Seventh Lecture
Moving Coil Instruments
Moving Coil Instruments
There are two types of moving coil instruments namely, permanent magnet moving coil type
which can only be used for direct current, voltage measurements and the dynamometer type
which can be used on either direct or alternating current, voltage measurements.
Permanent Magnet Moving Coil Mechanism (PMMC)
In PMMC meter or (D’Arsonval) meter or galvanometer all are the same instrument, a
coil of fine wire is suspended in a magnetic field produced by permanent magnet. According to
the fundamental law of electromagnetic force, the coil will rotate in the magnetic field when it
carries an electric current by electromagnetic (EM) torque effect. A pointer which attached the
movable coil will deflect according to the amount of current to be measured which applied to the
coil. The (EM) torque is counterbalance by the mechanical torque of control springs attached to
the movable coil also. When the torques are balanced the moving coil will stopped and its angular
deflection represent the amount of electrical current to be measured against a fixed reference,
called a scale. If the permanent magnet field is uniform and the spring linear, then the pointer
deflection is also linear.
Mathematical Representation of PMMC Mechanism
Assume there are (N) turns of wire and the coil is (L) in long by (W) in wide. The force
(F) acting perpendicular to both the direction of the current flow and the direction of magnetic
field is given by:
where N: turns of wire on the coil
I: current in the movable coil
F  N BI L
B: flux density in the air gap L: vertical length of the coil
Electromagnetic torque is equal to the multiplication of force with distance to the point of
suspension
W
W
in one side of cylinder
in the other side of cylinder
TI1  NBIL
TI 2  NBIL
2
2
The total torque for the two cylinder sides
W

where A: effective coil area
TI  2 NBIL   NBILW  NBIA
2

This torque will cause the coil to rotate until an equilibrium position is reached at an angle θ with
its original orientation. At this position
Electromagnetic torque = control spring torque
TI = Ts
Since
Ts = Kθ
NBA
NBA
  CI
So
where
Thus

I
C
K
K
The angular deflection proportional linearly with applied current
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Seventh Lecture
Moving Coil Instruments
pointer
F
B
S
F
W
I
L
I
N
B
1- D.c Ammeter:
An Ammeter is always connected in series with a circuit branch and measures the current
flowing in it. Most d.c ammeters employ a d’Arsonval movement, an ideal ammeter
would be capable of performing the measurement without changing or distributing the
current in the branch but real ammeters would possess some internal resistance.
+
Im
Rm
Extension of Ammeter Range:
Since the coil winding in PMMC meter is small and light, they can carry only small
currents (μA-1mA). Measurement of large current requires a shunt external resistor to
connect with the meter movement, so only a fraction of the total current will passes
through the meter.
Vm  Vsh
Im Rm  IshRsh
Ish  I T  Im
Im Rm
Rsh 
I T  Im
+
I range=IT
Ish
Rsh
Im
Rm
_
2
Seventh Lecture
Moving Coil Instruments
Example:
If PMMC meter have internal resistance of 10Ω and full scale range of 1mA.
Assume we wish to increase the meter range to 1A.
Sol.
So we must connect shunt resistance with the PMMC meter of
Rsh 
Im Rm
I T  Im
Rsh 
1  10 3  10
1  1  10  3
 0.01001
a) Direct D.c Ammeter Method (Ayrton Shunt):
The current range of d.c ammeter can be further extended by a number of shunts selected
by a range switch; such ammeter is called a multirange ammeter.
Rsh 
Im Rm
Ir  Im
+
Ish3
Ish2
Ish1
Rsh3
Rsh2
Rsh1
Im
Rm
I range2
I range3
I range1
_
b) Indirect D.C Ammeter Method:
Ir Rm  R

Im
r
Where R=Ra+ Rb+ Rc
And
r = parallel resistors
branch with the meter
Ir1
Ra
Im
Ir2
+
Ir3
Rb
Rm
Rc
_
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Seventh Lecture
Moving Coil Instruments
Example (1):
Design a multirange ammeter by using direct method to give the following ranges 10mA,
100mA, 1A, 10A, and 100A. If d’Arsonval meter have internal resistance of 10Ω and full
scale current of 1mA.
Sol:
Rm=10Ω Im=1mA
Rsh 
Rsh2 
Rsh4 
Im Rm
Ir  Im
Rsh1 
1  10 3  10
100  10  10  3
1  10 3  10
10  1  10  3
 0.101
Rsh3 
 0.0011
1  10 3  10
10  1  10  3
1  10 3  10
 0.0101
1  10  10  3
Rsh5 
 1.11
1  10 3  10
100  1  10  3
 0.00011
+
Im
Rsh4 Rsh3
Rsh5
Rsh2
1mA
Rm
10Ω
Rsh1
100mA
10A 1A
_
10mA
100A
Example (2):
Design an Ayrton shunt by indirect method to provide an ammeter with current ranges
1A, 5A, and 10A, if PMMC meter have internal resistance of 50Ω and full scale current of 1mA.
Sol.:
Rm=50Ω
IFSD=Im=1mA
Ir Rm  R

Im
r
1A
10A
Rm
Rb
Rc
For 1A Range:
I1 Rm  R

Im
R
Im
5A
+
Where R=Ra+ Rb+ Rc
And
r = parallel resistors
branch with the meter
1-
Ra
_
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Seventh Lecture
2-
1A 50  R

1mA
R
For 5A Range:
I 2 Rm  R

Im Rb  Rc
3-
Moving Coil Instruments
R=0.05005Ω
r =Rb+Rc
5 A 50  0.05005

1mA
Rb  Rc
Ra=R-(Rb+Rc)
For 10A Range:
Rb+Rc= 0.01001Ω
Ra=0.05-0.01001=0.04004 Ω
I 3 Rm  R
r =Rc

Im
Rc
10 A 50  0.05005
Rc=5.005x10-3 Ω

1mA
Rc
Rb=0.01001-5.005x10-3= 5.005x10-3 Ω
2- D.C Voltmeter:
A voltmeter is always connect in parallel with the element being measured, and measures
the voltage between the points across which its’ connected. Most d.c voltmeter employ PMMC
meter with series resistor as shown. The series resistance should be much larger than the
impedance of the circuit being measured, and they are usually much larger than Rm.
Rs  RT  Rm
Vrange
Rs 
 Rm
Im
Im=IFSD
The ohm/volt sensitivity of a voltmeter
Is given by:
Rm
1

Sv 

 rating
VFSD I FSD V
+
Rs
Im
VRange
Rm
_
Rm  Rs
1



VRange
I Range V
So the internal resistance of voltmeter or the input resistance of voltmeter is
S Range 
Rv= VFSD x sensitivity
Example:
We have a micro ammeter and we wish to adapted it so as to measure 1volt full scale, the meter
has internal resistance of 100Ω and IFSD of 100μA.
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Seventh Lecture
Moving Coil Instruments
Sol.:
V
1
 Rm
Rs 
 100  9900  9.9 K
Im
0.0001
So we connect with PMMC meter a series resistance of 9.9KΩ to convert it to voltmeter
Rs 
Extension of Voltmeter Range:
Voltage range of d.c voltmeter can be further extended by a number of series resistance
selected by a range switch; such a voltmeter is called multirange voltmeter.
a) Direct D.c Voltmeter Method:
In this method each series resistance of multirange voltmeter is connected in direct with
PMMC meter to give the desired range.
Rs1
V
Rs    Rm
Im
Im
V1
Rs2
Rm
+
V2
Rs3
V3
o/p of voltmeter
_
b) Indirect D.c Voltmeter Method:
In this method one or more series resistances of multirange voltmeter is connected with
PMMC meter to give the desired range.
Rs1 
Rs 2 
V1
 Rm
Im
V 2  V1
Im
V 3 V 2
Rs 3 
Im
Rs1
Rs2
Rs3
Im
V2
Rm
V1
V3
+
_
O/P
Example (1):
A basic d’Arsonval movement with internal resistance of 100Ω and half scale current
deflection of 0.5 mA is to be converted by indirect method into a multirange d.c voltmeter with
voltages ranges of 10V, 50V, 250V, and 500V.
Sol:
IFSD = IHSD x 2
IFSD = 0.5mA x 2 =1mA
V1
10
Rs1 
 Rm
Rs1 
 100  9.9 K
Im
1mA
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Seventh Lecture
Rs 2 
Rs 2 
Rs 3 
Rs 4 
V 2  V1
Im
50  10
1  10  3
250  50
Moving Coil Instruments
Rs1
 40 K
3
Rs4
Rs3
Im
50V
Rm
 200 K
1  10
500  250
1  10  3
Rs2
250V
500V
10V
 250 K
+
_ O/P
Example (2):
Design d.c voltmeter by using direct method with d’Arsonval meter of 100Ω and full
scale deflection of 100μA to give the following ranges: 10mV, 1V, and 100V.
Sol:
Rs1
V
Rs    Rm
Im
Rs1 
Im
Rm
V1
 Rm
Im
100mV
Rs2
+
1V
Rs3
100V
o/p of voltmeter
_
10mV
 100  0
100A
1
Rs 2 
 100  9.9 K
100  10  6
100
Rs 3 
 100  99.9 K
100  10  6
Rs1 
3- Ohmmeter and Resistance measurement:
When a current of 1A flows through a circuit which has an impressed voltage of 1volt, the
circuit has a resistance of 1Ω.
V
R
I
There are several methods used to measure unknown resistance:
a) Indirect method by ammeter and voltmeter.
This method is inaccurate unless the ammeter has a small resistance and voltmeter have a
high resistance.
Rx
Rx
A
V
high resistance
A
V
Low resistance
7
X=fixed,
σ=change
Seventh Lecture
Moving Coil Instruments
b) Series Ohmmeter:
Rx is the unknown resistor to be measured, R2 is variable adjusted resistance so that
the pointer read zero at short circuit test. The scale of series ohmmeter is nonlinear with
zero at the right and infinity at extreme left. Series ohmmeter is the most generally used
meter for resistance measurement.
E
R2
A
∞
0
Rx
c) Shunt Ohmmeter:
Shunt ohmmeter are used to measure very low resistance values. The unknown
resistance Rx is now shunted across the meter, so portion of current will pass across this
resistor and drop the meter deflection proportionately. The switch is necessary in shunt
ohmmeter to disconnect the battery when the instrument is not used. The scale of shunt
ohmmeter is nonlinear with zero at the left and infinity at extreme right.
E
R2
S
0
A
∞
Rx
d) Voltage Divider (potentiometer):
The meter of voltage divider is voltmeter that reads voltage drop across Rs which
dependent on Rx. This meter will read from right to left like series ohmmeter with more
uniform calibration.
R2
Rs
V
∞
0
Rx
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