Electrical & Electronic Measurements Formulas for GATE EE Exam

# Electrical & Electronic Measurements Formulas for GATE EE Exam | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE)

``` Page 1

MEASUREMENTS & INSTRUMENTATION
1. MEASURING INSTRUMENT
CHARACTERISTICS
Generalized Measuring Instrument: The block diagram of generalized measuring
system may be represented as:
IMPORTANT DEFINITIONS:
Accuracy: Closeness with which an instrument reading approaches the true value
of the variable being measured. It can be improved by recalibration.
Precision: It is a measure of the degree to which successive measurement differ
from one another.
? It is design time characteristic.
High precision does not mean high accuracy. A highly precise instrument may be
inaccurate.
Ex: If reading are 101, 102, 103, 104, 105. Most precise value is 103
Resolution: The smallest change in measured value to which the instrument will
respond. It is improved by re-calibrating the instrument.
Sensitivity: It is ratio of change in output per unit change in input quantity of the
instrument. It is design time characteristic.
Drift: It means deviation in output of the instrument from a derived value for a
particular input.
Reproducibility: It is degree of closeness with which a given value may be
measured repeatedly for a given period of time.
Repeatability: It is degree of closeness with which a given input is repeatably
indicated for a given set of recordings.
Errors:
1. Absolute Error/Static Error/Limiting Error:
T
A A A
m
? ? ? A
m
? Measured value of quantity of actual value
T
A ? True value of quantity or nominal value
2. Relative Error:
T
T T
A A A
A A
m
r
? ? ? ? ? ? 3. Percent Error:
T
A
% 100
A
r
? ? ? ? Instrument Error is generally given in percent error.
4. Percentage Error at reading ‘x’:
,
% [% , Full scale]
r x r
x
? ? ? ? ? ? ? ? ? ?
Page 2

MEASUREMENTS & INSTRUMENTATION
1. MEASURING INSTRUMENT
CHARACTERISTICS
Generalized Measuring Instrument: The block diagram of generalized measuring
system may be represented as:
IMPORTANT DEFINITIONS:
Accuracy: Closeness with which an instrument reading approaches the true value
of the variable being measured. It can be improved by recalibration.
Precision: It is a measure of the degree to which successive measurement differ
from one another.
? It is design time characteristic.
High precision does not mean high accuracy. A highly precise instrument may be
inaccurate.
Ex: If reading are 101, 102, 103, 104, 105. Most precise value is 103
Resolution: The smallest change in measured value to which the instrument will
respond. It is improved by re-calibrating the instrument.
Sensitivity: It is ratio of change in output per unit change in input quantity of the
instrument. It is design time characteristic.
Drift: It means deviation in output of the instrument from a derived value for a
particular input.
Reproducibility: It is degree of closeness with which a given value may be
measured repeatedly for a given period of time.
Repeatability: It is degree of closeness with which a given input is repeatably
indicated for a given set of recordings.
Errors:
1. Absolute Error/Static Error/Limiting Error:
T
A A A
m
? ? ? A
m
? Measured value of quantity of actual value
T
A ? True value of quantity or nominal value
2. Relative Error:
T
T T
A A A
A A
m
r
? ? ? ? ? ? 3. Percent Error:
T
A
% 100
A
r
? ? ? ? Instrument Error is generally given in percent error.
4. Percentage Error at reading ‘x’:
,
% [% , Full scale]
r x r
x
? ? ? ? ? ? ? ? ? ? MEASUREMENTS & INSTRUMENTATION
Error due to combination of quantities:
1. Error due to Sum/Difference of quantities
1 2
X x x ? ? 1 1 2 2
1 2
X
%
X X X
r
x x x x
x x
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2. Error due to product or quotient of quantities
1 2 3
X x x x ? Or
1
2 3
x
x x
or
1 2 3
1
x x x
3 1 2
1 2 3
X
X
x x x
x x x
? ? ? ? ? ? ? ? ? ? ? ? ? ? 3. Composite factors
1 2
1 2
1 2
X
X x .
X
n m
x x
x n m
x x
? ? ? ? ? ? ? ? ? ? ? ? ? CLASSIFICATION OF ERRORS:
Standards of EMF:
(a) Saturated Weston cell is used for Primary standard of emf.
Its emf is 1.01864 volt, maximum current drawn is 100 A. ? It contains
4
CdSO crystal and its internal resistance is 600 to 800 . ? ? (b) Unsaturated Weston cell is used for secondary standards. Its emf is 1.0180
to 1.0194 volt and does not have
4
CdSO crystal.
Standard of Resistance:
Maganin (Ni + Cu + Mn)
Nickel 4%
Magnese12% [High Resistivity and low temperature coefficient]
Copper 84%
Inductive effect of resistance can be eliminated, using Bifilar winding.
Standard of Time and Frequency:
Atomic clock is used as primary standard of time and frequency. Quartz, Rubidium
crystal is used as secondary standard of time and frequency. Example: Cesium 133,
hydrogen maser etc.
Page 3

MEASUREMENTS & INSTRUMENTATION
1. MEASURING INSTRUMENT
CHARACTERISTICS
Generalized Measuring Instrument: The block diagram of generalized measuring
system may be represented as:
IMPORTANT DEFINITIONS:
Accuracy: Closeness with which an instrument reading approaches the true value
of the variable being measured. It can be improved by recalibration.
Precision: It is a measure of the degree to which successive measurement differ
from one another.
? It is design time characteristic.
High precision does not mean high accuracy. A highly precise instrument may be
inaccurate.
Ex: If reading are 101, 102, 103, 104, 105. Most precise value is 103
Resolution: The smallest change in measured value to which the instrument will
respond. It is improved by re-calibrating the instrument.
Sensitivity: It is ratio of change in output per unit change in input quantity of the
instrument. It is design time characteristic.
Drift: It means deviation in output of the instrument from a derived value for a
particular input.
Reproducibility: It is degree of closeness with which a given value may be
measured repeatedly for a given period of time.
Repeatability: It is degree of closeness with which a given input is repeatably
indicated for a given set of recordings.
Errors:
1. Absolute Error/Static Error/Limiting Error:
T
A A A
m
? ? ? A
m
? Measured value of quantity of actual value
T
A ? True value of quantity or nominal value
2. Relative Error:
T
T T
A A A
A A
m
r
? ? ? ? ? ? 3. Percent Error:
T
A
% 100
A
r
? ? ? ? Instrument Error is generally given in percent error.
4. Percentage Error at reading ‘x’:
,
% [% , Full scale]
r x r
x
? ? ? ? ? ? ? ? ? ? MEASUREMENTS & INSTRUMENTATION
Error due to combination of quantities:
1. Error due to Sum/Difference of quantities
1 2
X x x ? ? 1 1 2 2
1 2
X
%
X X X
r
x x x x
x x
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2. Error due to product or quotient of quantities
1 2 3
X x x x ? Or
1
2 3
x
x x
or
1 2 3
1
x x x
3 1 2
1 2 3
X
X
x x x
x x x
? ? ? ? ? ? ? ? ? ? ? ? ? ? 3. Composite factors
1 2
1 2
1 2
X
X x .
X
n m
x x
x n m
x x
? ? ? ? ? ? ? ? ? ? ? ? ? CLASSIFICATION OF ERRORS:
Standards of EMF:
(a) Saturated Weston cell is used for Primary standard of emf.
Its emf is 1.01864 volt, maximum current drawn is 100 A. ? It contains
4
CdSO crystal and its internal resistance is 600 to 800 . ? ? (b) Unsaturated Weston cell is used for secondary standards. Its emf is 1.0180
to 1.0194 volt and does not have
4
CdSO crystal.
Standard of Resistance:
Maganin (Ni + Cu + Mn)
Nickel 4%
Magnese12% [High Resistivity and low temperature coefficient]
Copper 84%
Inductive effect of resistance can be eliminated, using Bifilar winding.
Standard of Time and Frequency:
Atomic clock is used as primary standard of time and frequency. Quartz, Rubidium
crystal is used as secondary standard of time and frequency. Example: Cesium 133,
hydrogen maser etc.
MEASUREMENTS & INSTRUMENTATION
2. CLASSIFICATION OF ELECTRICAL
INSTRUMENTS
Absolute Instrument: It gives the value of parameters under measurement in terms
of the physical constant of the instrument.
e.g.? Transient Galvanometer, Rayleigh current balance etc.
Secondary Instrument:
It gives the value of parameter for directly under measurement.
e.g.? voltmeter, thermometer, pressure gauge etc.
Note: Absolute instruments are highly accurate than secondary instrument as they
contain less number of moving mechanical parts resulting in a lower operational of
power consumption.
1. Indicating type:  Voltmeter, Ammeter, Wattmeter .
2. Recording type: Recorders.
3. Integrating type: Energy meter.
4. Comparison type: Potentiometer and bridges or null deflection.
5. Deflecting type: PMMC
Note: Null deflecting instruments are highly accurate as compression to deflecting
instrument as their operational power consumption at zero deflection is zero.
Magnetic effect: Moving Iron, PMMC, Dynamometer
Induction effect: Energy meter
Heating effect: Thermocouple and Hotwire type, Bolometer
Electro static effect: Electro static type voltmeter
Hall Effect: Poynting vector type voltmeter, Flux-meter
Damping system used in indicating instruments:
It is provided in the instrument which helps the moving system of the instrument to
reach to final position at earliest.
Page 4

MEASUREMENTS & INSTRUMENTATION
1. MEASURING INSTRUMENT
CHARACTERISTICS
Generalized Measuring Instrument: The block diagram of generalized measuring
system may be represented as:
IMPORTANT DEFINITIONS:
Accuracy: Closeness with which an instrument reading approaches the true value
of the variable being measured. It can be improved by recalibration.
Precision: It is a measure of the degree to which successive measurement differ
from one another.
? It is design time characteristic.
High precision does not mean high accuracy. A highly precise instrument may be
inaccurate.
Ex: If reading are 101, 102, 103, 104, 105. Most precise value is 103
Resolution: The smallest change in measured value to which the instrument will
respond. It is improved by re-calibrating the instrument.
Sensitivity: It is ratio of change in output per unit change in input quantity of the
instrument. It is design time characteristic.
Drift: It means deviation in output of the instrument from a derived value for a
particular input.
Reproducibility: It is degree of closeness with which a given value may be
measured repeatedly for a given period of time.
Repeatability: It is degree of closeness with which a given input is repeatably
indicated for a given set of recordings.
Errors:
1. Absolute Error/Static Error/Limiting Error:
T
A A A
m
? ? ? A
m
? Measured value of quantity of actual value
T
A ? True value of quantity or nominal value
2. Relative Error:
T
T T
A A A
A A
m
r
? ? ? ? ? ? 3. Percent Error:
T
A
% 100
A
r
? ? ? ? Instrument Error is generally given in percent error.
4. Percentage Error at reading ‘x’:
,
% [% , Full scale]
r x r
x
? ? ? ? ? ? ? ? ? ? MEASUREMENTS & INSTRUMENTATION
Error due to combination of quantities:
1. Error due to Sum/Difference of quantities
1 2
X x x ? ? 1 1 2 2
1 2
X
%
X X X
r
x x x x
x x
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2. Error due to product or quotient of quantities
1 2 3
X x x x ? Or
1
2 3
x
x x
or
1 2 3
1
x x x
3 1 2
1 2 3
X
X
x x x
x x x
? ? ? ? ? ? ? ? ? ? ? ? ? ? 3. Composite factors
1 2
1 2
1 2
X
X x .
X
n m
x x
x n m
x x
? ? ? ? ? ? ? ? ? ? ? ? ? CLASSIFICATION OF ERRORS:
Standards of EMF:
(a) Saturated Weston cell is used for Primary standard of emf.
Its emf is 1.01864 volt, maximum current drawn is 100 A. ? It contains
4
CdSO crystal and its internal resistance is 600 to 800 . ? ? (b) Unsaturated Weston cell is used for secondary standards. Its emf is 1.0180
to 1.0194 volt and does not have
4
CdSO crystal.
Standard of Resistance:
Maganin (Ni + Cu + Mn)
Nickel 4%
Magnese12% [High Resistivity and low temperature coefficient]
Copper 84%
Inductive effect of resistance can be eliminated, using Bifilar winding.
Standard of Time and Frequency:
Atomic clock is used as primary standard of time and frequency. Quartz, Rubidium
crystal is used as secondary standard of time and frequency. Example: Cesium 133,
hydrogen maser etc.
MEASUREMENTS & INSTRUMENTATION
2. CLASSIFICATION OF ELECTRICAL
INSTRUMENTS
Absolute Instrument: It gives the value of parameters under measurement in terms
of the physical constant of the instrument.
e.g.? Transient Galvanometer, Rayleigh current balance etc.
Secondary Instrument:
It gives the value of parameter for directly under measurement.
e.g.? voltmeter, thermometer, pressure gauge etc.
Note: Absolute instruments are highly accurate than secondary instrument as they
contain less number of moving mechanical parts resulting in a lower operational of
power consumption.
1. Indicating type:  Voltmeter, Ammeter, Wattmeter .
2. Recording type: Recorders.
3. Integrating type: Energy meter.
4. Comparison type: Potentiometer and bridges or null deflection.
5. Deflecting type: PMMC
Note: Null deflecting instruments are highly accurate as compression to deflecting
instrument as their operational power consumption at zero deflection is zero.
Magnetic effect: Moving Iron, PMMC, Dynamometer
Induction effect: Energy meter
Heating effect: Thermocouple and Hotwire type, Bolometer
Electro static effect: Electro static type voltmeter
Hall Effect: Poynting vector type voltmeter, Flux-meter
Damping system used in indicating instruments:
It is provided in the instrument which helps the moving system of the instrument to
reach to final position at earliest.
MEASUREMENTS & INSTRUMENTATION
Electromagnetic damping: Galvanometer and moving coil type
Eddy current damping: PMMC voltmeter and energy meter
Air frictional damping: Moving iron and dynamometer
Fluid friction damping: Electrostatic type voltmeter
? PMMC Instruments are used only for DC measurements.
? Induction type instruments are used only for AC measurements.
? Hotwire and Thermal type instruments measure RMS value of input.
? Electrostatic type instruments are used to measure high voltages in kV.
? Rectifier type instruments responds to average value.
Permanent Magnet Moving Coil instruments:
? These are also called self shielding instruments.
? Aluminium former is used to provide eddy current damping.
? Magnetic field in these is in range of 0.1 to
2
1wb/ m which is strong field.
? Control spring which is made of phosphor-bronze material in these instruments
provides a control force and also provides a path for current entering to moving
coil.
? If control spring is broken, current through the coil is zero and instrument reads
zero.
? It is used for measurement of DC only.
? Material used for magnet in PMMC is Alnico and Alcomax (Al + Co +Ni).
? Torque to weight ratio of the moving system should be high and equal to 0.1,
0.1 ; It decides sensitivity which is high in PMMC
T
weight
? ? It can sense a current upto 50 ? A.
? Deflecting torque (T
d
) = NBAI
? Controlling torque (T
c
) = k? At balance T
d
= T
c
G NBA
I I
K K
? ? ? N ? Number of turns A ? Area of cross section of vowing coil
B ? Magnetic flux I ? Current through coil
Key points:
The control spring in PMMC have dual utility, they not only produce controlling
torque but also used to lead the current into the system.
Source of Errors:
? Ageing effect of the permanent magnet (can be reduced by using a pre-edged
magnet)
? Temperature effect of coil and the control spring.
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## GATE Notes & Videos for Electrical Engineering

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## GATE Notes & Videos for Electrical Engineering

28 videos|342 docs

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