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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.
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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).
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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.
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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.
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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.
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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.
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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)
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Example 2
 Kirchhoff Law when applied to capacitor and inductor
usually produce differential equations.
 KVL
dI
L  IR  VC  Vs (t )  0
dt
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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.
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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
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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
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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
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1.0
Current Measurement
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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
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Permanent Magnet Moving Coil
Instrument (PMMC)
 There are TWO(2) types of moving coil
instruments;
 Permanent Magnet Moving Coil
 Dynamometer Type
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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.
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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.
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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.
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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
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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
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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.
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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.
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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
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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.
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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
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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
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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
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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

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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.
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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.
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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
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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 )
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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.
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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.
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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.
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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.
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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.
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Galvanometer – Application
 Are used to position the pens of analog chart (example:
electrocardiogram)
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