CHAPTER 2
DC CURRENT METER
2.1
Introduction
A meter is any device built to accurately detect and display an electrical quantity in a
form readable by a human being. Usually this "readable form" is visual: motion of a
pointer on a scale, a series of lights arranged to form a "bargraph," or some sort of display
composed of numerical figures.
The display mechanism of a meter is often referred to as a movement, borrowing from its
mechanical nature to move a pointer along a scale so that a measured value may be read.
Though modern digital meters have no moving parts, the term "movement" may be
applied to the same basic device performing the display function.
The design of digital "movements" is beyond the scope of this chapter, but mechanical
meter movement designs are very understandable. Most mechanical movements are
based on the principle of electromagnetism: that electric current through a conductor
produces a magnetic field perpendicular to the axis of electron flow. The greater the
electric current, the stronger the magnetic field produced. If the magnetic field formed by
the conductor is allowed to interact with another magnetic field, a physical force will be
generated between the two sources of fields. If one of these sources is free to move with
respect to the other, it will do so as current is conducted through the wire, the motion
(usually against the resistance of a spring) being proportional to strength of current.
The essential requirements of a measuring instrument are:
a) that its introduction into the circuit where measurements are to be made, should
not alter the circuit.
b) the power consumed by it be small.
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Types of instrument are mainly used as ammeter and voltmeters are:
1) PMMC (For DC measurement only)
2) Moving Iron
3) Electrodynamometer
4) Hot wire
5) Thermocouple
6) Induction Type
7) Electrostatic
8) Rectifier
PMMC instrument is the most accurate type for DC measurement.
2.2
Construction and function of Permanent Magnet Moving coil (PMMC)
meter movement
The basic moving coil system generally referred to as a D’Arsonval meter movement or
Permanent Magnet Moving Coil (PMMC) meter movement.
Figure 2.1: The Construction of D’Arsonval meter movement
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Figure 2.1 shows a horseshoe shaped permanent magnet with soft iron pole pieces
attached to it. Between the north-south pole pieces is a cylindrical-shaped soft iron core
about which a coil of fine wire is wound. This fine wire is wound on a very light metal
frame and mounted in a jewel setting so that it can rotate freely. A pointer attached to the
moving coil deflects up scale as the moving coil rotates.
Operation:
Figure 2.2: The D’Arsonval meter movement
Current from a circuit in which measurements are being made with the meter passes
through the windings of the moving coil (refer to Figure 2.2). 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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A meter designed to measure electrical current is popularly called an "ammeter" because
the unit of measurement is "amps."
In ammeter designs, external resistors (low resistance), Rsh added to extend the usable
range of the movement are connected in parallel with the meter movement resistance,
Rm. This is because we want to divide the measured current, not the measured voltage,
going to the movement, and because current divider circuits are always formed by
parallel resistances.
Figure 2.3 shows the basic dc ammeter circuit.
Im
Rm
Ish
Rsh
I
Figure 2.3: D’Arsonval meter movement used in an ammeter circuit
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
Voltage drop across the meter movement, Vm = Im Rm
Voltage drop across the shunt resistance, Vsh = Ish Rsh
Since the shunt resistance, Rsh is in parallel with the meter movement, therefore,
Vsh = Vm
The total current or full scale deflection current for the ammeter, I = Im + Ish
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∴Ish = I - Im
To determine the shunt resistance, Rsh
Rsh =
Vsh
I R
= m m
I sh I − I m
Example:
Calculate the value of the shunt resistance required to convert a 1mA meter movement
with a 100Ω internal resistance into 0 to 10mA ammeter.
Solution
The purpose of designing the shunt circuit is to allow us to measure a 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
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We know
Rsh =
Vsh
I R
= m m
I sh I − I m
=
I m Rm
nI m − I m
=
Rm
n −1
Example:
A 100µA meter movement with an internal resistance of 800Ω is used in a 0 to 100mA
ammeter. Find the value of the required shunt resistance.
Solution:
The multiplication factor, n =
∴ Rsh =
2.3
I
100mA
=
= 1000
I m 100 µA
Rm
800
800
=
=
≈ 0.80Ω
n − 1 1000 − 1 999
The Ayrton Shunt
For a multiple range ammeter, the Ayrton shunt or the universal shunt, is frequently a
more suitable design. The advantages of the Ayrton shunt are that it eliminates the
possibility of the meter movement being in the circuit without any shunt resistance and it
may be used with wide range of the meter movements. Figure 2.4 shows the Ayrton shunt
circuit.
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Im
Rm
Rsh
Rc
Rb
Ra
I − Im
I3
I1
I2
I
Figure 2.4: The Ayrton shunt circuit
Refer to Figure 2.4, the shunt resistance, Rsh = Ra + Rb + Rc
At range T1:
Rsh1 = Ra + Rb + Rc is parallel with Rm, where Ish1 = I1 – Im
Vsh1 = Ish1 Rsh1 = Ish1 (Ra + Rb + Rc) = Vm = Im Rm
At range T2:
Rsh2 = Rb + Rc, is parallel with (Rm + Ra)
Rsh1 = Ra + Rb + Rc
Vsh2
= Ish2 (Rb + Rc) = Vm + Im Ra
(I2 – Im)(Rb + Rc)
I2 (Rb + Rc)
= Im Rm + Im Ra
= Im (Rm + Ra) + Im (Rb + Rc)
= Im (Rm + Ra + Rb + Rc)
= Im (Rm + Rsh)
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(Rb + Rc)
=
I m ( Rm + Ra )
I2
At range T3:
Rsh3 = Rc, is parallel with Rm + Ra + Rb
Vsh3
= Ish3 (Rc)
= Im (Rm + Ra + Rb)
(I3 – Im) Rc
= Im (Rm + Ra + Rb)
I3 Rc
= Im (Rm + Ra + Rb + Rc)
Rc
=
Rsh1 = Ra + Rb + Rc
I m ( Rm + Rsh )
I3
∴Rb = (Rb + Rc) - Rc
Example:
Compute the value of the shunt resistors for the circuit in Figure 2.5.
Im = 100 µA
Rm = 1kΩ
Rsh
Rc
Rb
Ra
I 3 = 1A I 2 = 100mA I 1 = 10mA
Figure 2.5: Ayrton shunt circuit
Solution:
At terminal 1, I = I1 = 10mA
The multiplication factor, n =
I1
10m
=
= 100
I m 100µ
The total shunt resistance, Rsh1 =
Rm
1k
=
= 10.1Ω
n − 1 100 − 1
∴Rsh1 = Ra + Rb + Rc = 10.1Ω
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At terminal 2, I = I2 = 100mA
The total shunt resistance, Rsh2
Rsh 2 = Rb + Rc =
I m( Rm + Ra ) 100µ (10.1 + 1k )
=
= 1.01Ω
100m
I2
Ra = Rsh1 – Rsh2
= (Ra + Rb + Rc) – (Rb + Rc)
= 10.1 – 1.01
=9.09Ω
At terminal 3, I = I3 = 1A
The total shunt resistance, Rsh3
Rsh 3 = Rc =
I m ( Rm + Rsh1 ) 100µ (1k + 10.1)
=
= 0.101Ω
1
I3
Rb = Rsh2 – Rsh3 =(Rb + Rc) – Rc = (1.01 – 0.101) = 0.909Ω
2.4
D’Arsonval meter movement used in a DC voltmeter
The basic D’Arsonval meter movement can be converted to a dc voltmeter by connecting
a multiplier Rs in series with the meter movement as shown in Figure 2.6.
Im
Rs
Rm
Figure 2.6: The D’Arsonval meter movement used in a dc voltmeter
The purpose of the multiplier is to extend the voltage range of the meter and to limit
current through the D’Arsonval meter movement to a maximum full-scale deflection
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current. To find the value of the of the multiplier resistor, we must determine the
sensitivity, S of the meter movement.
Sensitivity, S =
1 Ω
(
)
V
I fs
and
Rs = S X Range – Internal Resistance
Example:
Calculate the value of the multiplier resistance on the 50V range of a dc voltmeter that
used a 500µA meter movement with an internal resistance of 1kΩ.
Solution:
Sensitivity, S =
1
1
=
= 2k Ω
V
I fs 500µ
Multiplier, Rs = S X Range – internal Resistance
= (2k X 50) – 1k
= 99kΩ
2.5
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 than without. Therefore, the voltage across
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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.
Examples:
Two different voltmeters are used to measure the voltage across resistor R2 in the circuit
of Figure 2.7. The meters are as follows.
Meter A
: S = 1kΩ/V, Rm = 0.2kΩ, range = 10V
Meter B
: S = 20kΩ/V, Rm = 1.5kΩ, range = 10V
Calculate:
a) Voltage across R2 without any meter connected across it.
b) Voltage across R2 when meter A is used.
c) Voltage across R2 when meter B is used
d) Error in voltmeter readings.
RA = 25kΩ
E = 30V
RB = 5kΩ
Figure 2.7: Circuit for voltmeter loading
Solution:
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2.6
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.
R1
X
Ie =
Ie
E
R1
E
Y
Figure 2.8: Expected current value in a series circuit
R1
X
Im =
Im
Rm
E
Y
Figure 2.9: Series circuit with ammeter
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E
R1 + Rm
hence;
Im
R1
=
I e R1 + Rm
Therefore
⎛ I ⎞
Insertion error = ⎜⎜1 − m ⎟⎟ x100%
Ie ⎠
⎝
2.7
The Ohmmeter (Series ohmmeter)
The ohmmeter consists of battery, resistor and PMMC. The basic ohmmeter circuit is
shown in Figure 2.10.
Rz
Ifs
0.1Rz
Rm
0 .9 R z
E
X
Y
Figure 2.10: Basic ohmmeter circuit
The full-scale deflection current, I fs =
E
R Z + Rm
Function of RZ and Rm are to limit the current through the meter.
To determine the value of unknown resistor, Rx, The Rx is connected to terminal X and
Y. Figure 2.11 shows the basic ohmmeter circuit with unknown resistor, Rx connected
between probes.
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Rz = variable resistor
Rz
Ifs = 50 µA
R1
0.1Rz
Rm = 1kΩ
0.9 Rz
E = 1.5V
X
Y
Rx
Figure 2.11
: Basic ohmmeter circuit with unknown resistor, Rx connected between
probes.
The circuit current, I =
E
RZ + Rm + R x
The ratio of the current, I to the full-scale deflection current, Ifs is
E
R + Rm + R x
R Z + Rm
I
P=
= Z
=
E
R Z + Rm + R x
I fs
RZ + R m
Example
A 1mA full-scale deflection current meter movement is to be used in an ohmmeter
circuit. The meter movement has an internal resistance, Rm, of 100Ω, and a 3V battery
will be used in the circuit. Mark off the meter face for reading resistance.
Solution:
The value of Rz, which will limit current to full-scale deflection current, is
RZ =
E
3
− Rm =
− 100 = 2.9kΩ
I fs
1m
The value of Rx at 20% full-scale deflection is
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Rx =
=
R Z + Rm
− ( R Z + Rm )
P
2.9k + 0.1k
− (2.9k + 0.1k )
0 .2
= 12kΩ
The value of Rx at 40% full-scale deflection is
Rx =
3k
− 3k = 4.5kΩ
0 .4
The value of Rx at 50% full-scale deflection is
Rx =
3k
− 3k = 3kΩ
0.5
The value of Rx at 75% full-scale deflection is
Rx =
3k
− 3k = 1kΩ
7 .5
P (%)
Rx (kΩ)
Rz + Rm(kΩ)
20
12
3
40
4.5
3
50
3
3
75
1
3
100
0
3
Table 2.1: Scale of ohmmeter
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Figure 2.12: Ohmmeter scale showing nonlinear characteristics
2.8
Shunt type Ohmmeter
The shunt type of ohmmeter given in Figure 2.13 consists of a battery in series with
adjustable resistor Rz, and a D’Arsonval movement. The unknown resistance is connected
in parallel with the meter, across the terminal X and Y.
Figure 2.13: Shunt type ohmmeter
In this circuit it is necessary to have an ON/OFF switch to disconnect the battery from the
circuit when the instrument is not used.
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2.9
Multiple range ohmmeters
The ohmmeter circuit discussed in the previous section is not capable of measuring
resistance over a wide range of values.
∴need to extend our discussion of ohmmeters to multi range ohmmeters. Figure 2.14
shows a circuit for multi range ohmmeter.
Ifs = 50 µA
Rm = 2kΩ
R ×1
Rs = 28kΩ
10Ω
R ×10 100Ω
R ×100
E = 1.5
X
1kΩ
Y
Figure 2.14: Circuit for multi range ohmmeter.
This instrument makes use of a basic meter movement with an internal resistance, Rm. An
additional resistance is provided by Rz, which includes a fixed resistance and zeroing
potentiometer. Rz is necessary to limit the current through the meter movement when a
test probes connected to X and Y are shorted together.
When the instrument is on the Range X 1, a resistor R1 is parallel with the meter
movement.
∴the internal resistance Rm, of the ohmmeter on the R X 1 range is R1 in parallel
with (Rm + Rz), which approximate to R1. This mean the pointer will deflect to midscale
when a Rt (value of Rt equal to R1) is connected across X and Y.
When the instrument is set to the range R X 10, the total resistance of the
ohmmeter is equal to R2 in parallel with (Rm + Rz), which approximately R2.
∴the pointer deflects to midscale when a R2 resistor is connected between the test
probes. Midscale is marked as R1. Therefore, the value of the resistor is determined by
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multiplying the reading by the range multiplier of 10 producing a midscale value of R2
(R1 X 10).
When our ohmmeter is set on the R x 100 range, the total resistance of the
instrument is R3 in parallel with (Rm + Rz), which still approximately R3. Therefore, the
pointer deflects to midscale when we connect the test probes across a test resistor, Rt (Rt
= R3). This provides us a value for the midscale reading of 10 multiplied by 100.
Example:
1) In Figure 2.15, determine the current through the meter, Im, when a 20kΩ resistor
between terminals X and Y is measured on the R X 1 range.
2) Show that this same current flows through the meter movement when a 200Ω
resistor is measured on the R X 10 range.
3) Show that the same current flows through the meter movement when a 2kΩ
resistor is measured on the R X 100 range.
Rm = 2kΩ
E = 1.5V
R = 10Ω
Rs = 28kΩ
Rx = 20Ω
X
Y
Figure 2.15: Circuit for ohmmeter
Solution:
a) At R X 1 range,
VR
=
10
X 1.5V
10 + 20
= 0.5V
The current through the meter, Im
=
0 .5
= 16.6 µA
30 K
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b) At R X 10 range,
VR
=
100
X 1.5V
100 + 200
= 0.5V
The current through the meter, Im
=
0 .5
= 16.6 µA
30 K
=
0 .5
= 16.6 µA
30 K
c) At R X 100 range,
VR
=
1k
X 1.5V
1k + 2k
= 0.5V
The current through the meter, Im
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