Electrical Measurements and
measuring Instruments
3 Hours/Week
6 Units
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CHAPTER ONE
System of Units
The principle aspects of the scientific
method
are
accurate
selective
analysis,
and
measurement,
mathematical
formulation. Note that the first and most
important is accurate measurements.
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Measurement: is the process by which
one can convert physical parameters to a
meaningful number.
Instrument: may be defined as a device
for determining the value or magnitude
of a quantity or variable.
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Fundamental and Derived Units
To measure an unknown we must have acceptable unit
standard for the property that is to be assessed. Since
there are virtually hundreds of different quantities
that man is called upon to measure, it would seem
that hundreds of different standard units would be
required.
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The basic units are called fundamentals,
while all the others which can be
expressed in terms of fundamental units
are called derived units, and formed by
multiplying or dividing fundamental
units.
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The primary fundamental units which
most commonly used are length, mass,
and time, while measurement of certain
physical quantities in thermal, electrical
Current, and illumination disciplines are
also represented by fundamental units.
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 Every derived unit originates from some
physical law defining that unit.
For example, the voltage [volt]:
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A derived unit is recognized by its dimensions,
which can be defined as the complete algebraic
formula for the derived unit. The dimensional
symbols for the fundamental units of length,
mass, and time are L, M, and T, respectively. So
the dimensional symbol for the derived unit of
voltage is
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Table (1) shows the six basic S.I quantity and
units of measurement, with their unit symbol:
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Multiples and Submultiples of units
The units in actual use are divided into
submultiples for the purpose of measuring
quantities
smaller
than
the
unit
itself.
Furthermore, multiples of units are designated
and named so that measurement of quantities
much larger than the unit is facilitated.
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Basic Definitions:
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Factors Effecting Instrument selection
1) Accuracy
2) Precision
3) Range
4) Span
5) Sensitivity
6) Resolution
7) Error
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Accuracy
Its represent how closeness with which an
instrument reading approaches the true
value of the variable being measured.
The deviation of the measured value from the
true value is the indication of how accurately
reading has been made.
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Precision
It’s specified the repeatability of a set of
reading each made independently with the
same instrument.
An estimate of precision is determined by the
deviation of different reading from the mean
(average) value.
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Range
It is defined as that region enclosed
by
the
limits
within
which
a
particular quantity is measured.
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Span
It is algebraic difference of the upper and
lower limits of the range.
Example:
The span of (0 to 10) voltmeter is
Span= 10-0=10 state
But the span for (-10 to +10) voltmeter is
Span= 10-(-10) =20 state
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Sensitivity
It’s represent the ratio of output signal to a
change in input, or its represent the response
output of the instrument to a change of its
input.
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Resolution
The smallest change in measurement
quantity that can be observed
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Error
The deviation of the measured value
from the true value.
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Types of Errors
Systematic Errors
Random Errors
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Systematic Errors
These types of errors have known reasons, and we
can avoided, reduce or eliminated, and estimated it.
These errors are subdivided into:
1) Gross (Human) Errors (any error that can be
avoided with care)
2) Instrumentation (Equipment) Errors
3) Environmental Errors
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Random Errors
Those due to causes that can not be directly
established because of unknown events that
causes small variation in measurement, quite
random and unexplained. We can reduce this
type of errors after treatment the systematic
errors by taking many reading for the
measuring value and apply statistical analysis to
determine the best true estimate of
measurement readings.
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MEASUREMENT OF ERRORS
In practice, it is impossible to measure the
exact value of the measurand. There is always
some difference between the measured value
and the absolute or true value of the unknown
quantity (measurand), which may be very small
or may be large. The difference between the true
or exact value and the measured value of the
unknown quantity is known as the absolute
error of the measurement.
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If δA be the absolute error of the measurement,
Am and A be the measured and absolute value of
the unknown equantity then δA may be
expressed as:
δA=Am – A
R=500 Ω ± 10Ω
 The relative error (𝜀𝑟 )is the ratio of absolute
error to the true value of the unknown quantity
to be measured,
δA
Absolute error
𝜀𝑟 =
× 100% =
× 100%
A
True value
R=500 Ω ± 10%
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When the absolute error (δA) is negligible, i.e.,
when the difference between the true value A and
the measured value Am of the unknown quantity
is very small or negligible then the relative error
may be expressed as,
δA
Absolute error
𝜀𝑟 =
× 100%=
× 100%
Am
Measured value
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The measured value of the unknown quantity may be
more than or less than the true value of the measurand.
So the manufacturers have to specify the deviations
from the specified value of a particular quantity in
order to enable the purchaser to make proper selection
according to his requirements. The limits of these
deviations from specified values are defined as limiting
or guarantee errors.
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The magnitude of a given quantity having a specified
magnitude Am and a maximum or a limiting error ±δA
must have a magnitude between the limits.
Am – δA and Am + δA
Or
A = Am ± δA
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Example1
A component manufacturer constructs certain
resistances to be anywhere between 1.14 kΩ and
1.26 kΩ and classifies to be 1.2 kΩ resistor. What
tolerance should be stated ?
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VR1
=
E=VR1+VR2
∆𝑉1 + ∆𝑉2
VR2
=
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Example2
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E=VR1-VR2
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Example3
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Example4
An 820 Ω
resistor with an accuracy of
± 10% carries a current of 10 mA. The current
was measured by an analog ammeter on a 25 mA
range with an accuracy of ±2% of full scale.
Determine the accuracy in the Power
in the
resistor.
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