Download Employ ammeter shunts and voltage multipliers

Contents
Introduction
3
Ammeter shunts
4
Voltage multipliers
12
Digital instruments
16
Digital ammeter ‘shunts’
16
Digital voltmeter multipliers
17
Summary
21
Answers
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Introduction
The basic analogue meter movement or digital module responds to a limited
range of currents or voltages. If we want to measure quantities outside this
limited range, we need to incorporate additional resistors, either within a
multi-range instrument, or external to the instrument.
In this section, you will learn how to extend the range of an instrument using
voltage multipliers and ammeter shunts. This section will help you to
understand the construction of multi-range digital and analogue meters.
After completing this topic, you should be able to:

select an appropriate meter in terms of units to be measured, range,
loading effect and accuracy for a given application

explain how multi-range ammeters and voltmeters are built from a basic
meter movement plus additional resistors

select and use external ammeter shunts for heavy currents

follow safety precautions when measuring large currents and voltages.
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Ammeter shunts
An ammeter is connected in series with the circuit being monitored, so the
circuit current flows through the ammeter. A typical analogue meter
movement requires 15 mA for full-scale deflection.
To measure currents in excess of this, we use an ammeter shunt, which is a
resistor connected in parallel with the meter that diverts a known fraction of
the current. With the shunt in place, the full-scale deflection of the meter
now occurs at higher currents, and so the shunt serves to extend the range of
the instrument.
An ammeter shunt is a low-resistance conductor connected in parallel with
the moving-coil circuit of an ammeter as shown in Figure 1.
Figure 1: Ammeter shunt connection
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Figure 2: Arrangement of ammeter external shunt
Ammeter shunts are used internally to a meter to provide the usual switchselectable current ranges of the instrument. For measurement of even larger
currents, low-resistance shunts can be connected externally on some
instruments. Usually the shunt is separate if the current range is greater than
25 A.
An ammeter shunt must have enough capacity to prevent overheating when
being used. The resistance of the shunt must be such that almost the entire
current is carried by the shunt; only a small definite portion of the total
current is required to operate the moving coil. Because of this definite
relationship between the total current and the instrument current, the scale is
usually marked to indicate the total current directly.
With switchboard ammeters, the shunts are generally connected directly to
the busbars at the switchboard panels and are provided with special flexible
leads for connection to the instruments. As the resistance of these leads is
included in that of the moving coil when the instrument and its shunt are
being calibrated, it is important not to shorten or alter these leads, otherwise
the accuracy of the instrument will be affected. This applies also to the leads
provided with an instrument which has a set of external shunts to enable it
to be used as a multi-range ammeter. In every case, when connecting these
leads make sure there is effective contact.
Ammeter shunts are practically always constructed of manganin, an alloy of
copper, nickel and manganese. Manganin has a low resistivity, so a shunt of
manganin is reasonably small. However, the main advantage is that
manganin has a temperature coefficient of resistance of practically zero.
Therefore, its resistance is substantially constant and unaffected by
temperature variation. If an internal shunt is employed, it is very often in the
form of a wire connected across the instrument terminals. An external shunt
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of manganin brazed into slots cut in heavy copper terminal blocks is
illustrated in Figure 2.
The resistance of a shunt for a specific use may be calculated, since the moving
coil and the shunt form a parallel circuit of two branches. The voltage drop
across the instrument and the shunt is the same. Consider the instrument shown
in Figure 3 which has an initial range of 15 milliampere and 5 ohm resistance,
and suppose that it is required to operate as an ammeter capable of indicating
currents up to a maximum of 5 ampere. When the pointer of the instrument in
Figure 3 indicates a full-scale deflection, the p.d. across the moving coil is 75
millivolt and the current is 15 milliampere.
Figure 3: Digital instrument scale reading
As this full-scale position is to correspond to a current of 5 ampere in the
line, then the pd across the shunt must be 75 millivolt, and have a current of
(5 – 0.015) = 4.985 ampere.
Therefore from Ohm’s Law the resistance of the shunt is:
RS 
V
Is
0.075
4.985
RS  0.015 

The same result could be obtained from the fact that in a parallel circuit the
current in the branches is inversely proportional to their resistances, that is,
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I S RC

I c RS
RS 
I c Rc
Is
0.015  5
4.985
 0.015 

Note that in each case:
IS = current in shunt
RS = resistance of shunt
IC = current in moving coil
RC = resistance of moving coil.
In addition to requiring a resistance of 0.015 ohm, this shunt must be able to
carry 5 ampere without overheating.
For accurate indications the current must always divide between the coil and
the shunt in the same proportion, that is, the ratio must remain constant.
To make sure this happens despite the different temperature coefficients of
the manganin shunt and the copper coil, we use a swamping resistor as
shown in Figure 2. This swamping resistor consists of a manganin-wire
resistor connected in series with the moving coil, and its resistance
comprises almost the entire resistance of the moving-coil circuit. In this way
the moving-coil circuit is the equivalent of a circuit with a negligible
temperature coefficient of resistance and thus remains constant.
The initial range of a meter is increased when a shunt, with the appropriate
multiplying power, is connected in parallel for the required extended range.
total current
instrument current
I

IC
Multiplying power 
Example 1
A moving-coil galvanometer has an initial range of 50 milliampere. A shunt
enables it to function as an ammeter with a full-scale deflection of 10 A.
Determine:
(a) multiplying power of shunt
(b) current in shunt:
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Solution
(a ) Multiplying power
(b) Shunt current I S

I
IC

10
0.05
200
I  Ic
10  0.05
9.95 A
total current
instrument current
total current
multiplying power current




Multiplying power

Instrument current

That is, instrument current is:
IC 
1
 ITotal
multiplying power
the remainder being carried by the shunt.
Figure 4: Diagram for example 1
Example 2
The moving-coil movement has a resistance of 4.98 . Determine the
resistance of a shunt which would have a multiplying power of 250 when
used with this instrument to measure a circuit current of 1 A.
Ra  4.98 
I
 250
Ia
RS  ? 
I 1 A
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Figure 5: Moving coil with swamping resistor
Instrument current:
total current
multiplying power
 0.004 A
Ia 
Shunt current:
I s  I  IC
 I  0.004
I s  0.996 A
Rs 
I A  RA

Is
0.004  4.98
0.996
Rs  0.02 

A single meter can be made to measure various ranges of current by the use
of different shunts and a multi-position, single-pole switch as shown in
Figure 6.
Figure 6: Shunts and a multi-position, single-pole switch
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The higher the current range, the more current the shunt has to carry, and
consequently, the lower will be the shunt’s resistance in relation to the
resistance of the meter.
Activity 1
Work through the questions below.
1
Explain why ammeters are designed to have a very low resistance.
_____________________________________________________________________
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2
Explain why voltmeters are designed with a very high resistance.
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_____________________________________________________________________
3
Explain why a moving-coil type meter is a polarised one, that is, it is only suitable for
operation on dc.
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_____________________________________________________________________
4
Explain why and how a moving-coil meter could be used as either an ammeter or a
voltmeter.
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_____________________________________________________________________
5
Of what material are ammeter shunts normally made, and why?
_____________________________________________________________________
_____________________________________________________________________
6
If the resistance of a moving-coil meter movement is 3 Ω and its full-scale deflection
20 mA, determine the resistance of the shunt necessary to increase the meter range to:
(a) 0.5 ampere
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___________________________________________________________________
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(b) 3 ampere.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
7 Check your answers with those given at the end of the section.
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Voltage multipliers
A voltmeter is connected in parallel with the circuit component whose
voltage is being monitored, and uses the same moving coil or moving iron
or digital meter movement as does an ammeter. These movements will reach
full scale deflection at a relatively low voltage. Additional components are
required to allow these basic meters to measure larger voltages.
A voltage multiplier is a resistor connected in series with the basic meter
movement, so that a known fraction of the total measured voltage is dropped
across this resistance. With a voltage multiplier in place, the full-scale
deflection of the movement now represents a higher measured voltage, so
the multiplier extends the range of the basic instrument movement.
We can convert a moving-coil meter into a voltmeter by connecting a
voltmeter multiplier of high resistance in series with the moving coil, as
shown in Figure 7. The resistance of a voltmeter multiplier must be such
that with full-scale voltage applied, the current in the moving coil is limited
to the small value required for full-scale deflection.
Figure 7: Converting a moving-coil meter into a voltmeter
The value of the series resistor (the multiplier) may be determined by
applying Ohm’s law as shown in the following example.
Example 1
A moving-coil instrument has an initial range of 75 millivolt and a
resistance of 5 ohm. Determine the resistance of a voltmeter multiplier to be
connected in series with the coil to allow this instrument to operate as a
voltmeter capable of indicating to 150 volt.
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Figure 8: A moving coil instrument with a multiplier
Full-scale deflection current:
I
initial voltage range
RV
0.075
5
 0.015 A
= 15 mA

0.015 ampere is the maximum current which the moving coil should carry.
Hence total resistance of circuit to limit the current to 0.015 ampere when a
potential difference of 150 volt is applied, is expressed as:
R
V
Ic
150
0.015
 10 000 

The instrument coil has a resistance of 5 ohm and the resistance of the
multiplier:
= 10 000 – 5
= 9995 Ω
Note from Figure 8 that the potential difference across the multiplier:
= 150 – 0.075
= 149.925 volt
Voltmeter multipliers are usually wound with fine-gauge insulated
manganin or similar wire of low resistance temperature coefficient. The
resistance of the moving coil is such a small portion of the total resistance
that the resistance variation with temperature is negligible.
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A voltmeter multiplier may be either internal or external. A single
instrument may be a multi-range voltmeter if it is provided with a set of
multipliers. If the multiplier is internal, it may be tapped to provide various
ranges. The ranges may be selected by switching, or in some cases a separate
terminal is provided for each range. Sometimes a multi-range voltmeter has
a separately marked scale for every range and sometimes the scale is only
marked for one range. In the latter case, it is necessary to use a conversion
factor to obtain the correct measured value. For example, if a multi-range
voltmeter has a scale graduated from 0 to 150 V and it is connected to the 0
to 15 V range, any apparent value indicated by the instrument pointer will
have to be divided by 10 to obtain the correct value.
With the calculation of suitable size series resistors, any instrument can be
designed to measure any desired voltage.
A typical circuit is shown in Figure 9.
Figure 9: Multi range voltmeter with multipliers
You will observe from this diagram that the multipliers are simply a tapped
series resistor. The higher the voltage to be measured, the higher the
resistance needed.
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Activity 2
Work through the questions below.
1 A moving-coil meter has a full-scale deflection of 50 mV and a resistance of 4 Ω.
Determine the multiplier resistance needed to increase the range of the meter to:
(a) 30 V
(b) 150 V
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2
Describe what is meant by voltmeter sensitivity. How is it expressed?
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_____________________________________________________________________
3
Why is it necessary that a voltmeter not ‘load-up’ a circuit?
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
Check your answers with those given at the end of the section.
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Digital instruments
Digital meter modules also have a limited range, and again, we use external
resistors to increase the range of the instrument. The characteristic of the
digital module are however quite different from the analogue movement. In
particular:

The digital meter module responds to voltage, rather than current.

The digital meter module typically has very high input resistance.
Digital ammeter ‘shunts’
A digital ammeter can be built from the basic digital voltage module by
including a shunt resistor. The value of the shunt resistor is chosen so the
maximum current for that range causes a voltage drop across the shunt
resistor equal to the full-scale input voltage of the digital module. The
digital module takes almost no current, so the calculation is a simply based
upon Ohm’s Law. The circuit arrangement is shown in Figure 10.
Figure 10: Digital ammeter with shunt resistor
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Example 3
Calculate the value of a shunt resistor for a current range of 2 A for a digital
module that has a full-scale input voltage of 200 mV.
I in  200 mV
I FSD  2 A
Rshunt  ?
Rshunt 
Vin
I FSD
200  10 3
2
 100  10 3

 0.1 
Digital voltmeter multipliers
Unlike the analogue voltmeter which uses a single resistor in series with the
movement, the digital voltmeter uses a voltage divider network to reduce the
voltage being monitored to the level required by the basic digital module
(usually 200 mV). The concept is shown in Figure 11.
Figure 11: Digital voltmeter with voltage divider
Because of the way in which the voltage reduction network is connected, the
input resistance of a digital voltmeter is the same for all ranges. It is usually
around 10 megohm. By comparison the input resistance of an analogue
voltmeter depends on the voltage range that the meter is set to. The typical
value of input resistance for an analogue voltmeter is around 20 000 ohms
per volt.
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Example 4
Calculate the value of R1 in the circuit shown below to allow the digital
module to reach its full-scale input voltage of 200 mV if an input of 20 V is
being measured.
Figure 12: Circuit for example 4
Current flowing in R2 is:
200 mV
10 k
 2 105 V
= 20 μV
I
Therefore current flowing in R1 must also be 2 × 10–5 A.
The voltage drop across R1 is:
20  VR2  20  0.2
 19.8 V
Therefore:
19.8
2 105
 990 000 
R1 
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Activity 3
1
For the circuit shown in Figure 13, calculate the resistance and power rating of
resistors R1, R2, R3 and R4. Assume the digital module has a full scale input voltage of
200 mV.
Figure 13
2
For the circuit shown in Figure 14, calculate the voltage at the digital module terminals
(ignore any current flowing to the digital module). Assume the digital module has a
full scale input voltage of 200 mV.
Figure 14
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______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
Check your answers with those given at the end of the section.
If you have Hampson, check the hazards and precautions with instruments
on pages 40 and 41.
If you have Jenneson, refer to Sections 7.4.4 and 7.4.5 on pages 134 and
135.
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Summary
This section covered single and multi-range digital and analogue meters and
the effects of analogue meters in circuits.
Measuring current An ammeter is connected in series with the circuit
being monitored, so the entire circuit current has to flow through the
ammeter.
Ammeter shunts An ammeter shunt is a low-resistance conductor
connected in parallel with the moving-coil circuit of an ammeter. The
resistance of the shunt must be such that almost the entire current is carried
by the shunt; only a small definite portion of the total current is required to
operate the moving coil. A digital ammeter has shunt resistors like those in
an analogue ammeter.
Measuring voltage A voltmeter is connected in parallel with the circuit
component whose voltage is being monitored. A voltmeter uses the same
moving coil or moving iron or digital meter movement as does an ammeter.
In order to convert these meter modules to usable voltmeters, additional
components are required.
Voltmeter multipliers The high resistance of a voltmeter multiplier must be
such that with full-scale voltage applied, the current in the moving coil is
limited to the small value required for full-scale deflection.
Analogue voltmeter The resistance of the voltmeter circuit for each volt of
full scale deflection is expressed in ‘ohm per volt’
Voltmeter multiplier connections Voltmeter multipliers are usually wound
with fine-gauge insulated manganin or similar wire of low temperature
coefficient. Any instrument can be designed to measure any desired voltage.
Digital voltmeter The digital voltmeter uses a voltage divider network to
reduce the voltage being monitored to the level required by the basic digital
module.
Loading effect of voltmeters in circuits The value obtained for the
resistance of the circuit whose voltage is being measured will be much
lower than the true value calculated. The ‘loading effect’ of a voltmeter, can
be reduced by using a voltmeter with a high sensitivity.
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Check your progress
1
The basic moving coil meter movement can be used to measure larger currents if used
in conjunction with a:
(a) series resistor
(b) multiplier resistor
(c) shunt resistor
(d) loading resistor.
2
( )
The basic moving coil meter movement can be used to measure higher voltages,
if used in conjunction with a:
(a) shunt resistor
(b) multiplier resistor
(c) parallel resistor
(d) loading resistor.
3
( )
A 2 mA meter movement has a resistance of 70 Ω. Calculate the value of a shunt
resistor to be used if the meter is required to measure 500 mA.
_____________________________________________________________________
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_____________________________________________________________________
_____________________________________________________________________
4
A 1.5 mA meter movement has a resistance of 150 Ω. Determine the value of a
multiplier resistance to be used to read 5 V.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
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Referring to the circuit shown in Figure 15 determine the voltage across R2 if the
voltmeter has:
(a) an infinite resistance
(b) a resistance of 20 k.
Figure 15
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_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
Check your answers with those given at the end of the section.
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Answers
Activity 1
1
A particular load needs a particular current o make it operate efficiently,
a lamp or a motor. If an ammeter connected in series with it has a high
resistance, it will reduce the circuit current and thus the load will not
operate successfully. If, however, it has a very low resistance, the circuit
current will change minimally and the load will operate efficiently.
2
By having a very high resistance voltmeters take very little current and
thus consume almost no power. Since they are placed in circuit not to
use up power, but only to give a voltage reading, it is imperative then
that they have this very high resistance. Voltmeters are connected
between points of different potential, so they must have a high
resistance in order to limit the current to just enough to make the meter
indicate.
3
The magnetic field produced by current flowing in the moving coil
reacts with the magnetic field from the surrounding permanent magnet
producing a torque and turning the moving coil. A pointer attached to
the coil likewise moves past a graduated scale giving a particular
reading depending on the amount of current in the moving coil.
If there was AC in the moving coil, the field produced by it would be
continuously changing in direction such that its reaction with the
permanent magnet field would alternate each one hundredth of a
second, by trying to move the pointer first upscale then downscale. The
result of this would see the pointer wavering around zero.
The meter then is only suitable for DC, and to produce an upscale or
readable deflection must have current flowing into its + terminal and
out of its—terminal.
24
4
The moving coil moves its pointer across to full-scale deflection when
a very small applied voltage (usually millivolts) causes a very small
current (usually milliamperes) to flow in it. The meter can thus be
graduated in millivolts to read this voltage or in milliamperes to read
the current. For higher values of voltage or current, multipliers or shunts
could be used to extend its range.
5
Ammeter shunts are normally made of manganin. It is a material with
an almost zero temperature co-efficient of resistance which means that
if it gets hot with large currents flowing through it, its resistance hardly
changes. We are confident then that the currents flowing through it and
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its associated meter don’t vary in ratio, and the meter will not have its
accuracy of reading affected.
6
(a)
Figure 16
VFSD  I FSD  Rmeter
 0.02  3
 0.06 V
I sh  I - I meter
 0.5  0.02
 0.48 A
Vsh  Vmeter
 0.06 V
Rshunt 
Vsh
I sh
0.06
0.48
 0.125 

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(b)
Figure 17
I sh  I  I meter
 3  0.02
 2.98 A
Vsh  Vmeter
 0.06 V
Rshunt 
Vshunt
I shunt
0.06
2.98
 0.0201 

Activity 2
1
(a)
Figure 18
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I meter 
Vmeter
Rmeter
 I multiplier
0.05
4
 0.0125 A

Vmultiplier  V  Vmeter
 30  0.05
 29.95 V
Rmultiplier 
Vmultiplier
I multiplier
29.95
0.0125
 2396 

(b)
Figure 19
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I meter (part A) = 0.0125A
Vmultiplier  V  Vmeter
 150  0.05
 149.95 V
Rmultiplier 
Vmultiplier
I multiplier
149.95
0.0125
 11 996 

2
Voltmeter sensitivity is a term which nominates the resistance of the
voltmeter load itself for each volt of full-scale deflection. It is expressed
in ‘Ohms per volt.’ It may be calculated from the simple equation:
Ohm/volt 
3
1
Full-scale deflection in amperes
Since a voltmeter is connected in parallel with a load the circuit current
splits up between them. The break-up of current depends on the
resistance of each. If RV is equal to the load resistance then the current
splits up, half in each. This we certainly don’t want as we would like
all, if possible, of the current to flow through the load. What we want
then is a voltmeter with a resistance at least 20 times bigger than the
load resistance, in order that only a small percentage of the current
flows in the voltmeter with most of it going through the load. A large
current through the voltmeter causes a loading effect in the circuit,
an effect that is undesirable.
Activity 3
1
R1 = 1 k
R2 = 1 
R3 = 0.1 
R4 = 0.01 
2
 R  R4 
Vter min als  Vinput  3

 Rtotal 
 100 k  
 16  

 10 M  
 160 mV
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Check your progress
1
(c)
2
(b)
3
0.281 
4
3183.3 
5
(a) 50 V
(b) 44.4 V
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