MEASUREMENT DEVICES

Measurement and Error 2

1.1 MEASUREMENT DEFINITION
(a) The process of converting physical attributes into meaningful numbers is known as

measurement.

(b) Measurement is the process of determining the amount, degree, or capability of something
by comparing it to the accepted standards of the system units in use (directly or indirectly).

Input Signal Measurement tools Output Signal
Physical Electrical

Figure 1.1 Block Diagram of Measurement Process

1.2 ELEMENTS OF MEASUREMENT SYSTEM

(a) The purpose of the measuring system is to provide data on the physical value of numerous
variables. A measuring system's operation can be explained in terms of the system's
functional elements. One or more of these functional aspects can be found in every
instrument and measuring system.

(b) The majority of measurement systems have three (3) basic functioning components:
i. Primary Sensing Element. Senses (transducer) and turns the needed information into a
more practical and usable form for the measuring system to manage.

ii. Variable Manipulation Element. Manipulate the signal supplied to it while maintaining
the signal's original character. An electronic amplifier, for example, turns a low-voltage
input signal to a high-voltage output signal.

iii. Data Presentation Element. Giving them quantitative information about the measurand
or measured variable. For example, analog indicator, digital display, graphical display,
printed output.

Measurement and Error 3

Measurand Primary Variable Data presentation
sensing manipulation element
element
element

Observer

Figure 1.2 Elements of Measurement System

1.3 MEASUREMENT TERMINOLOGIES

(a) Scale. A scale is an organized set of measurements, all of which measure one property.
Scale can be divided into two categories: linear and non-linear. Figure 1.3 (a) displays a
linear scale with uniformly spaced divisions or graduations. Figure 1.3 (b) depicts a non-
linear scale, in which the scale is tight at the start and the graduations are unequal across
the range..

(a) (b)

Figure 1.3 Linear and non-linear scale
(b) Range. Range is the ratio between the smallest and largest possible values of a changeable

quantity as shown in figure 1.4.

Measurement and Error 4

Figure 1.4

1.4 ERROR IN MEASUREMENT
Measurement is the process to obtain information about the physical value of several variables is
being measured. In practice, it is impossible to measure physical quantity with perfect certainty. Error
is defined as the difference between the measured value and expected value (true value) of the
quantity.
1.5 TYPES OF ERROR
There are four (4) types of error which are gross error, systematic error, absolute error and relative
error.

A Gross Error
The gross errors occur when a mistake in observed reading, using instruments, recording, or
calculating measurement results. These errors usually occur because of human mistakes and these
errors cannot be treated mathematically. These errors also occur due to improper use of an
instrument. The error can be avoided by taking proper care in reading and recording the
measurement parameter.

2 2V

3V

V

Figure 1.5 For example, the technician reads the 3 V reading while the actual reading is 2 V

Measurement and Error 5

B Systematic Error

Systematic errors are due to instrument, environmental effects, or observational errors. For example,
defective or worn parts, ageing, parallax error or wrong estimation reading scale. The error can be
minimized by;

1 Instrumental error: proper maintenance, use, and handling of instruments
2 Environmental error: air conditioning, using magnetic shields

Observational error: to avoid parallax errors, the position of the eye must be in line with the
3

reading to be taken, as in position

Figure 1.6 Parallax error
C Random Error
The random errors are due to unknown causes. For example, errors that remain after gross and
systematic errors have been substantially reduced. The error can be minimized by treated
mathematically (take at least 3 separate reading).

D Absolute Error

The absolute error is the difference between the measured value and expected or true value. The
absolute error is defined as

Eabsolute= � Xexpected -Xmeasured �

Measurement and Error 6

E Relative Error

The absolute error divided by the expected value is referred to as relative error and expressed in

percentage. The relative error is defined as

Erelative= Eabsolute
Xexpected

Hence,

%Erelative= Erelative x 100 %

1.6 APPLY CONCEPT OF ERROR IN MEASUREMENT

Example 1. The measured value of voltage across a resistor is 46.5 V and the true value is 50 V.
Calculate absolute error.

Solution:
Expected value, Xexpected = True value = 50 V
Measured value, Xmeasured = Observed value = 46.5 V
Eabsolute= �Xexpected – Xmeasured�= 50 V - 46.5 V= 3.5 V

Example 2. The measurement yields a current value of 20 mA. While the true value of the current
across a resistor is 30 mA. Calculate absolute error.

Solution:
Expected value, Xexpected = True value = 30 mA
Measured value, Xmeasured = Observed value = 20 mA

Eabsolute= �Xexpected –Xmeasured�= 30 mA-20mA = 10 mA

Measurement and Error 7
Example 3. The measured value of the resistance is 980.9 Ω. However, the expected value of
the resistance is 1 kΩ. Calculate (i) relative error (ii) percentage error in measurement.

Solution:

Expected value, Xexpected = True value = 1 kΩ

Measured value, Xmeasured = Observed value = 980.9 Ω

i) Erelative= Eabsolute = �Xexpected –Xmeasured� = 1kΩ-980.9 Ω = 0.019
Xexpected Xexpected 1kΩ

ii) %Erelative= Erelative x 100% = 0.019 x 100 = 1.91%

Example 4. The value of the current through a resistor is 30 mA. For all that the measurement
yields a current value of 23 mA. Calculate (i) relative error (ii) percentage error in measurement.

Solution:

Expected value, Xexpected = True value = 30 mA

Measured value, Xmeasured = Observed value = 23 mA

i) Erelative= Eabsolute = �Xexpected –Xmeasured� = 30 mA-23 mA = 0.23
Xexpected Xexpected 30 mA

ii) %Erelative= Erelative x 100% = 0.23 x 100 = 23.33 %

Example 5. The value of the voltage across a resistor is 100 V. On the other hand, the
measurement yields a voltage value across a resistor of 88 V. Calculate (i) Absolute error (ii)
relative error (iii) percentage of error.

Solution:
Expected value, Xexpected = True value = 100 V

Measurement and Error 8

Measured value, Xmeasured = Observed value = 88 V

i) Erelative= Eabsolute = �Xexpected –Xmeasured� = 100 V-88 V = 0.12
Xexpected Xexpected 100 V

ii) %Erelative= Erelative x 100% = 0.12 x 100 = 12 %

1.7 UNDERSTAND THE CHARACTERISTICS IN MEASUREMENT

There are four (4) characteristics in measurement which are accuracy, precision, resolution and
significant figure.

A Accuracy

Measurement of differences between expected value or true value with the measured value. The
closer the data measured is to the true or expected value, the more accurate the measurement. The
measurement accuracy of ±1% defines how close the measurement is to the actual measured quality.

Accuracy can be expressed as

Accuracy = Relative Accuracy
Accuracy, A = 1 - % error

Where A is the relative accuracy.

B Precision

Precision is a consistency or repeatability of measure in measurement. The precision is not the same
as accuracy of measurement, but they are related.

Precision can be expressed as Precision = 1- � xn -x̅n �
Where, x̅n

xn̅ = ∑x
n

Measurement and Error 9
xn is the value of the nth measurement
xn is the sum of the n measurement divide by n
Figure 1.7 below explain relationship between accuracy and Precision for a better understanding.
The results shown four situation. (1) Inaccurate but precise, the data shown the dot inaccurate with
target but the data repeatable which is precise. (2) Accurate and precise, the data shown all dot in
the target (accurate) and repeatable (precise). (3) Inaccurate and imprecise, the data shown all the
dot not close to the target (inaccurate) and all the dot not repeatable with each other result
(imprecise). (4) Accurate but imprecise, the data shown the four dot close to the target which is
accurate but the dot not repeatable result then it imprecise.

Figure 1.7 Differentials between accuracy and precision

C Resolution
The measurement precision of an instrument defines the smallest change in measured quantity that
can be observed. This smallest observable change is the resolution of the instrument.
The ability to detect fast a smallest change in the value of a measurement. This (smallest observable
change) is the resolution of the instrument.
As for example, in Figure 1.8, Weighing Scale is shown specified in digital and analog of resolution.
On the other hand, the resolution of an analogue weighing scale is limited by the mechanical
hysteresis caused by error of the pointer, it is also limited by the width of the scale pointer, vibration
of the pointer, the accuracy of printing of scale, zero calibration and the number of ranges. Mirrored
scale and larger meter movements are used to improve resolution.

Measurement and Error 10

D Significant Figure

The number of significant figures in which the result is expressed gives an indicator of the
measurement's precision. Significant figures give accurate information about a quantity's magnitude
and measurement precision.
The number of significant figures indicates the measurement's precision. The greater the number of
significant figures, the more precise the measurement.

Example 6. The significant figure of 0.0005 is four and the significant figure for 0.05 is two. So,
0.0005 is more precise than 0.05 since it has more significant figures.

Example 7. An analog voltmeter is used to measure voltage of 50 V across a resistor. The reading
value is 49 V. Find
i) Absolute error
ii) Percent error
iii) Accuracy or Relative accuracy
iv) Percent Accuracy

Solution:

i) Absolute error
Eabsolute= �Xexpected –Xmeasured�= 50 V - 49 V = 1V

ii) Percent error

%Erelative= Erelative x 100% = Eabsolute x 100% = 1V x 100% = 2%
Xexpected 50 V

iii) Accuracy or Relative accuracy
Accuracy, A = 1 - % error = 1 - 2% = 1 - 0.02 = 0.98

iv) Percent Accuracy

% Accuracy = 100% - 2% = 98 %

Measurement and Error 11

Example 8. An experiment conducted to measure 10 values of currents and the results shown in

the table below. Calculate the precision and percentage of the 7th experiment.

No. (mA)
15
2 6.2
38
47
5 10
6 11
78
89
9 9.8
10 4

Table 1 10 values of Current measured

Solution:

Precision = 1 - �xnx-n̅ x̅n�

xn̅ = ∑ x
n

The average value for the 10 value of measurement is given by

x̅n = ∑x = 5+6.2+8+7+10+11+8+9+9.8+4 = 7.8
n 10

For the 7th reading,

Precision = 1- �xnx-n̅ xn̅ � = 1- �87-7.8.8� = 1- 0.2 = 0.974
7.8

Percentage of 7th reading,

% Precision = precision x 100% = 0.976 x 100% = 97.6%

Measurement and Error 12

Example 9. Based on figure 1.9, calculate the % error and % of accuracy when ammeter reading
is 4.5 mA.

1

15 2

Figure 1.9

Solution:

IT=XExpected= Vsupply = 15V = 15 = 5mA
RT 1k+2k 3000

EAbsolute=|5.0mA-4.5mA| = 0.5mA

%Erelative= EAbsolute x 100% = 0.5m x100% = 10%
XExpected 5.0m

%Accuracy = 100% - %Erelative= 100%-10% = 90%

1.8 UNDERSTAND STANDARDS USED IN MEASUREMENT

A standard is actual representation of a unit of measurement. A standard is acknowledged as
accurate measure of physical quantity. There are four categories in standards of measurement.

A International Standards

• Defined by international agreements
• These standards (international system of unit) are maintained at the International Bureau of

Weight and Measures in Paris, Frances.
• They are examined and checked on a regular basis using absolute measurements in terms of

the fundamental units of physics.

Measurement and Error 13

• They reflect specific units of measurement to the best of the science and technology of
measurement's ability, and are used to compare to primary standards.

Base Unit Symbol Defining Constants Symbol Value
kilogram
metre Planck constant h 6.62607015 x10-34Js
second 299792458 m/s
ampere Speed of light in vacuum
kelvin
mole Hyperfine transition ∆ 9192631770 Hz
frequency of caesium atom
candela 1.620176634 x10-19C
Elementary charge 1.380649 x10-23J/K
6.02214076 x1023/mol
Boltzmann constant

Avogadro constant

Luminous efficacy of 683 lm/W

monochromatic radiation of
frequency 540 THz

Table 2 The International System of Units (SI)

B Secondary Standard

• Used as the basic reference standards used by measurement & calibration laboratories in the
industry

• Each industrial laboratory is completely responsible for its own secondary standards
• Each laboratory sends its secondary standards to the national standards (primary standards)

laboratory for calibration
• After calibration, the secondary standards are returned to the industrial uses with the

certification and checked periodically

C Working Standard

• Working standard is the principle tools of a measurement laboratory and the lowest level of
standards

• Used to check and calibrate the instruments used in the laboratory or to make comparison
measurement in industrial application

Measurement and Error 14

• Example: the standard resistor, capacitors, inductor which usually found in an electronics
laboratory are classified as working standards.

Quick Review Question
1. Define accuracy, precision, resolution and significant figure.
2. Give three example accuracy and precision.
3. Accuracy can be expressed as?
4. What do you understand by an International Standards? Give examples.
5. State the difference between International Standards and Primary Standards.
6. State the differences between Secondary Standard and Working standards.

Measurement and Error 15

Formula Eabsolute= �Xexpected -Xmeasured�
1. Absolute Error
2. Relative Error Erelative= Eabsolute
3. Accuracy Xexpected
4. Precision
%Erelative= Erelative x 100%

Accuracy = Relative Accuracy
Accuracy, A = 1 - % error

Precision = 1- � xn -x̅n �
x̅n

x̅n = ∑x
n



Basic of Multimeter 17

2.1 MULTIMETER
(a) Multimeter is a test equipment used to measure voltage, current and resistance. A multimeter

also known as a volt/ohm meter or VOM. Multimeter can be divided into two (2) types which
are analog multimeter and digital multimeter (DMM).

(b) Figure 2.1 (a) and (b) shows the analog and digital multimeters.

Figure 2.1 (a) Analog multimeter Figure 2.1 (b) Digital multimeter

2.2 ANALOG MULTIMETER

(a) Analog multimeter is commonly used by engineers and technicians in the laboratory. An
analog multimeter is a test equipment to measure voltage, current and resistance. In an
analog multimeter, microammater with a moving pointer or needle is used to display
readings. The function of analog multimeter can be changed by switching the range and the
pointer moves along a scale.

(b) Figure 2.2 shows the part of an analog multimeter. Battery power, overload protection,
mirrored scale, range switch, diode test and battery test are the common features of analog
multimeter.

Basic of Multimeter 18

Pointer indicator Mirrored scale

10 A DC input Zero scale

Range Selector Zero pointer
Common adjustment
Terminal
Zero ohms
adjustment
Positive terminal

Figure 2.2 Parts of an analog multimeter

2.2.1 Scales and Ranges

(a) Typically, an analog multimeter has several scales. Based on Figure 2.3, each scale
consists of an arched line that is marked off into segments or sections. A range shows the
high and low limits of a scale.

(b) Scale on an analog multimeter used for measuring resistance (Ω), DC voltage/ current
(DCV.A) and AC voltage (AC10V) scales as shown in Figure 2.3. An analog multimeter
may also consist scales for measuring decibels (dB) and checking batteries.

Basic of Multimeter 19

Ohmmeter scale DC voltage/
current
AC voltage scale
(scale: 10, 50, 250)
(scale: 10 V)

Figure 2.3 Scales of an analog multimeter

2.2.2 Reading an Analog Multimeter
This section provides the steps to read an analog multimeter in the proper way.

A Resistance Measurement
1. Set the function switch to Ohms (Ω) or Resistance.

Step 1

Basic of Multimeter 20
2. Connect the black test lead into the negative (COM) jack and connect the red test lead

into the positive jack with the Omega (Ohm symbol).

Step 2
3. Hold the test probe tips together and adjust the OHM Zero Adjust knob for a “0” reading.

Step 3

Basic of Multimeter 21
4. Connect the test probe tips across the circuit or part under test. It is best to disconnect one

side of the part under test so the rest of the circuit will not interfere with the resistance
reading.

Step 4
5. Read the resistance on the Ω scale.

Step 5

Basic of Multimeter 22

B DC Voltage Measurements
1. Set the function switch to an appropriate DC V range.

Step 1

2. Connect the black test lead into the negative (COM) jack and connect the red test lead
into the positive jack with the Omega (Ohm symbol).

Step 2

Basic of Multimeter 23
3. Touch the black test lead to the negative side of the circuit. Touch the red test lead to the

positive side of the circuit.

Step 3
4. Read the voltage on the DCV A scale.

Step 4

Basic of Multimeter 24

C DC Current Measurements
1. Set the function switch to an appropriate DCA range.

Step 1

2. Connect the black test lead into the negative (COM) jack and connect the red test lead
into the positive jack with the Omega (Ohm symbol).

Step 2

Basic of Multimeter 25
3. Take out the circuit to be measured and apply the black test lead to the negative side, and

the red test lead to the positive side of the circuit.

Step 3
4. Read the current on the DCV A scale.

Step 4



Basic of Oscilloscope 27

3.1 OSCILLOSCOPE

Figure 3.1: Oscilloscope in Laboratory
An oscilloscope is a test device that displays a graph of voltage against time on its screen to allow
you to examine the'shape' of an electrical signal. It's similar to a voltmeter, but with the added
benefit of displaying how the voltage changes over time. On the screen, a graticule with a 1cm
grid allows you to take voltage and time measurements.

A beam of electrons strikes the phasor coating of the screen, causing it to emit light, usually green
or blue, drawing the graph, also known as the trace. This is comparable to how a television picture
is made.

A vacuum tube with a cathode (negative electrode) at one end to emit electrons and an anode
(positive electrode) at the other end to speed them down the tube to the screen makes up an
oscilloscope. An electron cannon is the name for this setup. Electrodes in the tube deflect the
electron beam up and down, as well as left and right.

Basic of Oscilloscope 28
Because electrons are emitted by the cathode, they are referred to as cathode rays, and the
oscilloscope is referred to as a cathode ray oscilloscope, or CRO.
A dual trace oscilloscope can show two traces on the screen at the same time, making it easy to
compare the input and output of an amplifier, for example.
An oscilloscope is a device that displays graphs. It creates an electrical signal graph. The graph
also depicts the evolution of the signal over time. The horizontal (x) axis represents time, while the
vertical (y) axis represents voltage.
From the graph, can be read as:

• To determine the time and voltage values of a signal
• To calculate the frequency of an oscillating signal
• To see the moving parts of a circuit represented by the signal
• To identify a malfunctioning component is distorting the signal
• To identify noise of signal

VOLTS
Vertical axis
Y-axis

TIME
Horizontal axis
X-axis
Figure 3.2: X and Y Components of Displayed Waveform

Basic of Oscilloscope 29

VOLTS
Vertical axis
Y-axis

TIME
Horizontal axis
X-axis

Figure 3.3: X and Y Components of Displayed Waveform

3.1.1 Front Panel of Oscilloscope

The control parts of an oscilloscope's front panel are usually separated into Vertical, Horizontal,
and Trigger sections. There are also input ports and display controllers. A front panel of an
analogue oscilloscope is shown below.

Basic of Oscilloscope 30

Oscilloscope front panel
Figure 3.4: An Analog Oscilloscope Front Panel

3.1.2 Display Control of Oscilloscope

53 2 1
4

Figure 3.5: Display Control Oscilloscope

Basic of Oscilloscope 31
Display systems vary between analog and digital oscilloscope. Common control include:

1. Power to turn on and off.
2. Intensity Control to adjust the brightness of the waveform. As increase the sweep speed of

analog oscilloscope and need to increase the intensity level.
3. Trace Rotation Control to align the waveform trace with the screen’s horizontal axis.
4. Focus Control to adjust the sharpness of the waveform.
5. Cal Control to calibrate oscilloscope with produce square waveform with 2Vpp and 1kHz.
3.1.3 Vertical Control
The vertical position control moves the waveform up or down on the display screen.

Figure 3.6: Vertical Controls

Basic of Oscilloscope 32

6. 20MHz BWL
7. CURSOR POS - △V1/2
8. CH1 POSITION – C1
9. CH2 POSITION – C2
10. TRACE SEP
11. ALT/CHOP/ADD-INV
12. CH1 VOLTS/DIV
13. CH2 VOLTS/DIV
14. CH1-VAR
15. CH2-VAR
16. CH1 AC/DC
17. CH2 AC/DC
18. CH1 GND – P x10
19. CH2 GND – P x10
The vertical controls are broken into two parts. The left half for channel 1 and the right half for
channel 2. The volts per division (volt/div) setting varies the size of the waveform on the display
screen. Other than that, vertical control has two channels: CH1/CH2 or both while AC/DC is type
of input signal.

Figure 3.7: Input Coupling

The method of connecting an electrical signal from one circuit to another is referred to as coupling.
The connection between the test circuit and the oscilloscope is known as the input coupling. It's
possible to set the coupling to DC, AC, or ground. DC coupling displays the entire input signal. The
DC components of a signal and the waveform centre are blocked at zero volts by AC coupling.
The discrepancy is depicted in the diagram below.

Basic of Oscilloscope 33
0v

Figure 3.8: AC Coupling of the same signal
0v
Figure 3.9: DC Coupling of a 1Vp-p sine Wave with 2 V DC component

Basic of Oscilloscope 34
The ground setting disconnects the input signal from the vertical system, causing the screen to
display zero volts. The horizontal line on the screen will seem 0 volts when using grounded input
connection and auto trigger mode.

Figure 3.10: Alt / Chop / Add function
Multiple channels are displayed on analogue scopes using either an alternative or chop mode.
The oscilloscope completes one sweep on channel 1, then one sweep on channel 2, then a
second sweep on channel 1, and so on in alternate mode. By switching back and forth between
the signals in chop mode, the oscilloscope draws little portions of each signal.

Basic of Oscilloscope 35

Drawn
First

Drawn
Second
Figure 3.11: Alternate mode, CH1 and CH2 Drawn Alternately

Figure 3.12: Chop mode, CH1 and CH2 Drawn Alternately

Basic of Oscilloscope 36

For Add function is to allow the oscilloscope to add waveforms together, creating a new waveform
display. Analog oscilloscopes combine the signal while the digital oscilloscope mathematically create
new waveforms. Subtracting waveforms is another math operation. Figure below illustrate a third
waveform created by adding two different signals together.

Channel 1 Display

ADD Mode:
Channel 1 and
Channel 2
Combined

Channel 2 Display

Figure 3.13: Adding Channels

Basic of Oscilloscope 37

3.1.4 Horizontal Control

The horizontal position control moves the waveform left or right on the display screen.

22

21 23
20 24

Figure 3.14: Horizontal control

Basic of Oscilloscope 38

20. TIME/DIV
21. MAIN/ALT/DELAY—X-Y
22. H POSITION
23. x10 MAG—SETUPS LOCK
24. VAR

The second per division (sec /div) setting can select the rate at which waveform is drawn across
the screen and also known as the time base setting or sweep speed.

3.1.5 Trigger Controls

26

27
25

29 28
31 30

Figure 3.15: Trigger Controls

Basic of Oscilloscope 39

25. Mode
26. Level
27. Coupling
28. Source
29. Delay-ho
30. TV-V/TV-H
31. Slope

The trigger position control is found in the oscilloscope's horizontal control section. A signal can be
captured before a trigger occurrence by varying the horizontal position. Because digital
oscilloscopes process the input signal continuously, whether or not a trigger is received, they can
enable pretrigger viewing. The oscilloscope receives a constant stream of data; the trigger simply
instructs the oscilloscope to save the current data in memory. Analog oscilloscopes, on the other
hand, only display the signal after receiving the trigger.

Basic of Oscilloscope 40

3.1.6 Oscilloscope Probe

Probe is used to connect an input signal with an Oscilloscope. A commonly used 1:1 (or 1X) probe
or 10:1 attenuation ration (or 10X). Measuring a signal accurately with any type of probe is difficult
because of circuit loading. Circuit loading is an inaccuracy caused by the interaction of the probe
with the oscilloscope. To prevent this interaction, an attenuator is built into the probe. This probe
can be switched from 10x to 1x. 1x for weak signals. When using 10x, the amplitude is reduced by
a factor of 10, but the reading will be more accurate.

Capacitance Ground
correction clip/crocodile clip
trimmer
Rectangle hook tip

Hook cover

Ground cover Main body

Figure 3.16: Oscilloscope Probes

Basic of Oscilloscope 41

3.1.7 Procedure to Calibrate the Oscilloscope

Figure 3.17: Oscilloscope calibration

1. Turn on oscilloscope
2. Connect your oscilloscope probe to CH1 or CH2
3. Attach the oscilloscope probe to CAL connector
4. Find the voltage selector (AC/DC) switch and set it to AC volts
5. Set volt/div to 1 V/div and time/div to 0.5 ms/div
6. A peak-to-peak square wave 1 volt above the center division and 1 volt below the center

division. This means the oscilloscope is correctly calibrated at 2 Vpp.



Tutorial 43

Problem 1

The measurement process is converting a physical parameter through a measurement instrument to
an electrical parameter. State THREE (3) elements in measurement system.

Solution
A. Primary sensing element
B. Variable manipulation system
C. Data presentation element

Problem 2
Explain the THREE (3) types of errors.
Solution
1. Gross Error

– Generally the fault of the person using the instruments.
– Such as incorrect reading, incorrect recording, incorrect use, improper use of instruments, etc.
2. Systematic Error
– Due to : instrument’s problem or environmental effects or observational errors
– Example : defective or worn parts, ageing, parallax error and wrong estimation reading

scale
3. Random Error

– Due to: unknown causes.
– Example : Errors that remain after gross and systematic errors have been substantially

reduced

Tutorial 44

Problem 3
By referring the below question, classify all the situations.

P

Solution

A. Inaccurate but precise
B. Accurate and precise
C. Inaccurate and imprecise
D. Accurate but imprecise

Problem 4
The current through a resistor is 2 A, but measurement gives a value of 1.9 A. Calculate the absolute
error.
Solution

Expected value, Xexpected = True value = 2 A

Measured value, Xmeasured = Observed value = 1.9 A
Eabsolute= �Xexpected – Xmeasured�= 2 A - 1.9 A= 0.1 A