Induction type instruments - Engineering notes

Induction type instruments:

These instruments are based on the principle of induction motor.

Principle of Induction type instruments:

When a drum or disc of a non - magnetic conducting material is placed in a rotating magnetic field, eddycurrents are induced in it. The reaction between the rotating flux and the eddy current produced by it creates a torque which rotates the disc or drum. The rotating flux is produced by the current or voltage to be measured. The eddy current again is proportional to the flux.

The single phase supply is converted into two phases in the instrument, that is done by split phase or shaded pole arrangement. Accordingly induction instruments are classified as

1. Split phase type

2. Shaded pole type

1. Split phase type induction instrument:

Construction of Split phase type induction instrument:

This is also called ferraris type instrument and is shown in the fig. It consists of a laminated magnet with the pairs of poles at right angles to each other.  Coils are wound on the poles, the opposite poles being connected in series. The coils on the two pairs of poles are connected in parallel. One set of coil is connected through an inductance and another with a high resistance to create a phase difference of 90 degrees. The input to both the coils is the current to be measured. In the center of the yoke and coil is an aluminium drum. Inside the drum there is cylindrical laminated iron core to strengthen the magnetic field.

Split phase induction instrument

Working of Split phase type induction instrument:

When the instrument is connected in the circuit diagram flows through the coils. A rotating magnetic field is produced. This field induces eddy currents in the drum and a torque is produced by the reaction of magnetic field and current. This torque deflects the pointer attached to the drum. Controlling torque is produced by spring.

Deflecting torque of Split phase type induction instrument:

deflecting torque produced is given by

T  proportional   IR. IL. f cos a  sin b  / Z

For an ammeter,  T  proportional   I2. cos a. sin b  / Z

For an voltmeter,  T  proportional  V^2  cos a. sin b  / Z

Where IR  = current through resistor

IL = current through inductor

f = supply frequency

Z = impedance of eddy current path

a = phase angle between voltage and current in resistor

b = phase angle between currents in resistor and inductor

a is almost zero and R is very much larger than reactive part of eddy paths. Hence

T  proportional   I^2 . sin b  / R

Obviously  b should be as high as possible for high torque.

2. Shaded pole type induction instrument:

Construction of Shaded pole type induction instrument:

Shaded pole type instrument is as shown in the fig. A band of copper is placed in pole faces, this makes the two fluxes of shaded and unshaded portions differ in phase by 90 degrees. A metallic disc rotates between the pole faces. The damping is provided by another magnet as shown in the fig.

Shaded pole type induction instrument

Working of Shaded pole type induction instrument:

The current flowing through the exciting coil sets up flux. Eddy currents are induced in the copper band. Flux of the eddy current opposes the flux in the magnetic core and a two phase flux same as ferraris type instrument.

Permanent magnet moving coil instruments - Engineering notes

Permanent magnet moving coil instruments:

These instruments are employed either as ammeters or voltmeters and can be used for d.c work only.

Principle of  Permanent magnet moving coil instruments:

This type of instrument is based on the principle that when a current carrying conductor is placed in a magnetic field, mechanical force acts on the conductor. The coil placed in magnetic field and carrying operating current is attached to the moving system. With the movement of the coil the pointer moves over the scale.

Construction of Permanent magnet moving coil instruments:

It consists of a powerful permanent magnet with soft iron pieces and light rectangular coil of many turns of fine wire wound on aluminium former inside which is an iron core as shown in fig. The purpose of coil is to make the field uniform. The coil is mounted on the spindle and acts as the moving element. The current is led into and out of the coil by means of the to control hair springs, one above and the other below the coil. The springs also provides the controlling torque. Eddy current damping is provided by aluminium former.

Permanent magnet moving coil instrument

Working of Permanent magnet moving coil instruments:

When the instrument is connected in the circuit, operating current flows through the coil. This current coil is placed in the magnetic field produced by the permanent magnet and therefore, mechanical force acts on the coil. As the coil attached to the moving system, the pointer moves over the scale.

It maybe noted that if current direction is reversed, the torque will also be reversed since the direction of the field of permanent magnet is same. Hence, the pointer will move in the opposite direction, i.e it will go on the wrong side of zero. In other words, these instruments work only when current in the circuit is passed in a definite direction i.e. for d.c circuit only.

It is worthwhile to mention here that such instruments are called permanent magnet moving coil instruments because a coil moves in the field of a permanent magnet.

Deflecting torque of Permanent magnet moving coil instruments:

When current is passed through the coil, a deflection torque is produced due to the reaction between permanent magnetic field and the magnetic field of the coil as shown in the fig.

Let B = flux density in the air gap between the magnetic poles and iron core.

l = active length of the coil side in meters.

N = number of turns of coil.

If a current of i amperes flows in the coil in the direction shown, then force F acting on each coil side is given by

F = BI / N newtons

Td = Force * perpendicular distance

= F * 2r newton - meters

where r is the distance of coil side from the axis of rotation in meters

Td = NBIl * 2r newton - meters

If A ( = l * 2r) is the surface area of the coil, then

Td = NBIA newton - meters

Deflection torque = Ampere turns on coil (NI) * Area of coil (A) * flux density (B)

Td  proportional  I

Since the control by springs, therefore controlling torque is proportional to the angle of deflection i.e

Tc  proportional  I

The pointer will come to rest at a position when,

Td = Tc

Deflection  proportional  I

Thus, the deflection is directly proportional to the operating current. Therefore, such instruments have uniform scale.

Advantages of Permanent magnet moving coil instruments:

1. uniform scale.

2. Very effective  eddy current damping

3. Power consumption is low.

4. No hysteresis loss

5. As working field is very strong, therefore, such instruments are not affected stray fields.

6. Such instruments require small operating current.

7. Very accurate and reliable.

Disadvantages of Permanent magnet moving coil instruments:

1. Such instruments cannot be used for a.c measurements.

2. Costlier as compared to moving iron instruments.

3. Some errors are caused due to the ageing of control springs and the permanent magnet.

Dynamometer type instruments - Engineering notes

Dynamometer type instruments:

These instruments are the modified form of permanent magnet moving coils type. Here operating field is produced by a permanent but by another fixed coil. The moving system and the control system are similar to those of permanent magnet type. Such instruments can be used for both a.c and d.c circuits. They can be used as ammeters and voltmeters but are generally used as wattmeters.

Principle of Dynamometer type instruments:

These instruments are based on that principle the mechanical force exists between the current carrying conductors.

Construction of Dynamometer type instruments:

A dynamometer type instrument as shown in fig essentially consists of a fixed coil and a moving coil. The fixed coil is split into two  equal parts which are placed close together and parallel to each other. The moving coil is pivoted in between the two fixed coils. The fixed and moving coils may be excited separately or they may be connected in series depending upon the use to which the measurement is put. The moving coil is attached to the moving system so that under the action of deflecting torque, the pointer moves over the scale.

Dynamometer type instrument

The controlling torque is provided by two springs which also serve the additional purpose of leading the current into and out of the moving coil. Air friction damping is provided in such instruments.

Working of Dynamometer type instruments:

When instrument is connected in the circuit, operating currents flow through the coils. Due to this, mechanical force exists between the coils. The result is that the moving coil moves the pointer over the scale. The pointer comes to rest at a position where deflecting torque is equal to the controlling torque.

by reversing the current, the field due to fixed coils is reversed as well as the current in the moving coil, so that the direction of deflecting torque remains unchanged. Therefore, such instruments can be used for both d.c and a.c measurements.

Deflecting torque of Dynamometer type instruments:

Let 

If = current through fixed coil

Im = current through moving coil

Since If = Im because the fixed and coils are in series,

Td = I^2

Since the control is by springs, therefore, 

controlling torque is proportional to the angle of deflection

Tc  proportional  deflection 

The pointer will come to rest at a position when Td = Tc

we get deflection  proportional  I^2

It is clear that deflection of the pointer is directly proportional to the square of the operating current. Hence, the scales of these instruments is non - uniform being crowded in their lower parts and spread out at the top.

Advantages of Dynamometer type instruments:

1. These instruments can be used for both a.c and d.c measurements.

2. Such instruments are free from hysteresis and eddy current errors.

Disadvantages of Dynamometer type instruments:

1. Since torque / weight ratio is small, therefore, such instruments have  frictional errors which reduce sensitivity.

2. Scale is not uniform.

3. A good amount of screening of the instruments are required to avoid the effect of stray fields.

4. These instruments are costlier than types and, therefore, they are rarely used as ammeters and voltmeters.

Moving iron instrument - Engineering notes

Moving iron instrument:

Moving iron instruments are of two types:

1. Attraction type Moving iron instrument

2. Repulsion type Moving iron instrument

Attraction type Moving iron instrument:

Principle of Attraction type Moving iron instrument:

These instruments are based on the principle that when an unmagnetised soft iron piece is placed in the magnetic field of a coil, then the piece is attracted towards the coil. The moving system of the instrument is attached to the soft iron piece and the operating current is passed through a coil placed near it. The operating current sets up magnetic field which attracts the iron piece and thus moves the pointer over the scale.

Construction of Attraction type Moving iron instrument:

It consists of a hollow cylindrical coil or solenoid which is kept fixed as shown in the fig. An oval shaped soft iron pieces is attached to the spindle in such a way that it can move in or out of the coil.The pointer is attached to the spindle so that it is deflected with the motion of the soft iron piece. The controlling torque on the moving system is provided by spring control method while damping is provided by air friction.

Attraction type Moving iron instrument

Working of Attraction type Moving iron instrument:

When the instrument is connected in the circuit, the operating current flows through the coil. The current sets up magnetic field in the coil. In other words, the coil behaves like a magnet and, therefore, it attracts the soft iron piece towards it. The result is that the pointer attached to the moving system moves from zero position.

If current in the coil is reversed, the direction of magnetic field also reverses and so does the magnetism produced in soft iron piece. Therefore, the direction of deflecting torque remains unchanged. It follows, therefore, that such instruments can be used for both D.C as well as A.C work.

Deflecting torque of Attraction type Moving iron instrument:

Field strength h produced by the coil.

Pole strength m developed by the piece

F  proportional   mH

F  proportional   H^2

Td  proportional  F  proportional  H^2

If permeability of iron is assumed constant then

H  proportional   I

Td  proportional  I^2

If the controlling torque is provided by the springs,

Tc  proportional   deflection

In the steady state position of deflection,

Td  =  Tc

Deflection   proportional   I^2

Deflection   proportional   Irms

Scale of such instruments is non-uniform, being crowded in the beginning. In order to make the scale of such instruments uniform, suitably shaped iron piece is used.

Repulsion type moving iron instruments:

Principle of Repulsion type moving iron instruments:

These instruments are based on the principle of repulsion between the two iron pieces similarly magnetized.

Construction of Repulsion type moving iron instruments:

It consists of a fixed cylindrical hallow coil which carries operating current. Inside the coil, there are two soft iron pieces or vanes, one of which is fixed and other is movable. The fixed iron piece is attached to the coil whereas the movable iron piece is attached to the pointer shaft. Under the action of deflecting torque, the pointer attached to the moving system moves over the scale. The controlling torque is produced by spring  control method and damping torque by air friction damping.

Working of Repulsion type moving iron instruments:

When the instrument is connected in the circuit, current flows through the coil. This current sets up magnetic field in the coil. The magnetic field magnetizes both iron pieces in the same direction i.e. both pieces become similar magnets and hence they repel each other. Due to this force of repulsion only movable iron piece moves as the other piece is fixed and cannot move. The result is that the pointer attached to the moving system moves from zero position.

Repulsion type moving iron instruments:

Deflecting torque of Repulsion type moving iron instruments:

The deflecting torque results due to the repulsion between the similarly magnetized iron pieces. If two pieces develop pole strengths m1 and m2 respectively, then,

Instantaneous deflecting torque  proportional to   repulsive force

proportional  m1.m2

Since pole strengths developed are proportional to H, therefore

Instantaneous deflecting torque, Td  proportional   H^2

Assuming constant permeability, h  proportional  current i through the coil

Td  proportional   i^2

Controlling torque provided by springs,  Tc  proportional  deflection

In the steady position of deflection,

Td  =  Tc

Deflection  proportional  i^2

proportional  I^2

Proportional  Irms

Since deflection is proportional to square of current through the coil, therefore, scale of such instruments in non-uniform being crowded in the beginning. However, scale of such instruments can be made uniform by using tongue shaped iron pieces.

Advantages of moving iron instruments:

1. These are cheap, robust and simple in construction.

2. The instruments can be used for both A.C as well as D.C circuits.

3. These instruments have high operating torque.

4. These instruments are reasonable accurate.

Disadvantages of moving iron instruments:

1. Such instruments have non-uniform scale.

2. These instruments are not very sensitive.

3. Errors are introduced due to changes in frequency in case of a.c measurements.

4. Higher power consumption.

Induction type wattmeter - Engineering notes

Induction type wattmeter:

The induction type wattmeter is used to measure a.c power only.

Principle of Induction type wattmeter:

The principle of operation of an induction wattmeter is same as that of induction ammeters and voltmeters i.e. induction principle. However, it differs from induction ammeter or voltmeter in so far that separate two coils are used to produced the rotating flux in place of one coil with phase split arrangement.

Construction of Induction type wattmeter:

The principle parts of an induction wattmeter is as shown in the fig below. It consists of two laminated electromagnets. One electromagnet, called shunt magnet is connected across supply and carries current proportional to the applied voltage. The coil of this magnet is made highly inductive so that the current in it lags behind the supply voltage by 90 degrees. The other electromagnet, called series magnet is connected in series with supply and carries the load current. The coil of this magnet is made highly non inductive so that the angle of lag or lead is determined fully by the load.

Induction type wattmeter

A thin aluminium disc mounted on the spindle is placed in between the two magnets so that it cuts the fluxes of both the magnets. The controlling torque is provided by spiral springs. The damping is electromagnet and is usually provided by a permanent magnet embracing the aluminium disc. Two or more closed copper rings, called shading rings are provide on the central limb of the shunt magnet. By adjusting the position of these rings, the shunt magnet flux can be made to lag behind supply voltage by exactly 90degrees.

Working of Induction type wattmeter:

When the wattmeter is connected in the circuit to measure a.c power, the shunt magnet carries current proportional to the supply voltage and the series magnet carries the load current. The two fluxes produced by the magnets induce eddy currents in the aluminium disc. The interaction between the fluxes and eddy currents produce the deflecting torque on the disc, causing the pointer connected to the moving system to move over the scale.

 

Vector diagram

Deflecting torque of Induction type wattmeter:

let V = Applied voltage

Ic = Load current carried by the series magnet

Iv = Current carries by the shunt magnet

cos a = Lagging power factor of the load

The vector diagram of this wattmeter is shown in the fig below. the current Iv in the shunt magnet lags the applied voltage V by 90 degrees and so does the flux  av produced by it. The current Ic in the series magnet is the load current and hence lags behind the applied voltage by a' . The flux ac produced by this current Ic is in phase with it. Therefore the two currents Ic in the current coil and Iv in the voltage coil and also corresponding fluxes av and ac are (90 - a') apart.

The flux ac  induces the eddy currents iv in the aluminium disc which lags behind the flux by 90degrees. Similarly, flux ac  induces eddy currents ic which again lags behind flux ac  by 90 degrees.

Mean deflecting torque, Td   proportional  ac sin (90 - a ) 

Td  proportional  V I cos a

Td  proportional  a.c power

Since control is by springs, therefore  

Tc  proportional   deflection

For steady deflected position, Td  = Tc

Deflection  proportional  power

Hence, such instruments have uniform scale.

Dynamometer type wattmeter - Engineering notes

Dynamometer type wattmeter:

A dynamometer type wattmeter is most commonly employed for measurement of power in a.c as well as d.c circuits.

Principle of Dynamometer type wattmeter:

It is based on the principle that mechanical force exists between two current carrying conductors.

Construction of Dynamometer type wattmeter:

It essentially consists of two coils, namely fixed coil and moving coil. The fixed coil is split into two equal parts which are placed close together and parallel to each other. The moving coil is pivoted between the two fixed coils and is placed on the spindle to which the pointer is attached.

the fixed coils are connected in series with the load and carry the circuit current. It is, therefore called current coil. The moving coil is connected across the load and carries current proportional to the voltage. It is therefore called potential coil. Generally, a high resistance is connected in series with potential coil to limit the current through it.

The controlling torque is provided by springs which also serve the additional purpose of leading current into and out of the moving coil. Air friction damping is employed in such instruments.

Dynamometer type wattmeter 

Working of Dynamometer type wattmeter:

When power is to be measured in a circuit, the instrument is suitably connected in the circuit. The current coil is connected in series with load so that it carries the circuit current. The potential coil is connected across the load so that it carries current proportional to the voltage.

Due to the current in the coils, mechanical force exists between them. The result is that the moving coil, moves the pointer over the scale. The pointer comes to rest at a position where deflecting torque is equal to the controlling torque.

Reversing the current, reverses the field due to fixed coil as well as the current in the moving coil so that the direction of the deflection torque remains unchanged. Therefore, such instruments can be used for the measurement of a.c as well as d.c power.

Dynamometer type wattmeter circuit diagram

Deflecting torque:

It can be easily proved that deflecting torque is proportional to the power in the circuit.

Operation on d.c:

suppose that in a d.c circuit

V = voltages across load

I = current through load

Current through fixed coil If is proportional to I

Current through moving coil Im is proportional to V

Deflecting torque Td is due to the current If and Im

Td  proportional   Im.If  proportional  V.I  proportional    power

Operation on a.c:

suppose that in an a.c circuit

e = instantaneous voltage across load

i = instantaneous current through load

If the load has a lagging power factor of cos a, then equation become

e = Em. sinwt

i = Im sin (wt - a)

Current through fixed coil If is proportional to i

Current through moving coil Im is proportional to e

Due to large inertia of the moving system, the deflection will be proportional to the average torque.

Mean deflecting torque   proportional   Average of im.if

proportional    E I cos a

hence, dynamometer type wattmeter can be used for the measurement of a.c as well as d.c power.

We have seen that, 

Td   proportional    power 

Tc  proportional   deflection 

Deflection   proportional   power

Dynamometer type wattmeter instruments have uniform scale.

Single phase induction type energy meter

Induction type single phase energy meter:

Single phase induction type energy meter is extensively used to measure energy supplied to a single phase circuit.

Operating principle of Single phase induction type energy meter:

The operation of induction type energy meter depends on the passage of alternating current through two suitably located coils producing rotating magnetic field which interacts with a metallic disc suspended near to the coils and cause the disc to rotate.

The current coil carries the line current and produces field in phase with the line current. The pressure coil is made highly inductive so that the current through it lags behind the supply voltage by 90 degrees. Thus, a phase difference of 90 degrees exists between the fluxes produced by the two coils. This sets up rotating field which interacts with the disc to cause it to rotate.

Construction of Single phase induction type energy meter:

A single phase induction type energy meter generally has:

1. Moving system

2. Operating mechanism

3. Recording mechanism

 

Single phase induction type energy meter diagram

1. Moving system: The moving system consists of a light aluminium disc mounted on a vertical spindle. The spindle is supported by a up-shaped jewelled bearings at the bottom end and has a spring journal bearing at the top end.

There is no pointer and control spring so that the disc makes continuous rotation under the action of deflecting torque.

2. Operating mechanism:  It consists of series magnet, shunt magnet and breaking magnet.

Series magnet:  The series magnet consists of a number of U-shaped laminations assembled together to form a core. A thick wire of few turns is wound on both legs of the U-shaped laminated core. The wound coil is known as current coil and is connected in series with the load so that it carries the load current. The series magnet is placed underside the aluminium disc and produces magnetic field proportional to and in phase with the current.

Shunt Magnet: The shunt magnet consists of a number of M-shaped laminations assembled together to form a core. A fine wire of large turns is wound on the central limb of this magnet. The wound coil is known as pressure coil and is connected across the load so that it carries current proportional to supply voltage. the shunt magnet is placed above the aluminium disc as shown.

In order to obtain deflecting torque, current in the pressure coil must lag  behind the supply voltage by 90 degrees. This necessary phase shift is obtained by placing a copper ring over central limb of shunt magnet. This copper ring acts as a short circuited transformer secondary. As its inductance is high as compared with its resistance, the current circulating in the ring will lag by nearly 90 degrees behind the voltage producing it.

Braking magnet: The speed of aluminium disc is controlled to the required value by the C-shaped permanent braking magnet . The magnet is mounted so that the disc revolves in the air gap between the polar extremities. As the disc rotates, currents are induced in the disc because it cuts the flux produced by the breaking magnet. The direction of the current in the disc is such that it opposes the rotation of the disc. Since the induced currents in the disc are proportional to the speed of the disc, therefore, breaking torque is proportional to the disc speed.

3. Recording mechanism: The number of revolutions of the disc s a measure of the electrical energy passing through the meter and is recorded on dials which are geared to the shaft.

Working: 

When the energy meter is connected in the circuit to measure electrical energy, the current coil carries the load current whereas the pressure coil carries current proportional to the supply voltage. The magnetic field due to current coil is in phase with line current whereas the magnetic field produced due to pressure coil lags approximately 90 degrees behind the supply voltage.

The current coil field produces eddy currents in the disc which reacts with the field due to the pressure coil. Thus, a driving force is created which causes the disc to rotate.

The braking magnet  provides the braking torque on the disc. By altering the position of this magnet, desired speed can be obtained. The spindle is geared to the recording mechanism so that electrical energy consumed in the circuit is directly registered in kWh.

Measurement of High Resistance - Engineering notes

High Resistance:

• Resistances of 100 kilo ohms and above are usually termed as high resistances.
• Measurement of high resistances are required for determination of insulation resistance of components and built up electrical equipment of all types volume, resistivity of a material, surface resistivity and resistance of high resistance circuit elements.

Measurement of High Resistance:

1. Three wires are required to represent a high resistance. 
2. The third, guard terminal, G is utilized to reduce the errors because of leakage currents caused by insulation.
3. The methods are used for the measurement of high resistance are

• Loss of discharge method
• Direct deflection method
• Mega ohm bridge resistance method
• Megger

 

1. Loss of charge method:

 

Schematic diagram of  Loss of charge method 

2. Direct deflection method:

Schematic diagram of Direct deflection method

This method is suitable for the measurement of volume resistivity, surface resistivity of any insulating material available in sheet form. A guard terminal surrounding resistance terminal is connected to the battery side as a micro-ammeter. The guard terminal and the resistance  terminal are almost at the same potential and hence there is no flow of current between them. The leakage current IL which would otherwise flow through the micro-ammeter , bypasses the micro-ammeter. The micro-ammeter indicates the current IR only. The resistance value is determined by the readings of voltmeter and ammeter as, 

R = V / IR ohm

3. Mega ohm bridge resistance method:

Schematic diagram of Mega ohm bridge resistance method

By connecting the guard terminal to one of the terminals of galvanometer. We can make the insulation resistance not effects the value of high resistance to be measured.

AG, BG are the insulation resistances of the order of 1Mohm.

4. Megger Method:

This the most commonly used method for measurement of high resistance. The essential parts of the megger are as shown in the fig below. It consists of a hand driven d.c generator and a direct reading ohmmeter. Permanent magnets provided field for both. The moving element consists of three coils, one current coil, potential or pressure coil and compensating coil. The coils are mounted over a rigid shaft and are free to rotate over a C-shaped stationary iron core. The coils are connected to the circuit by means of flexible leads or ligaments. E and L, are test terminals. The current coil is connected in series with the terminal L. The series resistance R' protects the current coil in case the test terminals are short-circuited and controls range of the instrument. The pressure coil, in series with a compensating coil and  protection resistance R is connected across the generator terminals. Compensating coil is provided for better scale proportions and to make the instrument astatic.

 

Schematic diagram of Megger method

When the current from the generator flows through pressure coil, the coil tends to align itself at right angles to the permanent magnet field. When test terminals are open i.e, at infinite resistance no current flows through the current coil and pressure coil governs the motion of the moving element causing it to move its extreme counter-clockwise position, the point under this condition is marked infinite resistance. Current coil produces clockwise torque on moving element. When the terminals L and E are short circuited, the current flowing through current coil is large enough to move the pointer to its extreme clockwise position, marked zero. For any resistance connected between L and E, the opposing torque of the coils balance each other so that pointer comes to rest at some intermediate point on the scale.

 

Measurement of Low resistance - Engineering Notes

Low Resistance:

• Resistances of about 1ohm and less are included in this class.
• Measurement of low resistances are required for determination of resistances of armatures and series field windings of large machines, ammeter shunts, cable length, contacts etc.

Measurement of Low Resistance:

1. Four wires are used for representation of low resistance.
2. This can be measured by 

• Ammeter - voltmeter method
• Kelvin's double bridge method
• Potentiometer method

1. Ammeter Voltmeter Method:

Voltmeter - Ammeter method:

Voltmeter - Ammeter method for measurement of medium resistance

Measured value of resistance, Rml = (VR + Va ) / IR

where R is the true value of the resistance.

Error = Ra% = Ra / R

• In this method, always the measured value of resistance is greater than true value of resistance.
• This  method is suitable for measurement of high resistance, among the range.

Ammeter - voltmeter Method:

Ammeter - Voltmeter method for measurement of medium resistance

Measured value of resistance, Rm2 = VR / I

where I = IR = IV = (VR / R1) +( VR / Rv)

then Rm2 = R / ( 1 +( R / Rv))

Error  = Rm2 - R = Rm2

% error = -Rm2 / Rv = -R / Rv

• In this method, always the measured value of resistance is less than true value of resistance.
• This  method is suitable for measurement of low resistance, among the range.

The resistance where both the methods give same error is obtained by equating the two errors.

Ra / R = R / Rv

R = sq root (Ra.Rv)

2. Kelvin's double bridge method: 

 It is modification of the wheatstone bridge  and provides increased accuracy. It incorporates the idea of second set of ratio arms, hence the name double bridge and the use of four terminal resistances for the low resistance arms. The circuit diagram is shown in the figure.

P, Q and p ,q are two pairs of known non - inductive resistances and one pair P , p or Q, q is variable. the ratio p /q is made equal to P /Q.
Where R = unknown resistance
S = Standard resistance of the order of magnitude as R
r = Connecting link of low resistance

Schematic diagram of Kelvin's double bridge method

Vad = Vam + Vmd = I2.R + I2. r . P/ (p+q+r)

R = S . P. q.r .[ P/Q - p/q]  /  Q. (p+q+r)

3. Potentiometer Method:

It is based on comparison of one resistance against another. The unknown resistance R, an ammeter A and a variable resistance for limiting current and a standard resistance S are connected in series with a low voltage, high current supply. The current flowing through the circuit is adjusted so that the potential difference across each of the resistor is about 1v. The voltage drop across both the unknown resistor R and standard resistor S are measured by a d.c potentiometer.

 

Cathode ray oscilloscope - Electrical measurements

Cathode ray oscilloscope:

• The cathode ray oscilloscope is an electronic instrument that presents a high fidelity graphical display of the rapidly changing voltage at its input terminals. The cathode ray oscilloscope is probably the most versatile and useful instrument available for signal measurement.
• Unlike meters, which only allow the user to measure amplitude information, the oscilloscope allows the user to view the instantaneous voltage versus time such displayed plot of the signal can be used for various measurements like peak voltage, frequency, phase, time period, rise time etc. It can also indicate the nature and magnitude of noise that may be corrupting the measurement signal. The more expensive models can measure signals at frequencies up to 500 MHz and even the cheapest models can measure signals at frequencies up to 20 MHz. One particularly strong merit of the oscilloscopes its high input impedance, typically 1M, which means that the instrument has a negligible loading effect in most measurement situations. As a test instrument, it is often required to measure voltages whose frequency and magnitude are totally unknown.
• However, it is not a particularly accurate instrument and is best used where only an approximate measurement is required. Further disadvantages of oscilloscopes include their fragility and their moderately high cost.
• There are two main classes of oscilloscopes: analog oscilloscopes and digital oscilloscopes.
• A simplified block diagram of an analog oscilloscope is shown in below figure.

 

Analog oscilloscope block diagram

• The display section of the cathode ray oscilloscope has two inputs to it namely vertical input and horizontal input. The signals applied to these inputs are driven to corresponding deflection plates and control the position of the electron beam that plots the waveform on the screen. There are two types of plots that can be displayed based on mode of operation of oscilloscope.

Important measurements that can be made by cathode ray oscilloscope:

1. Measurement  of impedance.
2. Measurement of power and power factor.
3. Measurement  of degree of modulation.
4. Measurement of checking of switching times.
5. Tracing of hysterisis loop for magnetic material.
6. Study of transistors phenomenon.
7. Fault testing of windings of electrical machines.
8. determination of characteristics of thermionic values.

Oscilloscope specifications:

• Sensitivity: A series of attenuators and pre-amplifiers exist at the input to the oscilloscope. These condition the measured signal to the optimum magnitude for input to the main amplifier and vertical deflection plates, thus enabling the instrument to measure a very wide range of different signal magnitudes. Selection of the appropriate input amplifier / attenuator is made by setting a volt/div control associated with each oscilloscope channel. This defines the magnitude of the input signal that will cause a deflection of one division on the screen.
• Bandwidth: One important oscilloscope specification is related to the speed of the waveforms that can be measured. This is determined by the bandwidth of the oscilloscope and it is found that the capability of the oscilloscope to accurately display the waveform falls off with increasing frequency. The bandwidth is defined as the range of frequencies over which the oscilloscope amplifier gain is within 3db of its peak value. The oscilloscope specifications for bandwidth will typically be quoted in the format: Bandwidth = -- 3db at 1500 MHz. The - 3db specification means that an oscilloscope with a specified inaccuracy of +- 2 % and bandwidth of 100MHz will have an inaccuracy  of +- 5% when measuring 30MHz signals, and this inaccuracy will increase still further at higher frequencies. Thus, when applied to signal amplitude measurement, the oscilloscope is only usable at frequencies up to about 0.3 times its specified bandwidth. In most oscilloscopes, the amplifier is direct coupled, which means that it amplifies d.c voltages by the same factor as low frequency a.c ones. For such instruments, the minimum frequency measurable is zero and the bandwidth can be interrupted as the maximum frequency where the sensitivity is within 3 db of the peak value. In all measurement situations, the oscilloscope chosen for use must be such that the maximum frequency to be measured is well within the bandwidth.
• Rise time: The rise time is the transit time between the 10% and 90% levels of the response when a step input is applied to the oscilloscope. The oscilloscope must have a sufficiently fast rise time to capture the rapid transitions accurately, otherwise important information may not be displayed and the results could be misleading. oscilloscopes are normally designed such that

 Bandwidth * Rise time  = 0.35.

Types of Oscilloscopes:

1. Analog oscilloscope: This is traditional form of oscilloscope that has been used n labouratories for many years. It relies on analog techniques and takes in the vertical and sometimes horizontal signals, amplifying them in  an analog format and displaying them on a cathode ray tube.
2. Digital Storage oscilloscope:It is the conventional form of digital oscilloscope. It uses a raster type screen like that used on a computer monitor or television and in this way displays an image that fills the screen and may include other elements in addition to the waveform. These additional items may include text on the screen and the like.
3. Digital phosphor oscilloscope: It is a highly versatile form of oscilloscope that uses a parallel processing architechture to enable it to capture and display signals under circumstances that may not be possible using a standard DSO. The key element of a DPO is that it uses a dedicated processor to acquire waveform images. In this way it is possible to capture transient events that occur in digital systems more easily. These may include spurious pulses, glitches and transition errors. It also emulates the display attributes of an analog oscilloscope, displaying the signal in three dimensions: time , amplitude and distribution of amplitude overtime, all in real time.
4. Sampling oscilloscope: These oscilloscopes are used for analyzing very high frequency signals. They are used for looking at repetitive signals which are higher than the sample rate of the scope. They collect the samples by assembling samples from several successive waveforms, and by assembling them during the processing, they are able to build up a picture of the waveform. The oscilloscope specifications for these items may detail a frequency capability or bandwidth sometimes as high as 50GHz. However these scopes are very expensive.