EMI Presentation

Topics Covered:1. Voltmeter2. Transformer

PRESENTED BY: DIKSHA PRAKASH

140020204002

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.

• Voltmeter as an electronic meter can be characterized by a three port network:

ELECTRONIC METERINPUT SIGNAL OUTPUT SIGNAL

POWER SUPPLY

Types of Voltmeter

BASIS: 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

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.

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

FIGURE: PMMC Voltmeter’s Construction & Working

• 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.

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

FIGURE: Assembled 3D Arrangement

DEFLECTING TORQUE EQUATIONThe 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 IThe instrument is spring controlled so that, Tc α θThe 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.

• 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

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) radAt equilibrium, Tc=Td or (NBldI) =K Θ =

= 136

1.2 MOVING IRON VOLTMETER• Mainly used for AC measurements & can also be used for DC measurements.

• Two types of MI instruments:1. Attraction Type2. 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.

1.2.1 ATTRACTION TYPE

FIGURE: Construction of an Attraction Type MI Voltmeter

DEFLECTING TORQUE EQUATIONThe force F, pulling the soft -iron piece towards the coil is directly proportional to theField 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 = μiIf 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 θIn the steady position of deflection, Td = Tc

                                             θ α mean of i2 over a cycle                                   Thus, θ α I2

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 types1. Radial vane type: - vanes are radial strips of iron.2. Co-axial vane type:-vanes are sections of coaxial cylinders.

IMPORTANT OBSERVATIONThe 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).

TABLE: MI Instruments vs. PMMC Instruments

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 ‘

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).

Construction

FIGURE: Electrodynamometer (or Dynamometer) type Voltmeter

• 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.

FIGURE: Simplified circuit of Electrodynamometer Voltmeter

Expression for developed TorqueConsider the currents in fixed and moving coil as respectively. Let the fixed and moving coil have self-inductances 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:+M Thus, the equation for the torque developed can be written as: =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: =>

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, . 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

• For DC operations,

If the control is due to spiral springs, the controlling torque is proportional to the angle of deflection θ. Controlling torque : At steady deflection, =

=> ()

For AC operations,

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.

•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

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.

• 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 ‘’ 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 Rectifier2. Full Wave Rectifier

FIGURE: Construction of a Full wave Rectifier type voltmeter

FIGURE: Working of a Rectifier type voltmeter using Half wave bridge rectifiers

1.4.1 Half Wave Rectifier CircuitThe circuit for a half wave rectifier is:

Suppose the meter resistance is and that of multiplier is Neglect the forward resistance of the diode. When a DC voltage =V is applied to the circuit, the current through the meter is This current produces a full scale deflection. When the AC sinusoidal voltage is applied, V= Where, is peak value of AC voltage & ‘V’ is the RMS value of AC voltage.

• 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:

• 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.

1.4.2 Full Wave Rectifier CircuitThe 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.

Hence, the deflection with AC is 0.9 times that with DC for the same value of voltage, V.

• 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.

Extension of Range of Rectifier Type Instruments as Voltmeters

• FORMULA+DERIVATION+NUMERICAL

•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

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.

FIGURE: Induction type voltmeter.

• 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.

• 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.

• 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.

•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

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:

• 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):

The value of Multiplier resistance can be found out using the expression:

Where, is the meter resistance, is the series multiplier resistance , is the range of the voltmeter used & ‘S’ is the sensitivity of the meter used.Thus,

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,

Thus, =99 kohm

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.

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

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.

•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

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.

• 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.

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

• In practical, the VTVMs fall into the following category:1. Diode Type2. Single Triode Type3. Balanced Triode Type4. Rectifiers Amplifier Type5. 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.

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.

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.

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.

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 Multiplier2. Potential Divider Arrangement

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.

FIGURE: Multi-range Voltmeter Schematic in Express SCH.

Range Selector Switch

Meter

In the figure, The multiplier resistances can be connected in series with the meter by a range selector switch. Let the ranges desired be Then, the values of corresponding multiplier resistances can be obtained as:, & Where, &

(See Appendix B for equation derivation)

2. POTENTIAL DIVIDER ARRANGEMENT

FIGURE: Schematic of Multi-range Voltmeter using potential divider in Express SCH.

The connections are made at the junctions of resistances in series to obtain the voltages .The series resistances for the voltage ranges can be computed as follows:=Now,

=

Similarly, &

SAMPLE QUESTION:A basic d’Arsenoval meter movement with an internal resistance and a full scale current of 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=The voltage multiplying factors are:

Thus, the values of various resistances can be obtained as:==Similarly,

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.

• Three main parts of a transformer:1. Primary Winding 2. Secondary Winding3. Magnetic core of Transformer

FIGURE: Construction of a Transformer (Single Phase)

• 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-up2. Step-Down

• The turns ratio can be described as:•

( Assuming an ideal transformer and the phase angles:  ΦP ≡ ΦS )

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 = Thus, => => =

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.

Current Transformers

• 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.

• 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.

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.

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)

APPENDIX ‘B’• The value of the multiplier, required to extend the range of the

voltage, is calculated as under:• Let

• Thus, for the circuit, • V=(• Thus, • Introducing ‘’ as the multiplying factor, the result can

also be expressed in terms of ‘m’ :

• Theoretically, to increase the voltage range to 10 times the instrument range,

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