Limiting error:

Limiting error is defined as the difference between the measured quantity (A_m) and the true quantity (A_t).

Limiting error LE = A_m - A_t 

%Limiting error (%LE):

It can be calculated as the ratio of limiting error to the true quantity.

%LE = \(\frac{A_m -A_t }{A_t } \times 100\)

Guaranteed accuracy error (GAE):

It can be calculated as the ratio of limiting error to the full-scale value.

% GAE = \(\frac{Limiting\ error}{Full\ scale\ reading}\times 100=\frac{A_m -A_t }{Full\ scale\ reading} \times 100\)

Calculation:

GIven that,

Full-scale reading = 25 A

% GAE = 1 %

True value of ammeter = A_t

% GAE = \(\frac{Limiting\ error}{Full\ scale\ reading}\times 100=\frac{A_m -A_t }{Full\ scale\ reading} \times 100\)

⇒ 1 = (Limiting error / 25 ) x 100

∴ Limiting error = 0.25 A

% LE = (Limiting error / True value) x 100

⇒ % LE = (0.25 / 10) x 100

∴ % Limiting error = 2.5 %

Instrumentation Errors:

These errors arise due to three main reasons:

• Instrumental errors occur due to the wrong construction of the measuring instruments.
• These errors may occur due to hysteresis or friction.
• These types of errors include the loading effect and misuse of the instruments.

Environmental Errors: These errors are due to conditions external to the measuring device including conditions in the area surrounding the instrument. These may be effects of temperature, pressure, humidity, dust, vibrations or of an external magnetic or electrostatic field.

Observational Errors: These types of errors occur due to wrong observations or reading in the instruments. The wrong observations may be due to parallax. In order to reduce the parallax error highly accurate meters are needed. Ex: meters provided with mirror scales.

Precision: It is a measure of the reproducibility of the measurements, i.e. given a fixed value of quantity. It is a measure of the degree of agreement within a group of measurements.

Reproducibility: It is the degree of closeness with which given value may be repeatedly measured. It may be specified in terms of units for a given period of time.

Perfect reproducibility means that the instrument has no drift.

No drift means that with a given input the measured values do not vary with time.

Repeatability:

Reproducibility and repeatability are a measure of closeness with which a given input may be measured over and over again. Reproducibility is specified in terms of scale readings over a given period of time. Repeatability is defined as the variation of scale reading and is random in nature.

PMMC instruments:

PMMC instrument also called D'Arsonval meter.

These are used to measure the current and voltage in the DC circuit.

They are used eddy current type damping

The deflection angle can be calculated as

\(\theta = \frac {BANI}{K_c}\)

B = Flux density in Wb / sq.m 

A = Area of the frame

N = No. of turns

I = Current flow through the coil

K_c  = Spring control coefficient

Advantages:

• The scale is uniform (Linear scale)
• High torque to weight ratio compared to all the other type of instruments
• Frequency error or reactance error is absent
• High sensitivity
• Hysteresis loss is lesser
• No internal heating problem
• High accuracy
• Very less power consumption

Disadvantages:

• It works only for Dc not used for AC 
• Cost is very high

₁Moving Iron instrument:

Moving iron instrument works on the principle of Change in self-inductance or minimum reluctance property.

It can be work in both AC and DC.

The moving iron meter measures RMS current.

The deflection angle can be calculated by 

\(θ = \frac{1}{2}\frac{I^2}{K_c}\frac{dL}{dθ}\) rad

θ ∝ I²_rms

Calculation:

Given that,

θ₁ = 20° 

I₁ = 1 A

Current 

i₂ = 3 sin (314t) A

I₂ = 3 / √2 A 

θ ∝ I2rms

\(\Rightarrow \frac{{{θ _1}}}{{{θ _2}}} = {\left( {\frac{{{I_1}}}{{{I_2}}}} \right)^2}\)

\(\Rightarrow \frac{{20}}{{{θ _2}}} = {\left( {\frac{1}{{\frac{3}{{√ 2 }}}}} \right)^2}\)

\(\therefore {θ _2} = 20 \times \frac{9}{2} = 90^\circ \)

Points to remember:

• PMMC instrument measures DC values only. For AC quantities, it never reads the values.
• MI with CT measures AC quantity only.
• PMMC with rectifier measures both AC and DC values of the quantities.

The deflecting torque is used for deflection, the controlling torque acts opposite to the deflecting torque. So before coming to rest the pointer always oscillates due to inertia, so to bring the pointer rest within a short time by reducing oscillations, we use damping torque without affecting controlling torque (or) inertia.

The following mechanism can be used for producing damping torque.

1. Air friction damping

2. Fluid friction damping

3. Eddy current damping

The damping device should be such that it produces a damping torque only while the moving system is in motion. To be effective the damping torque should be proportional to the velocity of the moving current but independent of the operating current.

In the moving coil instrument type instruments, damping is provided by eddy current damping.

Eddy current damping:

• When a conductor moves in a magnetic field an emf is induced in it and if a closed path is provided, a current (known as eddy current) flows
• This current interacts with the magnetic field to produce an electromagnet torque which opposes the motion
• This torque is proportional to the strength of the magnetic field and the current produced

There are two common forms of eddy current damping devices:

1) A metal former which carries the working coil of the instrument

2) A thin aluminum disc attached to the moving system of the instrument, this disc moves in the field of a permanent magnet; The disc should be of conducting and non-magnetic material

Points to remember:

Based on the nature of the operation, instruments can be classified into three types.

Indicating Instruments: These indicate the quantity being measured by means of a pointer that moves on a scale. These instruments indicate the instantaneous value of the electrical quantity being measured at the time at which it is being measured.

Example: Ammeter, Voltmeter, Wattmeter

Recording Instruments: These instruments record continuously the variation of any electrical quantity with respect to time. In principle, these are indicating instruments but so arranged that a permanent continuous record of the indication is made on a chart or dial.

Any electrical quantity like current, voltage can be recorded by a suitable recording mechanism.

Example: A potentiometric type of recorder used for monitoring temperature records the instantaneous temperatures on a strip chart recorder, CRO, DSO.

Integrating Instruments: These instruments record the consumption of the total quantity of electricity, energy, etc. during a particular period of time. These instruments give reading for a specific period of time but no indication of reading for a particular instant of time.

The braking torque is not essential for the working of an indicating instrument.

The essential  torques for the working of an indicating instrument are given below:

Deflecting torque: The torque needed to move the pointer over a calibrated scale is known as deflecting torque and it can overcome the inertia of the moving system, controlling torque and damping torque.

Controlling torque: It is to control the pointer to a definite value that is proportional to the quantity being measured. In absence of controlling torque, the pointer will swing beyond its final steady-state position and the deflection will be indefinite.

Damping torque: Deflecting torque is used for deflection, the controlling torque acts opposite to the deflecting torque. So before coming to rest the pointer always oscillates due to inertia, so to bring the pointer rest within a short time by reducing oscillations, we use damping torque without affecting controlling torque (or) inertia.

Points to remember:

• Braking torque is used in integrated type energy meters.
• A permanent magnet is used for rotation of the Aluminum disc in the meter which controls the speed of the disc

We can classify the instruments into two types

Absolute Instruments:

• These instruments give the magnitude of the quantity under measurements in terms of physical constants of the instrument
• There is no necessity of calibrating or comparing with other instruments
• Tangent Galvanometer and Rayleigh’s current balance are examples of this class

Secondary Instruments:

• These instruments are so constructed that the quantity being measured can only be measured by observing the output indicated by the instrument i.e. deflection of the instrument
• These instruments are calibrated by comparison with an absolute instrument or any other secondary instrument which has already been calibrated against an absolute instrument
• A voltmeter, a glass thermometer, and a pressure gauge are typical examples of secondary instruments

Based on the nature of the operation, instruments can be classified into three types.

Indicating Instruments: These indicate the quantity being measured by means of a pointer that moves on a scale. These instruments indicate the instantaneous value of the electrical quantity being measured at the time at which it is being measured.

Example: Ammeter, Voltmeter, Wattmeter

Recording Instruments: These instruments record continuously the variation of any electrical quantity with respect to time. In principle, these are indicating instruments but so arranged that a permanent continuous record of the indication is made on a chart or dial.

Any electrical quantity like current, voltage can be recorded by a suitable recording mechanism.

Example: A potentiometric type of recorder used for monitoring temperature records the instantaneous temperatures on a strip chart recorder.

Integrating Instruments: These instruments record the consumption of the total quantity of electricity, energy etc. during a particular period of time. These instruments give reading for a specific period of time but no indication of reading for a particular instant of time.

Example: Ampere-hour meter, Energy meter, kilovolt ampere hour meter.

Hence

• The ohmmeter is an Indicating instrument.
• Watt-hour meter is an Integrating instrument.
• Null balance recorder is a recording instrument.
• Raleigh's current balance is an Absolute instrument.

Electrodynamometer type (EDM) instruments:

EDM type instruments are working on the principle of Change in mutual inductance (dM / dθ).

They work for both AC and DC.

These are transfer instruments and extensively used for measuring power

The deflection angle can be calculated as

\(\theta = \frac{I_1 I_2 cos\ ϕ }{K_c}\frac{dM}{d\theta}\)

I₁ = Current in the fixed coil

I₂  = Current in the moving coil

K_c = Spring control coefficient

For DC, ϕ = 0° 

Advantages:

• As the coils are air cored, these instruments are free from hysteresis and eddy current losses
• These instruments can be used for both DC and AC measurement
• Low power consumption
• High accuracy

Disadvantages:

• They have a non-uniform scale
• More expensive than other types of instruments
• The operating current of these instruments is large due to a weak magnetic field
• Torque to weight ratio is low
• Sensitivity is low
• More internal heating
• Temperature error is more
• Stray magnetic field error is more

Points to remember:

Stray magnetic field error can be eliminated by using an ASTATIC arrangement which produces an equal and opposite field to the stray field.