# Moving and Dynamometer Type Instruments

Solved Problems on Moving & dynamometer type instruments

Q1. Explain the working of a moving iron type instruments. Derive the expression for torque produced.
These instruments are widely used in laboratories and switch board at commercial frequencies because these are cheaper in cost, robust in construction and can be manufactured with required accuracy.
These are generally of two types:-

1. The attraction type.
2. The repulsion type.

The attraction type instrument operate on the principle of attraction of a single piece of soft iron into a magnetic field and repulsion type instrument operate on the principle of repulsion of two adjacent iron pieces magnified by the same magnetic field. Repulsion type instrument are more sensitive than attraction type instrument as in repulsion type instrument large separating torque is developed by having two iron element positional class together inside the field coil where the magnetizing effect is maximum.

In both type of these instruments, the current under measurement is passed through a coil of wire. This current carrying coil set up the necessary field depending on the magnitude of the current to be measured. The coil may be of a few turns of very heavy conductor or of many turns of fine wire. The instrument to be used as an ammeter is provided with a coil of few turns of thick wire in order to have low resistance and carry large current and that to be used as a voltameter is provided with a coil of large number of turns of wire in order to have high resistance and draw as small current as possible.

EXPRESSION FOR TORQUE

Let L be the self inductance corresponding to a total angular deflection of q radians and change in inductance be dL correponding to small change in deflection angel dq due to small change in current.

The change in energy of magnetic field,

dw = Td
Since change in energy dE = workdone, dw
Td dθ = ½ I2dL
Td = ½ I2dL/dθ

where I is in amperes, L is in Henry and θ is in Radians.

Thus toruqe is proportional to the square of the instrument current and to the rate of change of inductance with deflection.

Q2. An energy meter revolves 10 revolutions of disc for unit of energy. Find the number of revolutions made by it during an hour when connected across when connected 20A at 210V and 0.8 power factor leading. If energy meter revolves 350 revolutions, find the % error.

Energy consumed in one hour = VI cos φ / 1000

= 210 x 20 x 0.8 / 1000

= 3.360 kwh.

The number of revolution the meter should make it is correct = 3.360 x registration const in revolution per kwh

= 3.360 x 100

= 336

Number of revolution actually made = 350

% error = (350-336) x 100 / 350

% error = 0.1466 %

Q3. Explain how following torque are produced in pmmc instrument and attracted type moving iron instruments
1. Deflecting torque
2. Control torque
3. Damping torque

1. DEFLECTING TORQUE:- The deflecting torque is produced by making use of one of the magnetic, chemical, electrostatic and electromagnetic induction effects of current or voltage and causes the moving system of the instrument to move from its zero position when the instrument is connected in an electrical circuit to measure the electrical quantity. The method of producing this torque depend upon the type of instrument. In attracting the type of instrument, this torque to equal to
Td = 1/2 I2 dL/dθ
Whereas in Pmmc instruments

Td = Bilur
Where B - magnetic density
i - current flowing
l - length of coil
u - number of turn

2. CONTROLLING TORQUE:- The magnitude of the movement to the moving system would be somewhat indefinite under the influence of deflecting torque unless some controlling torque exist. This torque opposes the deflecting torque and increases with increase in deflection of the moving system without controlling system the irrespective magnitude of current and moreover, once deflected it would not return to its zero position on removing the current.
In attraction type instrument it is produced by spring control and in PMMC too it would be produced by spring control.

3. DAMPING TORQUE:- This torque is also necessary to avoid oscillation of the moving system about it's final deflected position owing to the inertia of the moving parts and to bring the moving system to rest in it's final deflected position quickly.

Q4. Explain in brief why energy meter reads energy while wattmeter does not. An energy meter has a registration constant of 100rev/kwh if the meter is connected to a load drawing 20A at 230V and 0.8 power factor for 5 hours. Find the number of revolution should be made by it of it is actually made 1800 revolutions. find the % age error and explain it from consumer point of view?

An energy meter is fitted with some type of registration mechanism whereby all the instantaneous reading of power are summed over a definite period of time.

ENERGY = POWER X TIME

So, an energy meter can read energy.
Whereas, a wattmeter indicates the value of power at a particular instant when it is read and hence it can not read energy.

Registration constant= 100 rev/Kwh
I = 20 A,     V = 230 V,     cos φ = 0.8
Energy in 5 hours = VI Cos φ x 5 / 1000
= 20 x 230 x 0.8 x 5 / 1000
= 18.4 Kwh

The number of revolution of the meter should make it is correct = 18.4 x 100 = 1840 revolution.
Number of revolution actually made = 1800 revolution
% error = 1840 - 1800 x 100
1840
= 0.0217%
It would be better from the customer point of view % age error is very less.

Q5. Briefly discuss the construction and working of a PMMC instrument. Why is the linear scale. How range is extended in moving coil ammeter and voltameter?
CONSTRUCTION:- In a permanent magnet with soft iron pole pieces, a cylindrical iron core is mounted between the two poles of the magnet giving very narrow air gap in which the sides of a pointted light rectangular coil lies. The rectangular coil is wound of many turns of coil. The purpose of using core is to make the field uniform and to reduce the reluctance of the magnetic circuit. A low reluctance helps to retain permeance of magnet for a longer period.
WORKING OF TORQUE EQUATION:- When the current to be measured is passed through the coil, say in the direction as shown in fig. (a), deflecting torque is produced. On account of relation between permanent magnetic field and coil magnetic field, the direction of deflecting torque can be determined by applying Fleming's left hand rule.
It is the current in amperes flowing through the coil of turns N and length l meters B is flux density in test as in air gap:-
Then, deflecting force F = BilN newtons.
If r is the distance in meters in between the centers of the coil and force F.
Then deflecting torque Td = F x r = BilNr Nm
From the above expression it is obvious that if flux density B in the air gap is constant, then
deflecting torque Td ∝ i , Tc= Td
So, θ ∝ i
And since q is directly proportional to current, the scale of the basic dc PMMC instrument are usually linearly spaced. Hence scale is linear.

Figure (a)

Q6. Discuss the construction and working of an electrodynamic wattmeter with the help of diagram?

This type of instrument is similar in design and principle to the dynanometer type ammeter and voltameter.

WORKING AND CONSTRUCTION:- When the instrument of this type is used as wattmeter, the fixed coil which is divided into two equal portions in order to provide them uniform field , is employed as current coil and moving coil is used as pressure coil. The fixed coil which is divided into two equal portion in order to provide them uniform field, is employed as current coil and the moving coil is used as pressure coil, i.e the fixed coil carries the current proportional to the voltage across the circuit. A high non inductive resistance is connected in series with the moving coil in order to limit current. The magnetic field of the fixed and moving coil react on one another causing the moving coil to turn about it's axis. The movement is controlled by hair springs which also leads the current into and out of the moving element. Damping is provided by light aluminium moving in an air dash pot. The pointer is fixed to the moving coil spindle and moves over a suitable caliberated scale.

THEORY:- Let us be the supply voltage, i the load current and R the load resistance of the moving coil circuit.
Current through fixed coil, if = i
Current through moving coil, im = V/R
deflecting torque, Td ∝ if     im ∝ V/R
For a DC circuit the deflecting torque is thus proportional to the power and for any circuit with fluctuating torque. The instantaneous to the instantaneous power.

Q7. A 50A, 230V meter on full load list makes 61 revolution in 37 seconds if the normal disc speed is 500 revolution per kwh find the % age error?

Energy consumed per hour = VI cos φ / 1000 Kwh

Energy consumed in 37 seconds
= VI cos φ X     37     Kwh
1000       60 x 60

= 230 x 215 x 1 X     37     Kwh (assuming PE to be unity)
1000           60 x 60

= 0.11819 kwh.

Energy consumption registered by the parameter = Number of revolution made / meter constant
= 61 / 1000 = 0.122 kwh.

% error = (Actual registration - True energy consumption) / True energy consumption
= (0.122 - 0.11819) x 100 / 0.11819
% error = 3.22 %

Q8. Explain the working principle of induction type wattmeter with the help of diagram?

Induction type wattmeter 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 current, proportional to the voltage across the 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. Correct disppointed between shunt and series magnet fluxes may be attained by adjusting the position of copper shading bonds.
The pressure coil circuit of introduction type instrument is made as inductive as possible so that the flux of the shunt magnet may lag by 90° behind the applied voltage.

Volt amperes and with some modifications for measuring power factor and frequency in an circuit. Hence it can be used for measuring as well as dc.

Q9. Compare merits and demerits of moving iron type instruments and dynamometer type instruments. Which one is superior why?

1. TORQUE HEIGHT RATIO:- Dynamometer type instruments have equal small torque height ratio.

2. FRICTION ERROR:- Dynamometer type instruments have considerable friction error.

3. FRICTION LOSS:- Owing to heavy moving system, dynamometer type instruments have more friction losses.

4. COST AND SENSITIVITY TO OVERLOAD:- As a result of measures to reduce the frictional error, the dynamometer type instruments are more sensitive to overloads and mechanical impactsis in comparison to moving iron type instruments.

5. SENSTIVITY:- The senstivity of dynamometer instrument is typically very poor due to poor deflecting torque.

6. POWER CONSUMPTION:- Dynamometer type instrument have comparatively higher power consumption.

7. EFFECT OF STRAY MAGNETIC FIELD:- There is no effect of stray magnetic field on moving iron type while dynamometer type are most sensitive towards it.

8. HYSTERISIS AND EDDY CURRENT ERRORS:- Dynamometer type instruments are free from these erors while moving iron have these errors.

9. EFFECT OF WAVE FORM:- Dynamometer type instruments are very useful for accurate measurement of runs voltage while frequency change serious e rrors in AC measurement in moving iron type instruments.

10. CALIBRATION:- Dynamometer type instruments have same calibration for AC and DC measurements while moving iron type have a difference between AC and DC calibration.

Clearly Dynamometer type instrument are superior because of it's inherent advantage

Q10. Differentiate amongst indicating, recording and integrating type of instruments giving example of each type?

(a) INDICATING INSTRUMENT:- These are those which indicates the magnitude of an electrical quantity at the time taken when it is being measured. The indications are given by a pointer moving over a graduated dial. Ordinary ammeters, voltmeters are example of it.

(b) RECORDING INSTRUMENT:- These are those which keep a continuous record of the variation of magnitude of an electrical quantity to be observed over a definite period of time. Such instruments are generally used in power houses where the current, voltage and power ect. are to be maintained within certain specified values.

(c) INTEGRATING INSTRUMENTS:- These are those which measure the total amount of either quantity of electricity or electrical energy supplied over a period of time. The summation given by such an instrument is the product of time and an electrical quantity under measure

Q11. Explain construction and principle of operation of dynamometer type instrument. Why is this instrument suitable for both AC and DC measurements?

Dynamometer type instruments are very similar to PMMC instrument except that the permanent magnetic field is replaced by a coil which carry the current to be measured. The coil are usually air-cored to avoid hysterisis, eddy currents and other errors when the instrument is used on dc. The fixed coil divided into two parts connected in series with the moving coil and placed together and parallel to each so as to provide a fairly uniform field within the range of the movement of the two halves of the fixed coil must be sufficient enough to allow the movement to moving coil shaft. The instrument develops deflecting torque by the interaction of magnetic field, one field due to current in a moving coil and the other due to current in the fixed coil is not constant but varies with the magnitude of current flowing through the fixed coil. Hence the deflecting torque of this instrument is determined not only by the moving coil current but also by the fixed coil current and due to it's this properly. This is determined not only by moving coil. This is a versatile measuring device for several other applications such as for measurment of power, reactive volt amperes and with some modifications for measuring power factor and frequency in ac circuit. Hence it can be used for measuring AC as well as DC

Q12. Why shunt is usually used voltmeter and ammeter? A moving coil instrument has a resistance of 5 Ω and gives full deflection of 100mv. Show how the instrument may be used to measure:-

1. voltage upto 50V
2. current upto 10A

Shunt is usually used in voltmeter and ammeter to extend the range of voltmeter and ammeters.

Rm = 5Ω
Vm = 100mv
Im = Vm/Rm = 100mv/5Ω = 20mA

1. For measuring voltage upto 50V.

Series resistance is used with the instrument whose resistance is

R = V/Im - Rm = 50/(20 x 10-3) - 5

R = 2.5 x 10-3 - 5 = R = 2495 Ω

2. Such resistance of resistance Rf is used to be connected

Rf = Rm/[I/Im - 1]

= 5/[10/20 x 10-3 -1] = 5 x 2/998

Rf = 0.01002004 Ω

Q13. A moving coil instrument gives full scale deflection with 15mA. The resistance of coil is 5Ω. It is desired to convert this instrument into an ammeter to read upto 2A. How to acheive it further how to convert this instrument to read upto 30V

Im = 15mA , Rm = 5Ω

1. Shunt of resistance R Ω is required to be connected with the instrument where

R = Rm/[I/Im-1]

= 5/[2/5 x 10-3-1]

= 5 x 15/[2 x 10-3-15]

= 5 x 15/ 1985

R = 0.03778 Ω

2. Series resistance Rs Ω is required to be connected with the instrument.

Rs = V/Im - Rm
= 30/15 x 10-3 - 5
= 2000 - 5
Rs = 1995 Ω

Q14. Explain the principle of operation of attraction type moving iron instruments and explain how the controlling and damping forces are obtained?

The earliest and simplest form of attraction moving iron instruments uses a solenoid and moving oval shaped soft iron pinoted eccentrically. To this iron a pointer is attached so that it may deflect along with the moving iron over a graduate scale. The iron is made of sheet metal specially shaped to give a scale as nearby uniform as possible. The moving iron is drawn into field of solenoid when current flows through it. The movement of the iron always from weaker magnetic field outside the coil into the stronger field inside the coil regardless the direction of flow of current. When the current to be measured is passed through the solenoid, a magnetic field is set up inside the solenoid, which in turn magnetises the iron. Thus the iron is attached into the coil causing the spindle and the pointer to rotate.
So much instruments normally have spring control and pneumatic damping forces.

Q15. A moving coil instrument gives a full scale detection of 20mA. When a potential difference of 50mV is applied. Calculate the series resistance to measure 500V on scale?

Im = 20mA

V = 250V

Vm = 50mV

R= V/Im - Rm

= (500/20) x 103 - 2.5

= 25000 - 2.5

R = 24997.5 Ω