Transcript chapter 2- wk2 - Portal UniMAP

1.0 Device for Current Measurement
1.1 Analog ammeter
1.2 Galvanometer
2.0 Device for Voltage Measurement
2.1 Analog voltmeter
2.2 Oscilloscope
2.3 Potentiometer
3.0 Device for Resistance Measurement
3.1 Ohmmeter
3.2 Megger
4.0
Multimeter
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A voltmeter is an instrument used for measuring the
potential difference between two points in an electric
circuit.
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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.
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.
A galvanometer full-scale current is very small: on the
order of milliamperes.
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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.
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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:


is to extend the voltage range of
the meter
to limit current through the
d’Arsonval meter movement to a
maximum full-scale deflection
current.
Fig 2-1 The basic d’Arsonval meter
Movement Used In A DC Voltmeter
8
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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  Range  Internal Resistance
9
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.
10
Sensitivity,
1
1
S

 2k 
V
I fs 500
Multiplier, Rs = S X Range – internal Resistance
= (2k X 50) – 1k
= 99k
11
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 than
without. 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.
12
Two different voltmeters are used to
measure the voltage across resistor RB
in the circuit of Figure 2-2. 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.
Fig. 2.2
13
(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 

25k

5k


 5V
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(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
Therefore, the voltage reading
obtained with meter A, determined
by the voltage divider equation, is
RB  RTA
Re1 
RB  RTA
5kΩ 10kΩ
5kΩ  10kΩ
 3.33kΩ

 Re1 
VRB  E 

R

R
A
 e1
3.33kΩ
 30V 
3.33kΩ  25kΩ
 3.53V
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(c) The total resistance that meter B presents to the circuit is
RTB = S x Range = 20k/V x 10 V = 200 k
The parallel combination of RB and meter B is
Re2 = (RB x RTB)/(RB + RTB) = (5kx200k)/(5k+200k) = 4.88 k
Therefore, the voltage reading obtained with meter B,
determined by use of the voltage divider equation, is
VRB = E(Re2)/(Re2+RA) = 30 V x (4.88k)/(4.88k+25k)
= 4.9 V
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(d)
(Expected value - Measured value)
Voltmeter A error 
100%
Expected value
Voltmeter A error = (5 V – 3.53 V)/5 V x (100%
= 29.4%
Voltmeter B error = (5 V – 4.9 V)/5 V x (100%)
=2%
17
Five principal meter movements used
in ac instrument
1. Electrodynamometer
2. Iron Vane
3. Electrostatic
4. Thermocouple
5. D’Arsonval with rectifier
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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
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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 frequency of perhaps 0.1Hz or lower
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• 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
21
Two types of PMMC meter used in
AC measurement :
1. Half wave rectification
2. Full wave rectification
22
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
 0.5Vp
Vave Vdc  0.318Vp
Vave 
Vp


2  Vrms

 0.45Vrms
23
Cont…
• 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.
24
Cont…
•Actually, the circuit would probably be designed for fullscale 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.
E dc
0.45E rms
Rs 
 Rm 
 Rm
I dc
I dc
Sac = 0.45Sdc
25
Cont..
Commercially produced ac voltmeters that use half wave
rectification also has an additional diode and a shunt as shown
in Figure below:
26
Cont…
•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.
27
Compute the value of the multiplier resistor
for a 15Vrms ac range on the voltmeter
shown in Fig. 1.
RS
Ifs = 1mA
Ein = 15Vrms
Rm = 300Ω
Fig. 1: AC voltmeter using half wave rectification
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Method 1
The sensitivity of the meter movement,
1
1
Sdc 

 1k / V
I fs 1m
Rs
= Sdc × Rangedc – Rm
= 1k ×
0.45E rms
1
- Rm
= 1k × 0.45(10) – 300
= 4.2k
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Method 2
The AC sensitivity for half wave rectifier,
Sac = 0.45Sdc = 0.45(1k) = 450/V
Rs
= Sac × Rangeac – Rm
= 450 × 10 –300
= 4.2k
30
Method 3
Rs
=
=
0.45E rms
 Rm
I fs
0.45  10
 300
1m
= 4.2k
31
Calculate the ac and dc sensitivity and the value of the multiplier
resistor required to limit the full scale deflection current in the
circuit shown in Fig above.
32
D’Arsonval meter movement used
with full wave rectification
Fig.
2:
Full
bridge
rectifier used in an ac
voltmeter circuit
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.
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Fig. 1-2: AC voltmeter using full wave rectification
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When the 10Vrms of AC signal is applied to the circuit
above, where the peak value of the AC input signal is
E p  2 xE 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.
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Or
E avg  0.636E p  0.636( 2 xE rms )  0.9E rms
This means an ac voltmeter using full wave
rectification has a sensitivity equal to 90% of
the dc sensitivity
Sac = 0.9 Sdc
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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
37
The dc sensitivity is
1
1
Sdc 

 1k / V
I fs 1mA
The ac sensitivity is
Sac = 0.9Sdc = 0.9 (1k) = 900 /V
38
Therefore the multiplier resistor is
Rs
= Sac x Range – Rm
= 900 x 10Vrms – 500
= 8.5k
39
Note:
Voltmeters using half wave and full wave
rectification are suitable for measuring
only sinusoidal ac voltages.
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An oscilloscope is a piece of
electronic test equipment that
allows signal voltages to be
viewed, usually as a twodimensional 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
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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,

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A potentiometer is a variable resistor that functions as
a voltage 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.
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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
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Any current flow through the Galvanometer, G, wpuld
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.


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
of analog signals (e.g. volume controls on audio
equipment) and as control inputs for electronic circuits
(e.g. a typical domestic light dimmer).
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
The resistances are classified as follow:
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.
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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.
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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.
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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.
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The megger is an
instrument used for
the measurement
high resistance and
insulation resistance.
The constructional
details are shown in
fig.2.15
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Multimeter is basically a
PMMC meter.
Consists of an ammeter,
voltmeter and
ohmmeter combined,
with a function switch.
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.


DC currrents are
measured making
use a suitably
designed shunt
resistors.
Multirange ohmmeter is built with
the meter
movement, battery
cells,shunt and
series resitors

To measure AC
voltage the output
voltage is rectified
before the current
passes through the
meter using half
wave rectifier.
(i)
(ii)
(iii)
Merits
It is single meter that
performs several
measuring functions.
It has a small size
and portable.
It can made
measurements with
reasonable accuracy
(i)
(ii)
Demerits
It cannot make
precise and accurate
measurements due
to the loading effect.
Technical skill is
required to handle it

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A multimeter or a
multitester is an electronic
measuring instrument
that combines several
functions in one unit.
The most basic
instruments include an
ammeter, voltmeter, and
ohmmeter
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DC Voltage Measurements
AC Voltage RMS Measurements
DC and AC Current Measurements
Resistance Measurements
Capacitance/Inductance Measurements
Frequency/Period Measurements
Diode Measurements