CHAPTER 2
DC and AC Meters
1
PART 1 (DC) PART 2 (AC)
• Introduction to DC • Introduction to AC
meters meters
• D’ Arsonval meter
• D’ Arsonval meter movement (half-wave
movement rectification)
• DC ammeter • D’ Arsonval meter
• DC voltmeter movement (full-wave
• DC ohmmeter rectification)
• Loading effects of AC
• Loading effects of DC meter
meter
2
PART 1 – DC METERS
Meters
Digital Meters
Measure the continuous voltage/ current signal at discrete points in time.
The signal converted from analog signal (continuous in time) to a digital signal
(discrete instants in time)
Analog Meters
Based on the d’Arsonval meter movement which implements the readout
mechanism.
3
INTRODUCTION
HOW CAN WE MEASURED CURRENT AND
VOLTAGE?
Im
Rm
Torque (T)
PMMC instrument
T = BxAxNxI [N.m]
4
ADVANTAGES AND DISADVANTAGES
OF MOVING COIL INSTRUMENT
AMMETER, VOLTMETER AND OHMMETER?
DC Ammeter : The shunting resistor Rsh and d’Arsonval
movement form a current divider
DC Voltmeter : Series resistor Rs and d’Arsonval movement
form a voltage divider.
Ohmmeter : Measures the current to find the resistance
Rs
Rsh
Rs
6
DC AMMETER
D’Arsonval movement, Rm || (shunt resistor), Rsh
To limit the amount of the current in the movement’s
coil by shunting some of it through Rsh
Rsh = resistance of the shunt
I Rm = internal resistance of the meter
movements (movable coil)
Ish Im
d'Arsonval movement
Ish = shunt current
Rsh Rm
Im = full scale deflection current of the
meter movement
I = full-scale deflection current for
the
ammeter | | = Parallel symbol 7
DC AMMETER
Vm = ImRm Vsh = IshRsh
Vsh = Vm
I
Ammeter Terminal
IshRsh = ImRm
Ish Im
Rsh = ImRm / Ish (Ω) ----(a)
d'Arsonval movement
Rsh Rm I = Ish + Im Ish = I – Im
Therefore, Rsh = ImRm/(I – Im)
Purpose I >>n Im , n = multiplying factor
n=I/Im
I = nIm ---(b)
Substitute b to a
Rsh = ImRm/(nIm – Im)
Rsh= Rm/(n-1) -----(c)
8
EXAMPLE 1 (DC AMMETER)
Example 1: DC Ammeter
A 100uA meter movement with an internal
resistance of 800Ω is used in a 0 - 100 mA
ammeter . Find the value of the required shunt
resistance.
Solution:
n = I/Im = 100 mA / 100 µA = 1000
Thus,
Rsh = Rm / (n – 1) = 800 / 999 = 0.8 Ω
9
THE ARYTON SHUNT
Rsh = Ra + Rb + Rc
Most sensitive
range 1A
Ra Im
Rm
1 mA Rsh ----(c)
n 1
S 5A
+ Rm
Rshunt
Rb
50
10A
Rc
-
•Used in multiple range ammeter
•Eliminates the possibility of the moving coil to
be in the circuit without any shunt resistance
10
THE ARYTON SHUNT
At point B, (Rb+Rc)||(Ra+Rm)
I1 Ra Im
Middle
sensitive S I2
B VRb Rc VRa Rm
range + Rb Rm
Rshunt
(Rb + Rc )(I2 -Im) = Im(Ra +Rm)
I3
Rc Since,
-
Ra = Rsh – (Rb + Rc),
yield,
I2 (Rb + Rc ) – Im(Rb+Rc) = Im [Rsh – (Rb + Rc ) + Rm]
I m ( Rsh Rm )
Rb Rc ----(d)
I2
11
THE ARYTON SHUNT
At point C, Rc||(Ra+Rb+Rm)
I1
Ra Im VRc VRa Rb Rm
I2
(I3-Im)Rc = Im(Ra+Rb+Rm)
+ Rb Rm
Rshunt
S
I3Rc = Im(Ra+Rb+Rc+Rm)
C
I3 I3Rc = (Rsh+Rm)
Rc
-
I m ( Rsh Rm )
Rc ----(e)
I3
12
THE ARYTON SHUNT
Substitute eqn (d) into eqn (e), yields
1 1
Rb I m ( Rsh Rm ) ----(f)
I 2 I3
Ra = Rsh – (Rb+Rc) ----(g)
13
EXAMPLE 2: THE ARYTON SHUNT
Calculate the value for Ra, Rb and Rc as shown, given the
value of internal resistance, Rm=1kΩ and full scale current of
the moving coil = 100 µA. The required range of current are:
I1 = 10 mA, I2 = 100 mA and I3 = 1A.
I1 Ra Im
I2
B
S
+ Rb
Rshunt
Rm
I3
Rc
-
14
AMMETER INSERTION EFFECT
R1 R1
X X
Ie Connect Im
Ammeter
E E Rm
Y I e I m 100% Y
E InsertionError E
Ie Ie
Im
R1 R1 Rm
Im R1
I e R1 Rm
InsertionError
Ie Im
100%
Ie
15
EXAMPLE 3: AMMETER INSERTION
EFFECTS
A current meter that has an internal resistance of 78Ω is used
to measure the current through resistor R1. Determine the
percentage of error of the reading due to ammeter insertion.
R1
X
Im
1kΩ
3V E Rm
16
SOLUTION EX:3
17
DC VOLTMETER
• DMM become VOLTMETER – multiplier Rs
in series with the meter movement.
To extend the
voltage range
PURPOSE
To limit current through the DMM to a
maximum full-scale deflection current
DMM = D’Arsonval Meter Movement
18
DC VOLTMETER
Rs Im
+
Rm
1 Unit derivation:
Sensitivit y (Ω/V)
I fs 1 1 ohms
Sensitivit y
Ifs= Im = full scale deflection current amperes volt volt
ohms
Rs + Rm= (S x Vrange)
It is desirable to make
R(voltmeter) >>R ( circuit)
19
EXAMPLE 4: DC VOLTMETER
Calculate the value of the multiplier resistance
on the 50 V range of a dc voltmeter that used a
500µA d’Arsonval meter with an internal
resistance of 1 kΩ.
20
MULTI-RANGE VOLTMETER
A multi-range voltmeter consists of a
deflection instrument, several multiplier
resistors and a rotary switch.
30 v R1 only one of the three multiplier resistors is
10 v connected in series with the meter at any time.
R2 The range of this meter is
S
V Im( Rm R)
+ 3v
R3
Im Rm
- Where the multiplier resistance,
R can be R1 or R2 or R3
Multi-range Voltmeter
21
MULTI-RANGE VOLTMETER
R1
30 v
10 v The multiplier resistors are connected in series, and
R2
S
each junction is connected to one of the switch
+ 3v terminals. The range of this voltmeter can be also
R3 calculated from the equation
V Im( Rm R)
Im Rm
-
A commercial version of a Where the multiplier, R, now can be
multi-range voltmeter
R1 or (R1 + R2) or (R1 + R2 + R3)
(Note: the largest voltage range must be
associated with the largest sum of the multiplier
resistance)
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EXAMPLE 5: MULTI-RANGE VOLTMETER
Calculate the value of the multiplier resistance for the
multiple range dc voltmeter circuit shown in Figure (a)
and Figure (b), if Ifs = 50μA and Rm = 1kΩ
R1
R1 30 v
3v 10 v
10 v R2
R2 S
S
+ 30 v
+ 3v
R3
R3
Im Rm
Im Rm
- -
Fig b
Fig a
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VOLTMETER LOADING EFFECT
RA
RT = Rs +Rm
Rs Im
E
VRB RB
Rm Req = RB //RT
Rs Rm
Ifs= Im Vrange
S
Rs= (S x Vrange) - Rm
Total voltmeter resistance, RT
Vrange = ( Rs + Rm) Im RT = Rs + Rm = S x Vrange
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VOLTMETER LOADING EFFECT
Calculation:
1) RT = Rs + Rm = S x Vrange
2) Req = RB // RT
RB
3) Without volt-meter VRB xE
(expected value) R R
A B
Req
VRB
m
4) With volt-meter xE
(measured value) Req R A
5) Insertion error
VRB VRB
m
x100%
VRB
25
EXAMPLE 6: VOLTMETER LOADING
EFFECT
RA
RT = Rs +Rm
Rs Im
E
VRB RB
Rm Req = RB //RT
A volt meter (0-10V) that has an internal resistance of
78Ω is used to measure the voltage across resistor RB.
Determine the percentage of error of the reading due to
voltmeter insertion. Let E = 4V, RA=RB = 1kΩ , S =
1kΩ/V
26
DC OHMMETER
Basic Ohmmeter circuit
Fixed portion
Rz
Ifs
0.1Rz 0.9Rz Rm
Variable E
X Y
portion
Rx
27
DC OHMMETER
Before measuring the Rx, the Ωmeter is set to “zero”-calibration
Definition zero = shorting the terminal x-y & adjust Rz to obtain
the full-scale deflection on the meter movement.
E
I fs w/o Rx
Rz Rm
I < Ifs
E
I with Rx
Rz Rm Rx
28
DC OHMMETER
Relationship between full-scale deflection to
the value of Rx is :
I Rz Rm
P
I fs Rz Rm Rx
This equation is used for marking off the scale on the
meter face of the ohmmeter to indicate the value of a
resistor being measured
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EXAMPLE 7:DC OHMMETER
A 1 mA 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 3 V battery will be used
in the circuit. If the measured resistor has resistance of 1kΩ,
mark off the meter face for the reading (20%, 40%, 50%, 75%
and 100%) .
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SOLUTION EX:7
Ohm
4.5k 3k
12k 50% 1k
40%
75%
20%
0
∞
0% 100%
Full scale
percentage
31
MULTIPLE-RANGE OHMMETER
The previous section is not capable of measuring resistance
over wide range of values.
We need to extend our discussion of ohmmeters to include
multiple-range ohmmeters Ifs R - fixed resistance &
z
zeroing potentiometer
Rm
R1
Rx1
R2
R x 10
R3
R x 100
E
X Y
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END OF PART 1
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