝑚 𝑖 𝑓
𝑑𝑀
𝑑𝜃
Mutual inductance ‘M ’ between the coils is a function of the deflection θ (i.e.
relative position of moving coil).
The equivalent inductance between fixed and moving coils can be found out as:
𝐿 𝑒𝑞 = 𝐿 𝑓 + 𝐿 𝑚 + 2𝑀
=> 𝑀 =
1
2
𝐿 𝑒𝑞 − 𝐿 𝑓 − 𝐿 𝑚

26. The maximum value of the mutual inductance occurs when the axes of the moving and
fixed coils are aligned with θ = 180º, as this position gives the maximum flux linkage
between coils.
When θ = 0º, M = −𝑀 𝑚𝑎𝑥 . If the plane of the moving coil is at an angle θ with the
direction of B that produced by the fixed coil, then the mutual inductance M is expressed
by
M = −𝑀 𝑚𝑎𝑥 𝑐𝑜𝑠𝜃
• For DC operations, 𝑖 𝑓 = 𝐼𝑓 & 𝑖 𝑚 = 𝐼 𝑚
𝑇𝑑 = 𝐼 𝑚 𝐼𝑓
𝑑𝑀
𝑑𝜃
= 𝐼 𝑚 𝐼𝑓 𝑀 𝑚𝑎𝑥 𝑠𝑖𝑛𝜃
If the control is due to spiral springs, the controlling torque is proportional to the angle of
deflection θ.
Controlling torque : 𝑇𝑐 = 𝑘 𝑠 𝜃
At steady deflection, 𝑇𝑑=𝑇𝑐
𝐼 𝑚 𝐼𝑓
𝑑𝑀
𝑑𝜃
= 𝑘 𝑠 𝜃
=> 𝜃 =
𝐼 𝑚 𝐼 𝑓
𝑘 𝑠
(
𝑑𝑀
𝑑𝜃
)

27. For AC operations,

28. Observations
• Thus the deflection is decided by the product of RMS values of
two currents, cosine of the phase angle (power factor) and rate of
change of mutual inductance.
• For DC use, the deflection is proportional to square of current and
the scale is non-uniform and crowded at the ends. For AC use the
instantaneous torque is proportional to the square of the
instantaneous current. The i2 is positive and as current varies, the
deflecting torque also varies.
• But moving system, due to inertia cannot follow rapid variations
and thus finally meter shows the average torque.

29. • Free from hysteresis & eddy current loss. (Due to air core)
• Can be used for both AC & DC.
• Low power consumption & light weight.
• Very accurate instruments when RMS value of voltage is
required.
Advantages
• Increased frictional losses & low sensitivity.
• Non linear scale.
• Weak magnetic field.
• Sensitive to overload and mechanical impacts
Disadvantages
• Stray magnetic field errors
• Temperature errors
• Frequency errors
• Eddy current errors (Eddy current interacts with instrumental
current to change the deflecting torque)
Errors

30. 1.4 RECTIFIER VOLTMETER
• Rectifier type voltmeter measures the AC voltage with the help of
rectifying elements and permanent magnet moving coil type of
instruments.
• Employs a rectifier element, which converts AC to a unidirectional
DC and then uses a meter responsive to DC to indicate the value of
rectified AC.
• The indicating instrument is PMMC instrument, which uses a
d’Arsonval movement.
• This method is very attractive since PMMC instruments have a
higher sensitivity than the electrodynamometer or the moving iron
instruments.

31. • It employs a rectifier element (Copper oxide or a Selenium cell,
Germanium or Silicon diode) which converts AC to a
unidirectional DC.
• The ‘Ge’ or ‘Si’ diodes are used as the rectifying elements due to
high ‘Peak Inverse Voltage’.
• A rectifier type element is primarily used as a voltmeter.
• The sensitivity of the instrument lies in the range of 1000 ohm/V
to 2000ohm/V.
• Suited for measurement on communication circuits & for all
other light current work where the ‘V’ is low and ‘R’ is high.
• Multiplier resistance ‘𝑅 𝑠’ is used to limit the value of current to
stop it from exceeding the current rating of PMMC.
• In practice, two types of rectifiers can be used:
1. Half Wave Rectifier
2. Full Wave Rectifier

32. FIGURE: Construction of a Full wave Rectifier type voltmeter
FIGURE: Working of a Rectifier type voltmeter using Half wave bridge rectifiers

33. 1.4.1 Half Wave Rectifier Circuit
The circuit for a half wave rectifier is:
Suppose the meter resistance is 𝑅 𝑚 and that of multiplier is 𝑅 𝑠. Neglect the forward
resistance of the diode. When a DC voltage 𝑉𝑑𝑐=V is applied to the circuit, the current
through the meter is 𝐼 𝑚 =
𝑉
𝑅 𝑚+𝑅 𝑠
This current produces a full scale deflection. When the AC sinusoidal voltage is
applied, V= 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 = 2𝑉𝑠𝑖𝑛𝜔𝑡
Where, 𝑉𝑚 is peak value of AC voltage & ‘V’ is the RMS value of AC voltage.

34. • This voltage gets rectified and a unidirectional pulsating voltage is
produced at the output of rectifier. The pulsating voltage produces the
pulsating current & hence a pulsating torque.
• Because of the inertia of moving parts, PMMC indicates a deflection
average value of applied voltage.
• The average value of voltage is: 𝑉𝑎𝑣 =
1
2Π 0
Π
𝑉𝑚 𝑠𝑖𝑛𝜔𝑡𝑑 𝜔𝑡 =
1
Π
𝑉𝑚 = 0.318 × 2𝑉 = 0.45𝑉
• Therefore, the deflection produced is 0.45 times that produced with DC
voltage of equal magnitude.
• Hence, the sensitivity of a Half wave Rectifier instrument with AC is
0.45 times its sensitivity with DC.

35. 1.4.2 Full Wave Rectifier Circuit
The circuit of a voltmeter using a Full Wave Rectifier is:
As the average voltage developed in case of Full Wave Rectifier is twice that in Half
Wave Rectifier.
𝑉𝑎𝑣 =
1
Π
0
Π
𝑉𝑚 𝑠𝑖𝑛𝜔𝑡𝑑 𝜔𝑡 =
2
Π
𝑉𝑚 = 0.636 × 2𝑉 = 0.9𝑉
Hence, the deflection with AC is 0.9 times that with DC for the same value of voltage, V.

36. • Since the current & voltages are expressed in RMS
values, the meter scales are calibrated in terms of RMS
values of a sinusoidal function although the meter
responds to average value of current.

37. Extension of Range of Rectifier
Type Instruments as Voltmeters
• FORMULA+DERIVATION+NUMERICAL

38. • Accuracy is about 5% under normal operating conditions
• The frequency of the range of operation can be extended to a large value
• Uniform scale on the meter
• Low operating value of voltage
Advantages
• The scale is calibrated in terms of RMS value of voltage
• The resistance of the rectifier bridge circuit is neglected during
calculations which can lead to a small amount of error
• The bridge has imperfect capacitance and hence bypasses the high
frequency currents
• The sensitivity is low in case of AC input voltage
Disadvantages
• Effect of Waveform
• Effect of Rectifier Resistance
• Effect of Temperature changes
• Difference in sensitivity for AC & DC operations
Factors
Affecting
Performance

39. 1.5 INDUCTION TYPE VOLTMETER
• Such instruments are suitable for ac measurements only in these
instruments the deflecting torque is produced by the eddy currents
induced in an aluminium or copper disc or drum by the flux created by
an electro-magnet.
• An induction meter can be of two types: Single Phase and Three
Phase.
• The main advantages of such instruments are that
(i) a full scale deflection can be obtained giving long and open scale
(ii) the effect of stray magnetic field is small
(iii) damping is easier and effective.

40. FIGURE: Induction type voltmeter.

41. • Induction type voltmeter consists of two laminate
electromagnets known as shunt electromagnet and series
electromagnet respectively.
• Shunt magnet is excited by the current proportional to the
voltage across load flowing through the pressure coil and
series magnet is excited by the load current flowing
through the current coil.
• A thin disc made of Cu or Al, pivoted at its centre, is
placed between the shunt and series magnets so that it cuts
the flux from both of the magnets.

42. • The deflection torque is produced by interaction of eddy
current induced in the disc and the inducing flux in order to
cause the resultant flux in shunt magnet to lag in phase by
exactly 90° behind the applied voltage.
• One or more copper rings, known as copper shading bond are
provided on one limb at the shunt magnet.
• Shading bands are wounded so as to make angle between the
flux and applied voltage equal to 90 degrees.
• The pressure coil circuit of induction type instrument is made
as inductive as possible so that the flux of the shunt magnet
may lag by 90° behind the applied voltage.
• The current flowing in the pressure coil is ‘Ip’ which lags
behind voltage by an angle of 90 degrees. This current
produces flux F.
• Moving System: Floating Disc.

43. • The special disc, actually it consists of small magnets on both upper and
lower surfaces.
The upper magnet is attracted to an electromagnet in upper bearing
while the lower surface magnet also attracts towards the lower bearing
magnet, hence due to these opposite forces the light rotating aluminium
disc floats. This arrangement reduces friction to a greater extent.
• The braking system is generally provided by a small permanent magnet
placed at the corner of Aluminium disc.
• Numbers marked on the meter are proportion to the revolutions made by
the aluminium disc, the main function of this system is to record the
number of revolutions made by the aluminium disc.
• The load current which is shown is flowing through the current coil
produces flux in the aluminium disc, and due this alternating flux there
on the metallic disc, an eddy current is produced which interacts with
the flux & results in production of torque. As we have two poles, thus
two torques are produced which are opposite to each other. Hence from
the theory of induction meter that we have discussed already above the
net torque is the difference of the two torques.

44. • Inexpensive as compared to MI instruments.
• Retain their accuracy for wide rang of
temperature and load.
Advantages
• The greater deflection causes more stresses in
the control springs.
• Variation in supply frequency may cause
serious errors unless compensating device is
employed
• Consume more power
Disadvantages

45. 2.1 AC Voltmeters
• Primarily used for AC measurements.
• There are modifications made on the existing voltmeters
to make them adaptable to AC measurements.
• When a sensitive meter movement needs to be re-ranged
to function as an AC voltmeter, series-connected
“multiplier” resistors and/or resistive voltage dividers
may be employed just as in DC meter design:

46. • Capacitors may be used instead of resistors, though, to
make voltmeter divider circuits. This strategy has the
advantage of being non-dissipative (no true power
consumed and no heat produced):

47. The value of Multiplier resistance can be found out using the expression:
𝑅 𝑠 + 𝑅 𝑚 = 𝑆 × 𝑉𝑟𝑎𝑛𝑔𝑒
Where, 𝑅 𝑚 is the meter resistance, 𝑅 𝑠 is the series multiplier resistance ,
𝑉𝑟𝑎𝑛𝑔𝑒 is the range of the voltmeter used & ‘S’ is the sensitivity of the meter
used.
Thus, 𝑅 𝑠 = 𝑆 × 𝑉𝑟𝑎𝑛𝑔𝑒 − 𝑅 𝑚
SOLVED EXAMPLE:
Find the value of multiplier resistance on a 50V range voltmeter that used a
500uA d’Arsnoval with the internal resistance as 1kohm.
SOLUTION: Given, 𝑉𝑟𝑎𝑛𝑔𝑒 = 50 𝑉
𝑆 =
1
𝐼𝑓𝑠
= 2
𝑘𝑜ℎ𝑚
𝑉
Thus, 𝑅 𝑠 = 𝑆 × 𝑉𝑟𝑎𝑛𝑔𝑒 − 𝑅 𝑚
=99 kohm

48. DC Voltmeters
• The types of voltmeters used for DC measurements only.
• They are broadly of two kinds: Direct coupled & Chopper
type.
• The basic d’Arsonval meter can be converted to a dc
voltmeter by connecting a multiplier ‘Rs’ in series with it.
(As shown in the figure below)
• The purpose of the multiplier is to extend the range of the
meter and to limit the current through the d’Arsonval
meter to the maximum full-scale deflection current.

49. Classification of AC & DC
Voltmeters
METER TYPE SUITABILITY
PMMC D.C. only
Moving Iron D.C & A.C
Electrodynamometer D.C & A.C
Rectifier D.C & A.C
Induction A.C only

50. Digital Voltmeters
• Digital voltmeters display the value of AC or DC voltage
being measured directly as discrete numerical instead of a
pointer deflection on a continuous scale as in analog
instruments.
• Analog voltmeters generally contain a dial with a needle
moving over it and hence displaying the value of the
same.
• They are also called DVMs.

51. • Read out of DVMs easily eliminates the observational
errors.
• Error on the account of parallax and approximation is
completely eliminated.
• Quick reading is possible.
• Output can be fed to memory devices for storage and
future computations.
• Versatile & accurate.
• Compact & cheap.
• Low power requirements.
• Portability is increased.
Advantages

52. Working
FIGURE: The circuit schematic of a DVM.
Here, the input signal signifies the voltage to be measured. Pulse generator is actually a
voltage source. It uses digital, analog or both techniques to generate a rectangular pulse.
The AND gate gives high output only when both the inputs are high. When a train pulse is
fed to it along with rectangular pulse, it provides us an output having train pulses with
duration as same as the rectangular pulse from the pulse generator. The ‘Decimal Display’
counts the numbers of impulses and hence the duration and display the value of voltage on
LED or LCD display after calibrating it.

53. • Unknown voltage signal is fed to the pulse generator which generates a
pulse whose width is proportional to the input signal.
• Output of pulse generator is fed to one leg of the AND gate.
• The input signal to the other leg of the AND gate is a train of pulses.
• Output of AND gate is positive triggered train of duration same as the
width of the pulse generated by the pulse generator.
• This positive triggered train is fed to the inverter which converts it into a
negative triggered train.
• Output of the inverter is fed to a counter which counts the number of
triggers in the duration which is proportional to the input signal i.e.
voltage under measurement.
• Thus, counter can be calibrated to indicate voltage in volts directly.

54. VTVMs & FET-VMs
• Were considered most useful instruments for measuring of
AC & DC voltages in the past.
• Even today, at times, VTVMs are used in laboratories.
FIGURE: A Vacuum Tube Voltmeter

55. • In practical, the VTVMs fall into the following category:
1. Diode Type
2. Single Triode Type
3. Balanced Triode Type
4. Rectifiers Amplifier Type
5. Amplifier Rectifier Type
• It is a combination of thermionic vacuum tube (electrons get
ejected from the electrodes when current passes through it) and
an indicating meter for the purpose of measuring voltage.
• The vacuum tube is used for its rectifying as well as amplifying
properties.
• It has the advantage of high gain and wide frequency coverage
in electronic communication systems.
• Today these circuits use a solid-state amplifier using field-effect
transistors, hence FET-VM, and appear in handheld digital
multimeters as well as in bench and laboratory instruments.

56. Loading Effect in a Voltmeter
• When a voltmeter is used to measure the voltage across a
circuit component, the voltmeter circuit itself is in parallel with
the circuit component. Since the parallel combination of two
resistors is less than either resistor alone, the resistor seen by
the source is less with the voltmeter connector than without.
• Therefore, the voltage across the component is less whenever
the voltmeter is connected. The decrease in voltage maybe
negligible or appreciable, depending on the Sensitivity of the
voltmeter being used. This effect is called voltmeter loading
and the resulting error is called loading error.

57. Accuracy
• Definition: How close the indicated value is to the true value of
the measured signal.
• Accuracy Criteria for Analog Voltmeters:
2/3rd of full scale deflection< Reading < Full scale deflection
• An analog voltmeter with |4|% accuracy is set to 0-100 V range.
Based on accuracy, its pointer can be (100X 0.04=4 V) below or
above the true reading. Say, the true, measured value is 87 V,
then, the meter might read between 83 V to 91 V.
• But for a true value of 10 V measured on 100 V scale of same
voltmeter, the voltmeter can read between 6V to 14 V or a |40| %
of actual reading. Hence, we select the analog meter range that
places the pointer between 2/3rd of full scale and full scale.

58. Range
• Practical laboratory voltmeters have the range of 1000-
3000 V.
• Most commercially manufactured voltmeters have several
scales, increasing in the power of 10; for eg: 0-1 V, 0-10
V, 0-100 V and 0-1000 V.

59. Multi-Range Voltmeter
• How?
Connecting a number of resistances along with a range
switch to provide greater number of workable ranges.
• Why?
Different full scale voltage ranges maybe obtained
• 2 Methods:
1. Individual Multiplier
2. Potential Divider Arrangement

60. 1. Individual Multiplier
• When different values of multiplier resistors are connected in
series with the meter, different voltage ranges can be obtained.
• The number of multipliers introduced equals to the number of
ranges required.

61. FIGURE: Multi-range Voltmeter Schematic in Express SCH.
Range Selector Switch
Meter

62. In the figure, The multiplier resistances 𝑅 𝑠1, 𝑅 𝑠2, 𝑅 𝑠3 &𝑅 𝑠4 can be
connected in series with the meter by a range selector switch. Let
the ranges desired be 𝑉1, 𝑉2, 𝑉3 &𝑉4.
Then, the values of corresponding multiplier resistances can be
obtained as:
𝑅 𝑠1 = (𝑚1 − 1)𝑅 𝑚, 𝑅 𝑠2 = 𝑚2 − 1 𝑅 𝑚
𝑅 𝑠3 = (𝑚3 − 1)𝑅 𝑚 & 𝑅 𝑠4 = (𝑚4 − 1)𝑅 𝑚
Where, 𝑚1 =
𝑉1
𝑣
, 𝑚2 =
𝑉2
𝑣
, 𝑚3 =
𝑉3
𝑣
& 𝑚4 =
𝑉4
𝑣
(See Appendix B for equation derivation)

63. 2. POTENTIAL DIVIDER
ARRANGEMENT
FIGURE: Schematic of Multi-range Voltmeter using potential divider in
Express SCH.

64. The connections are made at the junctions of resistances
𝑅1, 𝑅2, 𝑅3 & 𝑅4 in series to obtain the voltages 𝑉1, 𝑉2, 𝑉3 & 𝑉4.
The series resistances for the voltage ranges 𝑉1, 𝑉2, 𝑉3 & 𝑉4 can
be computed as follows:
𝑅1 =
𝑉1
𝐼 𝑚
− 𝑅 𝑚 =
𝑉1
𝑣
𝑅 𝑚
− 𝑅 𝑚 = 𝑚1 𝑅 𝑚 − 𝑅 𝑚=(𝑚1−1)𝑅 𝑚
Now, 𝑅2 =
𝑉2
𝐼 𝑚
− 𝑅 𝑚 − 𝑅1 =
𝑉2
𝑣
𝑅 𝑚
− 𝑅 𝑚 − (𝑚1−1)𝑅 𝑚
=𝑚2 𝑅 𝑚 − 𝑅 𝑚 − 𝑚1 − 1 𝑅 𝑚 = 𝑚2 − 𝑚1 𝑅 𝑚
Similarly, 𝑅3 = 𝑚3 − 𝑚2 𝑅 𝑚 & 𝑅4 = 𝑚4 − 𝑚3 𝑅 𝑚

65. SAMPLE QUESTION:
A basic d’Arsenoval meter movement with an internal resistance 𝑅 𝑚 = 100𝛺 and a
full scale current of 𝐼 𝑚 = 1 𝑚𝐴, is to be converted into a multi-range DC voltmeter
with ranges of 0-10V, 0-50 V, 0-250 V and 0-500V. Find the values of various
resistances using the potential divider arrangement.
SOLUTION:
Voltage across the meter movement, v=ImRm = 1 × 100 = 100mV
The voltage multiplying factors are:
m1 =
10
100 × 10−3
= 100, m2 =
50
100 × 10−3
= 500
m3 =
250
100 × 10−3
= 2500, m4 =
500
100 × 10−3
= 5000
Thus, the values of various resistances can be obtained as:
R1=(m1−1)Rm= 100 − 1 × 100 = 9900Ω
R2=(m2−m1)Rm= 500 − 100 × 100 = 40kΩ
Similarly, R3 = 200kΩ & R4 = 250kΩ

66. Transformer
• Function: Transforms the voltage level.
• Types of Transformer:
->Current Transformer
->Potential Transformer
• Current Transformer: Used when the current of an AC
circuit exceeds safe current of measuring instrument.
• Potential Transformer: When voltage of the circuit
exceeds 750 V.

67. • Three main parts of a transformer:
1. Primary Winding
2. Secondary Winding
3. Magnetic core of Transformer
FIGURE: Construction of a Transformer (Single Phase)

68. • A device which converts high AC to low AC and vice versa.
• Principle of operation: Mutual Induction of two coils.
• When the current in the primary coil is changed, the flux linked with
the secondary coil changes.
• AC passed through primary produces continuously changing flux
through the coil.
• Since the flux changes in amplitude and direction, the flux linked to
the coil also changes.
• Due to Faraday’s Law of EMI, an EMF is induced in secondary coil.
• Types:
1. Step-up
2. Step-Down
• The turns ratio can be described as:
•
𝑁 𝑃
𝑁 𝑆
=
𝑉 𝑃
𝑉 𝑆
= n = Turns Ratio
( Assuming an ideal transformer and the phase angles: ΦP ≡ ΦS )

69. SOLVED EXAMPLE:
A voltage transformer has 1500 turns of wire on its primary
coil and 500 turns of wire for its secondary coil. If 240 volts
RMS is applied to the primary winding of the transformer,
what will be the resulting secondary no load voltage.
SOLUTION:
The turns ratio of the transformer will be =
𝑁 𝑃
𝑁 𝑆
= 3: 1
Thus,
𝑁 𝑃
𝑁 𝑆
=
𝑉 𝑃
𝑉 𝑆
=>
3
1
=
240
𝑉 𝑆
=> 𝑉𝑆 =
240
3
= 80 𝑉𝑜𝑙𝑡𝑠

70. Instrument Transformer
• Transformers used in conjugation with instruments for
measurement.
• Can’t be used for DC measurements
• Only used in AC systems for measurement of basic
quantities like current, voltage, power, energy etc.

71. Current Transformers

72. • Used in conjugation with current measuring device.
• Primary winding is designed to be connected in series
with the line.
• Impedance of primary coil is very low.
• The current in secondary coil has to be reduced.
•
𝑁 𝑃
𝑁 𝑆
=
𝐼 𝑆
𝐼 𝑃

73. • RATED BURDEN: product of voltage and current on
secondary side when current transformer supplies to the
instrument.
• Operation is different than that of Power Transformer.
• They are air cooled but when used in high voltage lines,
its necessary to provide oil cooling.

74. Potential Transformer
• Used for measurement of high voltage by means of low
range voltmeter.
• They are step down in nature as they are meant to reduce
the voltage to a reasonable operating value.

75. APPENDIX ‘A’
Eddy Current
• Eddy currents are loops of electrical current induced
within conductors by changing magnetic field.
• Faraday’s Law of Induction: “Whenever there is a relative
motion between conductor(coil) and a magnetic field, the
flux linkage with a coil changes and this change in flux
induces a voltage across a coil.
• Eddy current produces a field that opposes the magnetic
field that created it. (Lenz’s Law)

77. APPENDIX ‘B’
• The value of the multiplier, required to extend the range of the
voltage, is calculated as under:
• Let 𝐼 𝑚 = 𝐼𝑓𝑠 = 𝑓𝑢𝑙𝑙 𝑠𝑐𝑎𝑙𝑒 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑒𝑡𝑒𝑟,
𝑅 𝑚 𝑏𝑒 𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑚𝑒𝑡𝑒𝑟 𝑚𝑜𝑣𝑒𝑚𝑒𝑛𝑡 & 𝑅 𝑠 𝑏𝑒
𝑡ℎ𝑒 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒.
• 𝑙𝑒𝑡 ′
𝑣′ 𝑏𝑒 𝑡ℎ𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑎𝑐𝑟𝑜𝑠𝑠 𝑚𝑒𝑡𝑒𝑟 𝑚𝑜𝑣𝑒𝑚𝑒𝑛𝑡 𝑓𝑜𝑟 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝐼 𝑚 & ′
𝑉′ 𝑏𝑒 𝑡ℎ𝑒 𝑓𝑢𝑙𝑙 𝑟𝑎𝑛𝑔𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑠𝑡𝑟𝑢𝑚𝑒𝑛𝑡.

78. • Thus, for the circuit, 𝑣 = 𝐼 𝑚 𝑅 𝑚
• V=𝐼 𝑚(𝑅 𝑚 + 𝑅 𝑠)
• Thus, 𝑅 𝑠 =
𝑉−𝐼 𝑚 𝑅 𝑚
𝐼 𝑚
=
𝑉
𝐼 𝑚
− 𝑅 𝑚
• Introducing ‘𝑚 =
𝑉
𝑣
’ as the multiplying factor, the result
can also be expressed in terms of ‘m’ :
• 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟, 𝑅 𝑠 = (𝑚 − 1)𝑅 𝑚
• Theoretically, to increase the voltage range to 10 times
the instrument range, 𝑅 𝑠 = 9𝑅 𝑚

79. BIBLIOGRAPHY
• A Course in Electrical & Electronic Measurements and Instrumentation – A.K.
Sawhney
• Electronic Instrumentation- H.S. Khalsi
• www.eleprocus.com
• www.electrical4u.com
• www.electronics-tutorials.ws
• www.4.bp.blogspot.com
• www.ipdgroup.com
• www.yourelectrichome.blogspot.in
• www.nptel.ac.in
• www.allaboutcircuits.com/
• www.ohio.edu
• https://sites.google/sites/gdguinstru