CHAPTER 2
Voltage and Current
Measurement
1
Introduction of Electric Circuit
The ultimate goal of the circuit theory is to predict
currents and voltages in complex circuits (circuit
analysis) and to design electrical circuits with desired
properties.
The circuits are built with circuit elements.
Some of these elements are voltmeters, ammeters,
wires, resistors, capacitors, inductors, and switches.
2
Ammeters
 Electrical currents can be measured with an ammeter.
 To measure the current in the wire shown in Fig. 1a, the wire
should be cut and the ammeter should be inserted.
 The current will flow through the ammeter (Fig. 1b).
3
Cont’…Ammeters
 An ideal ammeter should have a negligible effect on the
circuit. This means that the voltage difference between its
two terminals (A and B) should be zero.
 In other words, the internal resistance (impedance) of an
ideal ammeter is zero.
4
Voltmeter
 To measure voltage, the two terminals of a voltmeter
should be connected to two points in the circuit between
which the potential difference is measured. An ideal
voltmeter should not affect the circuit.
 Therefore, current through the voltmeter (this is current
in Fig.2) should be zero.
 In other words, internal resistance (impedance) of an
ideal voltmeter is infinity. A real voltmeter is never ideal
and its impedance is finite.
5
Kirchhoff Laws
 Kirchhoff laws are applicable to both the linear and not linear
circuits.
 They provide a universal tool for circuit analysis.
 Kirchhoff ’s Current Law (KCL)
 The sum of the currents entering a node is equal to the sum
of currents leaving the node.
 A node is a point where two or more wires are interconnected.
 Kirchhoff ’s Voltage Law (KVL)
 An algebraic sum of voltages across all elements along
any closed path is zero.
 Algebraic sum means that we should take “+” sign if the
voltage rises after a circuit element and “–“ sign if the
voltage drops after a circuit element.
6
Cont’…Kirchhoff Laws
Analysis of a circuit. General rules:
1. Identify every loop which does not contain another loop
(such a loop is called mesh). Assign a current for every
loop. The current direction can be chosen arbitrary. This
step ensures that the Kirchhoff’s current law is
automatically satisfied.
7
2.
Use Ohm’s law (or other relations between voltages and
currents if the circuit includes capacitors, inductors,
diodes, etc) to calculate the voltage across all elements
along every mesh and write equations (for every mesh)
using Kirchhoff’s voltage law. Important! If two
currents flow through an element, the currents should
be added like vectors (their directions are important!).
3.
Solve the equations.
Example 1
 Consider the circuit below.
 KVL @ mesh 1;
I1R1  ( I1  I 2 ) R3  V0  0 (1)
 KVL @ mesh 2;
I 2 R2  I 2 R4  ( I 2  I1 ) R3  0 (2)
8
Example 2
 Kirchhoff Law when applied to capacitor and inductor
usually produce differential equations.
 KVL
dI
L  IR  VC  Vs (t )  0
dt
9
Electrical Indicating Instruments and
Measurement
 Electrical instruments are classified into two (2)
1. Absolute instruments
 The value of the electrical quantity to be measured are
given by these instruments. The quantity are measured in
terms of constants and from deflection of the
instruments only.
 Example : Tangent galvanometer.
10
2. Secondary instruments
 The value of the electrical quantity to be measured
is determined from the deflection of these
instruments. With an absolute instrument these
instruments are calibrated.
 There are three categories of secondary instruments
 1. Indicating instruments
 2. Recording instruments
 3. Integrating instruments
11
Categories of Secondary Instruments
1.
Indicating instruments
 The value of the electrical quantity is indicated by these
instruments at the time when it is being measured. Pointers
moving over the scale give the indication.
• Examples: Ammeters, volmeters and wattmeter
2.
Recording instruments
 A continuous record of variations of the electrical quantity
over a long period of time is given by these instruments. It
has a moving system which carries an inked pen which rest
tightly on a graph chart.
 Examples: Graphic recorders and Galvanometer recorders
12
Cont’…
3. Integrating instruments
 The total amount of either electricity or electrical
energy supplied over a period of time is measured by
these instruments.
 Example : Ampere hour meters, watt hour meter,
energy meters
13
1.0
Current Measurement
14
Current
 Basic analog measurement of current –uses inductive force
on the current carrying conductor in magnetic field.
 This force can be used to measure the needle deflection on a
display.
 Direct Current (DC)
 Charges flow in one direction
 commonly found in many low-voltage applications,
especially where these are powered by batteries
 Alternating Current (AC)
 Flow of electric charge changes direction regularly
 Example: audio & radio signal
 Home & school use AC
15
Permanent Magnet Moving Coil
Instrument (PMMC)
 There are TWO(2) types of moving coil
instruments;
 Permanent Magnet Moving Coil
 Dynamometer Type
16
Construction
 It consists of a permanent magnet with soft iron pieces. The U-shape
magnet is widely used.
 A coil of many turn is wound on aluminium frame.
 The coil is can move freely move in the field of a permanent magnet.
 The soft iron coil is mounted between the poles of permanent
magnet giving a very narrow gap.
 The pointer is carried by the spindle and moving over a graduated
scale.
17
Cont’d…
 The control torque is provide by two phosphor bronze hair
springs.
 Eddy current damping is produced by movement of the
aluminium former moving in the magnetic fields of permanent
magnets.
 Phospher – bronze springs, pointer, jewel bearings etc.
 The current is passed into and out of the coil by means of
phospher bronze hair springs provided at both ends. The
springs also provide the controlling torque. The aluminium
frame supports the coil. It also provides a damping torque by
the eddy currents induced in it.
18
Operation
 When the current to be measured is passed to the moving
coil, a deflecting torque, Td is produced on account of
reaction of the permanent magnetic field with the coil
magnetic field.
 The direction of deflecting torque can be determined by
applying Fleming’ Left Hand Rule.
 The moving system turns through an angle q at which
position the tightened control spring produces a back
torque Tc equal to Td. The pointer stabilizes at this stage
and gives the reading.
19
Advantages
 It consumes very small power
 They have no hysteresis losses
 They have high torque-weight ratio
 Their scale is uniform
 They have very effective and efficient eddy
current damping
20
Disadvantages
 Some errors are set in due to ageing of
control springs and the permanent magnet.
 High cost
 These instruments cannot be used for AC
measurement
 Friction and temperature causes for error
21
Reason for use on DC only
 The depletion of a moving coil meter depend on
polarity of meter connection.
 For one polarity of connection, the deflecting
torque is acting forward.
 When connection is reversed, the deflection is also
reversed.
 So it is cannot be used for AC measurement but can
be used for DC measurement.
22
Dynamometer Type
 There are two fixed coils
F1 and F2 held parallel
to each other. They are
electrically connected in
series.
 When a current is passed
through them, a uniform
magnetic field is
produced between the
two fixed coils.
23
Cont’d…
 Within this magnetic field a moving coil is placed
and support by a spindle and jewel bearings.
 The spindle carries two control springs that also
serve as current leads to the moving coil.
 Moving coil can be connected either in series or
parallel with fixed coil.
 Series connection – voltmeter
 Parallel connection – ammeter
24
Advantages
 It is free from hysteresis and eddy current
losses because there is no iron core.
 It can be used for AC as well as DC
measurement.
 It has a fairly high degree of accuracy.
25
Disadvantages
 The power loss is high
 Torque/weight ratio is small
 Scale is non-uniform
 Subjected to errors by stray magnetic fields.
 Error due to mutual induction of coils while measuring AC.
 It is comparatively more expensive. Friction and temperature
causes for error
26
Ammeter
 An ammeter is an instrument for measuring the electric
current in amperes in a branch of an electric circuit.
 It must be placed in series with the measured branch, and
must have very low resistance to avoid significant alteration
of the current it is to measure.
 connecting an ammeter in parallel can damage the meter
27
Ammeter – Principle of Operation
 The earliest design is the D'Arsonval galvanometer or
moving coil ammeter (respond to ac only)
 It uses magnetic deflection, where current passing through
a coil causes the coil to move in a magnetic field
 The voltage drop across the coil is kept to a minimum to
minimize resistance across the ammeter in any circuit into
which the it is inserted.
 Moving iron ammeters use a piece or pieces of iron which
28
move when acted upon by the electromagnetic force of a
fixed coil of (usually heavy gauge) wire (which respond to
both dc & ac)
Ammeter Design
29
 An ammeter is placed in series with a circuit element to measure
the electric current flow through it.
 The meter must be designed offer very little resistance to the
current so that it does not appreciably change the circuit it is
measuring.
 To accomplish this, a small resistor is placed in parallel with the
galvanometer to shunt most of the current around the
galvanometer.
 Its value is chosen so that when the design current flows through
the meter it will deflect to its full-scale reading.
 A galvanometer full-scale current is very small: on the order of
milliamperes.
30
Basic DC Ammeter Circuit
In most circuits, Ish >> Im
Ammeter
Where

31
Rsh = resistance of the shunt

Rm = internal resistance of the
meter movement (resistance of the
moving coil)


Ish = current through the shunt
Im = full-scale deflection current
of the meter movement

I = full-scale deflection current
for the ammeter
D’Ársonval meter movement used in ammeter
circuit
 The voltage drop across the meter movement is
Vm  I m Rm
 The shunt resistor is parallel with the meter movement, thus the
voltage drop for both is equal
 Then the current through the shunt is,
Vsh  Vm
I sh  I  I m
 By using Ohm’s law, Then we can get shunt resistor as
Vsh I m Rm I m
Im
Rsh 


Rm 
Rm
I  I m 
I sh
I sh
I sh
32
Example 1.1
Calculate the value of the shunt resistance required
to convert a 1-mA meter movement, with a 100-ohm
internal resistance, into a 0- to 10-mA ammeter.
33
The Aryton Shunt
 The purpose of designing the shunt circuit is to allow to
measure current I that is some number n times larger than Im.

The number n is called a multiplying factor and relates total
current and meter current as
I  nI m
(1)
 We can get shunt resistance with n times larger than Im is
Rm
Rsh 
(2)
n 1
34
Examples 1.2
A 100 µA meter movement with an internal
resistance of 800 Ω is used in a
0 - to 100 mA ammeter. Find the value of
the required shunt resistance.
35
Advantages of the Aryton
 Eliminates the possibility
of the meter movement
being in the circuit
without any shunt
resistance.
 May be used with a wide
range of meter
movements.
Aryton shunt circuit
36
Cont’d...
 The individual resistance values of the shunts
are calculated by starting with the most
sensitive range and working toward the least
sensitive range
 The shunt resistance is
Rsh  Ra  Rb  Rc
 On this range the shunt resistance is equal to
Rsh and can be computed by Equation
37
Rm
Rsh 
n 1
Cont’...
I m ( Rsh  Rm )
Rb  Rc 
I2
I m ( Rsh  Rm )
Rc 
I3
Rb  ( Rb  Rc )  Rc
Ra  Rsh  ( Rb  Rc )
38
Ammeter Insertion Effects
 Inserting an ammeter in a circuit always increases
the resistance of the circuit and reduces the
current in the circuit.
 This error caused by the meter depends on the
relationship between the value of resistance in the
original circuit and the value of resistance in the
ammeter.
** For high range ammeter, the internal resistance in
the ammeter is low.
** For low range ammeter, the internal resistance in
the ammeter is high.
39
E
Ie 
R1
E
Im 
R1  Rm
Fig 2-4: Series circuit with ammeter
40
Cont’d...
hence;
Im
R1

I e R1  Rm
Therefore
Insertion error =
41
 Im 
1   100%
Ie 

Example 1.3
A current meter (ammeter) that has an
internal resistance of 78 ohms is used to
measure the current through resistor Rc in
Figure below. Determine the percentage of
error of the reading due to ammeter
insertion.
42
AMMETER SHUNT
 An ammeter may be use to measure
greater current than that which the
instrument itself can carry with the
help of shunts.
 An ammeter shunt is merely low
resistance that is placed in parallel
with the coil circuit of the
instrument in order to measure
fairly large current.
 The circuit diagram for a shunt and
milli-ampere meter for measuring
large current is shown.
43
Galvanometer
 It is an electromechanical
transducer that produces
a rotary deflection, through a
limited arc, in response
to electric current flowing
through its coil.
 Galvanometer has been applied
to devices used in measuring,
recording, and positioning
equipment.
44
Galvanometer – Principle of Operation
 Such devices are constructed with a small pivoting coil of wire in the
field of a permanent magnet. The coil is attached to a thin pointer that
traverses a calibrated scale. A tiny spring pulls the coil and pointer to
the zero position.
 In some meters, the magnetic field acts on a small piece of iron to
perform the same effect as a spring. When a direct current (DC) flows
through the coil, the coil generates a magnetic field.
 This field acts with or against the permanent magnet. The coil pivots,
pushing against the spring, and moving the pointer. The hand points at a
scale indicating the electric current.
 A useful meter generally contains some provision for damping the
mechanical resonance of the moving coil and pointer so that the pointer
position smoothly tracks the current without excess vibration.
45
Galvanometer – Application
 Are used to position the pens of analog chart (example:
electrocardiogram)
46
2.0
VOLTAGE MEASUREMENT
Voltmeter
47
 A voltmeter is an instrument used for measuring the
potential difference between two points in an electric
circuit.
 A voltmeter is placed in parallel with a circuit element to
measure the voltage drop across it and must be designed to
draw very little current from the circuit so that it does not
appreciably change the circuit it is measuring.
48
 A galvanometer full-scale current is very small: on the
order of milliamperes.
 To accomplish this, a large resistor is placed in series
with the galvanometer.
 Its value is chosen so that the design voltage placed
across the meter will cause the meter to deflect to its
full-scale reading.
49
 To allow meter movement to measure a greater voltage,
we need a voltage divider circuit (series
resistances) to proportion the total measured voltage
into a lesser fraction across the meter movement’s
connection points.
 A resistor is connected in series with the meter
movement and it is called a ”multiplier” resistor
because it multiplies the working range of the meter
movement as it proportionately divides the measured
voltage across it.
50
Principle of Voltmeter Operation
 The moving coil galvanometer is one example of this type
of voltmeter. It employs a small coil of fine wire suspended
in a strong magnetic field.
 When an electrical current is applied, the galvanometer's
indicator rotates and compresses a small spring.
 The angular rotation is proportional to the current that is
flowing through the coil.
 For use as a voltmeter, a series resistance is added so that
the angular rotation becomes proportional to the applied
voltage.
51
D’Ársonval Meter (DC Voltmeter)
 The basic d’Ársonval meter movement can be
converted to a dc voltmeter by connecting a multiplier
Rs in series with the meter movement
 The purpose of the multiplier:
 to extend the voltage range of the meter
 to limit current through the d’Arsonval meter
movement to a maximum full-scale deflection
current.
52
 To find the value of the multiplier resistor, first
determine the sensitivity, S, of the meter
movement.
1
Sensitivit y 
(/V)
I fs
Rs  S  Voltage Range   Internal Resistance
 V 
  Rm
Rs  
I 
 fsd 
53
Example 2.1
 Calculate the value of the multiplier resistance on the
50V range of a dc voltmeter that used a 500A meter
movement with an internal resistance of 1k.
 V = 50V; Ifsd = 500A ; Rm = 1k.
 V 


50
  R m  
Rs  
 1k  99k


I 
 500 
 fsd 
54
Multi-range Voltmeter
55
Example 2.2
 A D’Arsonval movement with a full scale deflection of
50µA and having an internal resistance of 500 Ω is to be
converted into a multi-range voltmeter. Determine the
value of multiplier required for 0-20 V, 0 – 50 V and 0100V using individual multipliers for each range.
Calculate the values of the individual resistor.
56
Multiplier in series arrangement
 R4 is low range multiplier with special manufactured to meet
circuit requirement
57
Example 2.3
 Convert a basic D’Arsonval movement with a full
scale deflection of 10mA and having an internal
resistance of 100 Ω into a multirange voltmeter
with ranges from 0-1V, 0 – 10 V and 0 - 100V
58
Voltmeter Impact On Measured Circuit
 A perfect voltmeter has infinite resistance, so that it draws no
current from the circuit under test.
 However, perfect voltmeters only exist in the pages of
textbooks, not in real life!
59
Voltmeter Loading Effects
 When a voltmeter is used to measure the voltage across a
circuit component, the voltmeter circuit itself is in parallel
with the circuit component.
 Since the parallel combination of two resistors is less than
either resistor alone, the resistance seen by the source is less
with the voltmeter connected. Therefore, the voltage across the
component is less whenever the voltmeter is connected.
 The decrease in voltage may be negligible or it may be
appreciable, depending on the sensitivity of the voltmeter
being used.
 This effect is called voltmeter loading. The resulting error is
called a loading error.
60
Example 2.4


Two different voltmeters are used to
measure the voltage across resistor RB in
the circuit. The meters are as follows.
Meter A: S = 1k/V,
Rm = 0.2k, range = 10V
Meter B: S = 20k/V,
Rm = 1.5k, range =10V
Calculate:
(a) Voltage across RB without any meter
connected across it.
(b) Voltage across RB when meter A is used.
(c) Voltage across RB when meter B is used
(d) Error in voltmeter readings.
61
Solution
(a) The voltage across resistor RB without either
meter connected is found Using the voltage
divider equation:


RB
VRB  E 



R

R
B 
 A
 5kΩ 
 30V 
 5V

 25k  5k 
62
(b) starting with meter A, the total resistance it
presents to the circuit is
RTA  S  Range  1k/V 10V  10kΩ
The parallel combination of RB and meter A is
RB  RTA 5kΩ  10kΩ
Re1 

 3.33kΩ
RB  RTA 5kΩ  10kΩ
Therefore, the voltage reading obtained with meter A,
determined by the voltage divider equation, is
VRB
63
 Re1 
3.33kΩ
 E
 30V 
 3.53V

3.33kΩ  25kΩ
 Re1  RA 
(c) The total resistance that meter B presents to the circuit
is
RTB  S  Range  20k/V 10V  200kΩ
The parallel combination of RB and meter B is
RB  RTB 5kΩ  200kΩ
Re 2 

 4.88kΩ
RB  RTB 5kΩ  200kΩ
Therefore, the voltage reading obtained with meter B,
determined by use of the voltage divider equation, is
 Re 2 
4.88kΩ
VRB  E 
 30V 
 4.9V

4.88kΩ  25kΩ
 Re 2  RA 
64
(d)
(Expected value - M easured value)
Voltmeter A error 
 100%
Expected value
(5 - 3.53)
Voltmeter A error 
 100%  29.4%
5
(5 - 4.9)
Voltmeter B error 
 100%  2%
5
65
Five principal meter movements used in
ac instrument
66
1.
Electrodynamometer
2.
Iron Vane
3.
Electrostatic
4.
Thermocouple
5.
D’Arsonval with rectifier
Application of meter movements
67
Meter
Movement
DC
Use
AC
Use
Applications
Electrodynamometer
YES
YES
Standards meter, wattmeter, frequency
meter
“Indicator” applications such as in
automobiles
Iron Vane
YES
YES
“Indicator” applications such as in
automobiles
Electrostatic
YES
YES
Measurement of high voltage when very
little current can be supplied by the
circuit being measured
Thermocouple
YES
YES
Measurement of radio frequency ac
signal
D’Arsonval
YES
YES with
rectifier
Most widely used meter movement for
measuring direct current or voltage and
resistance
PMMC Instrument on AC
 The PMMC instrument is polarized (terminals +ve & -ve) - it must
be connected correctly for positive (on scale) deflection to occur.
 When an AC with a very low frequency is passed through a PMMC,
the pointer tends to follow the instantaneous level of the AC.
 As the current grows positively, the pointer deflection increases to a
maximum at the peak of the AC.
 As the instantaneous current level falls, the pointer deflection
decreases toward zero. When the AC goes negative, the pointer
deflected (off scale) to the left of zero
 This kind of pointer movement can occur only with AC having a
68
frequency of perhaps 0.1Hz or lower
• At 50Hz or higher supply frequencies - the damping mechanism of
the instrument and the inertia of the meter movement prevent the
pointer from following the changing instantaneous levels.
• The average value of purely sinusoidal AC is zero.
• Therefore, a PMMC instrument connected directly to measure
50Hz AC indicates zero average value.
•
• It is important to note that although a PMMC instrument
connected to an ac supply may indicating zero, there can actually
be very large rms current flowing in its coils
69
Two types of PMMC meter used in AC
measurement
1. Half wave rectification
2. Full wave rectification
Voltmeters using half wave and full wave
rectification are suitable for measuring only
sinusoidal ac voltages.
70
D’Arsonval meter movement used
with half wave rectification
 To
convert alternating current (AC) to
unidirectional current flow, which produces
positive deflection when passed through a
PMMC, the diode rectifier is used. Several types
of rectifiers are selected such as a copper oxide
rectifier, a vacuum diode, or semiconductor or
“crystal diode”.
VP
Vrms 
2
 0.707Vp
Vave V dc 0.318Vp
Vave 
71
Vp


2  Vrms

 0.45Vrms
• For example, if the output voltage from a half wave
rectifier is 10Vrms so the dc voltmeter will provide an
indication of approximately 4.5V dc  Therefore, the
pointer deflected full scale when 10V dc signal is
applied.
• When we apply a 10Vrms sinusoidal AC waveform, the
pointer will deflect to 4.5V  This means that the AC
voltmeter is not as sensitive as DC voltmeter.
• In fact, an AC voltmeter using half wave rectification is
only approximately 45% as sensitive as a dc voltmeter.
72
 Actually, the circuit would probably be designed for full-
scale deflection with a 10V rms AC applied, which means
the multiplier resistor would be only 45% of the value of
the multiplier resistor for 10V dc voltmeter. Since we
have seen that the equivalent dc voltage is equal to 45%
of the rms value of the ac voltage.
Edc
0.45Erms
Rs 
 Rm 
 Rm
I dc
I dc
Sac = 0.45Sdc
73
Half-wave Rectifier Voltmeter
 Commercially produced
 An ac voltmeters that use half wave rectification has
an additional diode and a shunt as shown in Figure
below:
74
• The additional diode D2 is reverse biased on the positive
half cycle and has virtually no effect on the behavior of
the circuit.
• In the negative half cycle, D2 is forward biased and
provides an alternate path for reverse biased leakage
current that would normally through the meter
movement and diode D1.
• The purpose of the shunt resistor Rsh is to increase the
current flow through D1 during positive half cycle so that
the diode is operating in a more linear portion of its
characteristic curve.
• Although this shunt resistor improves the linearity of the
meter on its low voltage ac ranges, it also further reduces
the AC sensitivity.
75
Example 2.5
Compute the value of the multiplier resistor
for a 15Vrms ac range on the voltmeter
shown in Fig. 1.
RS
Ifs = 1mA
Ein = 15Vrms
Fig. 1: AC voltmeter using half wave rectification
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Rm = 300Ω
Solution
Method 1
The sensitivity of the meter movement,
1
1
Sdc 

 1k / V
I fs 1m
Rs
= Sdc × Rangedc – Rm
= 1kΩ/V × 0.45Erms
- Rm
= 1k × 0.45(15) – 300
= 6.45k
77
Cont’d…
Method 2
The AC sensitivity for half wave rectifier,
Sac = 0.45Sdc = 0.45(1k) = 450/V
Rs
= Sac × Rangeac – Rm
= 450 × 15 – 300
= 6.45k
78
Cont’d…
Method 3
Rs
=
=
0.45E rms
 Rm
I fs
0.45  15
 300
1m
= 6.45k
79
Example 2.6
Calculate the value of the multiplier resistor required
to limit the full scale deflection current in the circuit
shown in Fig above and the AC and DC sensitivity.
80
D’Arsonval meter movement used with full
wave rectification
Fig.
2:
Full
bridge
rectifier used in an ac
voltmeter circuit
81
During the positive half cycle, currents flows through diode D2,
through the meter movement from positive to negative, and through
diode D3. The polarities in circles on the transformer secondary are
for the positive half cycle. Since current flows through the meter
movement on both half cycles, we can expect the deflection of the
pointer to be greater than with the half wave cycle, which allows
current to flow only on every other half cycle; if the deflection remains
the same, the instrument using full wave rectification will have a
greater sensitivity.
82
Cont’d…
When the 10Vrms of AC signal is applied to the circuit
above, where the peak value of the AC input signal is
E p  2xE rms  1.414x(10)  14.14V
And the average full wave output signal is
E ave  E dc  0.636xE p  0.636x14.14  9V
Therefore, we can see that a 10Vrms voltage is equivalent
to 9Vdc for full-scale deflection.
83
Example 2.7
Compute the value of the multiplier resistor for a
10Vrms ac range on the voltmeter in Figure 1-2.
Fig. 1-2: AC voltmeter circuit using full wave rectification
84
Solution
The dc sensitivity is
1
1
Sdc 

 1k / V
I fs 1mA
The ac sensitivity is
Sac = 0.9Sdc = 0.9 (1k) = 900 /V
85
Cont’d…
Therefore the multiplier resistor is
Rs
= Sac x Range – Rm
= 900 x 10Vrms – 500
= 8.5k
86
Oscilloscope
 An oscilloscope is a piece of electronic test equipment that allows
87
signal voltages to be viewed, usually as a two-dimensional graph of
one or more electrical potential differences (vertical axis) plotted as
a function of time or of some other voltage (horizontal axis)
 Perform some computations using data taken from the voltage
waveform that is displayed such as:
• rms value
• Average Amplitude
• Peak-to-peak Amplitude
• Frequency
 An oscilloscope is easily the most useful instrument available for
testing circuits because it allows you to see the signals at different
points in the circuit.
 Using for signal/wave display – Winamp Music Player,
electrocardiogram,
Potentiometer
 A potentiometer is a variable resistor that functions as a voltage






88
divider
It is a simple electro-mechanical transducer
It converts rotary or linear motion from the operator into a
change of resistance, and this change is (or can be) used to
control any volume.
Schematic symbol for a potentiometer. The arrow represents the
moving terminal, called the wiper.
Usually, this is a three-terminal resistor with a sliding contact in
the center (the wiper) - user-adjustable resistance
If all three terminals are used, it can act as a variable voltage
divider
If only two terminals are used (one side and the wiper), it acts as
a variable resistor
Potentiometer Circuit
 Any current flow through the Galvanometer, G, would be a
result of an imbalance in the measured voltage, Vm and the
voltage imposed across points A to B, VAB.
 If Vm is not equal to VAB, a current will flow through the
galvanometer, G.
 Galvanometer detects current flow due to imbalance in
voltage Vm and VAB. When Vm = VAB, there is a balance and no
current, means no displacement in Galvanometer.
89
Application of Potentiometer
 In modern usage, a potentiometer is a potential
divider, a three terminal resistor where the position of
the sliding connection is user adjustable via a knob or
slider.
 For instance, when attached to a volume control, the
knob can also function as an on/off switch at the
lowest volume
 Potentiometers are frequently used to adjust the level
90
of analog signals (e.g. volume controls on audio
equipment) and as control inputs for electronic
circuits (e.g. a typical domestic light dimmer).
3.0
RESISTANCE MEASUREMENT
91
Resistance Measurement
 The resistances are classified as ;
 1. Low Resistance : All resistances of the order of 1 ohm
and below. Example: Machine armature, series field
winding shunt etc.
 2. Medium Resistance : All resistances of the order of 1
ohm to 100,000 ohms. Example: Winding resistance,
multiplier resistance.
 3. High Resistance : All resistances of the order of 100,000
ohm and above. Example: Insulation resistance of machines,
cables,
porcelain insulator etc.
92
Ohmmeter
 The purpose of an ohmmeter, is to measure the
resistance placed between its leads.
 This resistance reading is indicated through a mechanical
meter movement which operates on electric current.
 The ohmmeter must then have an internal source of
voltage to create the necessary current to operate the
movement, and also have appropriate ranging resistors to
allow just the right amount of current through the
movement at any given resistance.
93
 The original design of an ohmmeter provided a small battery
to apply a voltage to a resistance. It used a galvanometer to
measure the electric current through the resistance.
 The scale of the galvanometer was marked in ohms, because
the fixed voltage from the battery assured that as resistance
decreased, the current through the meter would increase.
 A more accurate type of ohmmeter has an electronic circuit
that passes a constant current I through the resistance, and
another circuit that measures the voltage V across the
resistance.
94
 The standard way to measure resistance in ohms is to supply
a constant voltage to the resistance and measure the current
through it.
 That current is of course inversely proportional to the
resistance according to Ohm's law, so that you have a nonlinear scale.
 The current registered by the current sensing element is
proportional to 1/R, so that a large current implies a small
resistance.
95
Series Type Ohmmeter
 It contains galvanometer connected
in parallel with shunting resistor R2.
 This parallel circuit is in series with
a resistance R1 and a battery of EMF,
E.
 This series circuit is connected to
the terminals A and B of the
unknown resistance R
 R1 current limiting resistor
 R2 zero adjusting resistor
 Rm internal resistance of
galvanometer
96
Operation
 Supply is given through the battery B and voltage E is supplied.
 If terminal A and B are short circuited by shunting the resistance R,
maximum power flows through the meter. Under this condition,
resistor R2 is adjusted until the pointer indicates full scale current
Ifs. The full scale current position of the pointer is marked ‘0’ Ω on
the scale.
 When R is removed from the circuit, the terminals are open, the
movement indicates zero, which is marked infinite ‘ ’ for zero
current.
 Intermediate scale markings may be placed on the scale by different
known values of resistance ‘R’ in the instrument. The accuracy of
these scale markings depends on the movement and the tolerance of
the calibrating resistors.
97
 Although the series type ohmmeter is a popular design and it is used
extensively is portable instrument for general service work.
 The important disadvantages of ohmmeter is internal battery, whose
voltage decreases gradually with time and age. So the full scale drops down
and meter does not read zero when the terminals are short circuited.
 Rectified AC given to some ohmmeter is the power source. In this case,
the voltage must be regulated and given.
98
Shunt Type Ohmmeter
 It consists of a battery in series with an adjustable resistor R1 and a basic
d’Arsonval movement (meter)
 The unknown resistance is connected across terminals A and B, parallel with the
meter.
 In this circuit it is necessary to have an ON-OFF switch to disconnect the battery
from the circuit when the instrument is not in use.
 When the unknown resistor, Rx = 0 (shorted), the meter current is zero. If the
unknown resistor
Rx =  (open), current find path only through the meter
and selecting a proper value for
resistance R1, the pointer may
be made to read full scale.
LHS( 0 = no current) and
RHS (  = full scale deflection current )
99
Megger
 The megger is an instrument used for the measurement
high resistance and insulation resistance.
100
Construction
 There are two pairs of permanent magnets, one set for ohmmeter
101
and the other for the generator.
 The moving coil consists of three coils namely control coil,
deflecting coil and compensating coil.
 The control coil and deflecting coil are fixed at right angles to one
another and free to move on a stationary C shaped iron core.
 The compensating coil in series with a control coil and protection
resistance R is connected across the generator terminals. The coils
are connected to the circuits system through flexible leads. These
leads do not exert any force on the moving system at anytime which
will therefore take up any position when the generator is not driven.
A resistor R is connected in series with deflecting coil to protect the
deflecting coil under short circuit condition. The guard ring bypasses
the leakage current, if any to negative terminal of the generation and
prevents leakage current from entering the deflecting coil.
Operation
 The unknown resistance is connected between the terminal L (line)
& E (earth).
 The generator handle is then steadily turned at uniform speed. There
is a slip mechanism in the drive which ensures a limited speed.
 When the resistance value is small, the current through the
deflecting coil will be high, its deflecting torque will be very high
and hence the pointer will move to the extreme clock wise position
‘0’ or very low resistance value.
 When the resistance value is high, the current through the current
coil will be high, its deflecting torque will be very high and hence
the pointer will be taken to the extreme anticlockwise position
indicating infinity or very high resistance value.
102
Multimeter
 A multimeter or a multitester is an
electronic measuring instrument that
combines several functions in one
unit.
 Multimeter is basically a PMMC
meter.
 The most basic instruments include an
ammeter, voltmeter, and ohmmeter
with a function switch.
103
DC Ammeter Section
 DC currents are measured making use a suitably designed
shunt resistors.
105
Multi-range Ohm-meter
 Multi-range ohm-meter is built with the meter movement,
battery cells, shunt and series resistors
106
DC Voltmeter Section
 The meter movement has a resistance of 2000 ohms.
 Suitable resistor are added as multiplier to get voltage
range from 2.5V to 250V.
107
Merits/Demerits of Multimeter
 Merits
 It is single meter that performs several measuring
functions.
 It has a small size and portable
 It can made measurements with reasonable accuracy
 Demerits
 It cannot make precise and accurate measurements
due to the loading effect.
 Technical skill is required to handle it
108
AC Voltmeter Section
 To measure AC voltage the output voltage is rectified
before the current passes through the meter using
half wave rectifier.
109
Multimeter – Capabilities
 DC Voltage Measurements

 AC Voltage RMS Measurements
 DC and AC Current Measurements
 Resistance Measurements
 Capacitance/Inductance Measurements
 Frequency/Period Measurements
 Diode Measurements
110
- End –
be continue…Chapter 3
111