Transcript EKT112 - Portal UniMAP

Week 2:
Voltage & Current Measurement
EKT112:PRINCIPLES OF MEASUREMENT
AND INSTRUMENTATION
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 (voltmeters, ammeters, wires, resistors,
capacitors, inductors, and switches) are
described below.
Voltmeters and 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).
Ammeters
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.
Voltmeter
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.
Kirchhoff laws
 Kirchhoff laws are applicable to both the
linear and not linear circuits.
 They provide a universal tool for circuit
analysis.
Kirchhoff laws
 Kirchhoff’s current law:
 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 laws
 Kirchhoff’s voltage law:
 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.
Kirchhoff laws (cont…)
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.
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)
usingKirchhoff’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
Example 2
Example 2
PART 2
EKT112
PRINCIPLES OF MEASUREMENT AND
INSTRUMENTATION
WEEKS 2-3
CURRENT, VOLTAGE & RESISTANCE
MEASUREMENT
Topics Outline
1.0Device 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 Wheatstone bridge circuit
4.0
Digital Multimeter
Objective
As introduction to the student into some
basic measurement device for current,
voltage & resistance.
1.0 CURRENT MEASUREMENT
 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
The D’Arsonval Meter Movement
 The basic moving coil
system generally referred to
as a d’Arsonval meter
movement or Permanent
Magnet Coil (PMMC) meter
movement.
 Current-sensitive device
capable of directly
measuring only very small
currents.
 Its usefulness as a
measuring device is greatly
increased with the proper
external circuitry.
Fig 1-1 The d’Arsonval meter movement
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Current from a circuit in which measurements are being made with the meter
passes through the windings of the moving coil. Current through the coil causes
it to behave as an electromagnet with its own north and south poles. The poles of
the electromagnet interact with the poles of the permanent magnet, causing the
coil to rotate. The pointer deflects up scale whenever current flows in the proper
direction in the coil. For this reason, all dc meter movements show polarity
markings.
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1.1 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
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
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
 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.
Basic DC Ammeter Circuit
Ammeter
Where
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
Fig. 1-2 D’Ársonval meter movement
used in ammeter circuit
In most circuits, Ish >> Im
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
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
Vsh  Vm
 Then the current through the shunt is,
I sh  I  I m
 By using Ohm’s law
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Cont.
Then we can get shunt resistor as
Vsh I m Rm I m
Im
Rsh 


Rm 
Rm..............1.0
I  I m 
I sh
I sh
I sh
Ohm
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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Solution:
Vm  I m Rm  1mA100  0.1V
Vsh  Vm  0.1V
I sh  I  I m  10mA  1mA  9mA
Vsh 0.1V
Rsh 

 11.11
I sh 9mA
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The Ayrton 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 = nIm
………1.1
 We can get shunt resistance with n times larger than
Im is
Rm
Rsh 
n 1
………1.3
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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.
Answ: ~ 0.80 ohm
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Advantages of the Ayrton:
 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.
Fig 1-3 Ayrton shunt circuit
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Cont.
 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 R  R  R  R
sh
a
b
c
 On this range the shunt resistance is equal to
Rsh and can be computed by Eqn
Rm
Rsh 
n 1
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Cont.
I m ( Rsh  Rm )
Rb  Rc 
I2
I m ( Rsh  Rm )
Rc 
I3
Ra  Rsh  ( Rb  Rc )
Rb  ( Rb  Rc )  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.
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Cont.
** 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
Fig. 2-3: Expected current value in a series circuit
E
Im 
R1  Rm
Fig 2-4: Series circuit with ammeter
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Cont.
hence;
Im
R1

I e R1  Rm
Therefore
Insertion error =
 Im 
1   100%
Ie 

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Example 1-3
A current meter that has an internal resistance
of 78 ohms is used to measure the current
through resistor Rc in Fig. 2.5. Determine the
percentage of error of the reading due to
ammeter insertion.
Fig. 2.5
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Solution:
Fig. 2-6
The current meter will be connected into the circuit between
points X and Y in the schematic in Fig. 2.6. When we look back into
the circuit from terminals X and Y, we can express Thevenin’s
equivalent resistance as
RTH  Rc 
Ra Rb 
Ra  Rb 
RTH = 1 k + 0.5 k = 1.5 k
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Cont.
Therefore, the ratio of meter current to expected
current:
Im
R1

I e R1  rm 
Im/Ie= 1.5 k/(1.5 k + 78) = 0.95
Solving for Im yields, Im = 0.95Ie
Insertion error = [1 – (Im/Ie)] x 100% = 5.0%
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1.2 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.
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.
Galvanometer – Application
 Are used to position the pens of analog chart (example:
electrocardiogram)