This document discusses voltage, current, resistance and power measurements using analog instruments. It describes the operating principles of moving coil meters for measuring DC current and voltage. A moving coil meter consists of a coil suspended in a magnetic field that deflects proportional to the current or voltage. Higher current and voltage ranges are achieved using shunt and multiplier resistors. The document also covers resistance measurement using an ohmmeter, and compares analog and digital instruments.

1. │ Topic 2 │
Voltage, current, resistance and
power measurements
EE2201
Measurements
& Instrumentation

2. Learning objectives:
 Operating principles of moving coil meter
 DC current and voltage measurement, shunt and
multiplier
 Resistance measurement, operating principles of
ohmmeter
 Multi-range ammeter and voltmeter, multimeter
 Power measurement
 Comparison of analogue and digital instruments
 DC Wheatstone Bridge and its application in
overcoming loading effect

3. Sensing Equipment: Moving Coil Instrument
 To measure the value of voltage and current, sensing
equipment is necessary. Permanent-magnet moving-coil
(PMMC) instrument is a simple sensing equipment. (Fig. 2-1)
 It consists of a coil of copper wire suspended in the field of
a permanent magnet.
 Current in the coil produces a magnetic field that interacts
with the field from the magnet, and causes the coil to
deflect in an anti-clockwise direction.
 A pointer connected to the coil deflects over a calibrated
scale, indicating the amount of current flowing in the coil.

4. Construction of PMMC instrument
Fig. 2-1

5. Construction of PMMC instrument
 Permanent magnet : provides two different poles at pole
shoes to generate magnetic field.
 Soft-iron core : to minimize the air gap so as to provide
strongest level of magnetic flux to the core.
 Moving coil : to sense the measured current. The larger
the current, the more the pointer deflects.
 Pointer : to indicate the measured value. It has counter
weight attached at the end to provide mechanical
balance of moving system.
 Spiral spring : to generate controlling force to balance
the deflecting force of pointer. Also it has a mechanical
zero control to set the pointer at zero scale.

6. Construction of PMMC
 Scale : to indicate the measured quantity. The scale
should be calibrated to the wanted range.
 Deflection Fundamental :
 Two forces are involved : deflecting force and
controlling force.
 Deflecting force is generated by the current
flowing into coil (Fig. 2-2a).
 Controlling force is generated by spiral spring to
balance the deflecting force (Fig. 2-2b)

7. Fig. 2-2a

8. Fig. 2-2b
At equilibrium,
Deflecting = Controlling,
torque, Td torque, Tc
Since Td ∝ I and
Tc ∝ θ
∴ I ∝ θ
i.e. current proportional to
angle of deflection,
the meter has a linear scale

9. Measurement of DC Current
Three basic rules:
• Connect the meter in series with the load.
Failure to observe this rule may result in
permanent damage to the instrument.
• Use a meter with a full-scale current rating that
is greater than the maximum current expected.
• Use a meter with internal resistance lower than
that measured. (i.e., <1:100)

10. Ammeter Circuit
 The current flowing in the meter is :
where
Im= meter current (A)
E = source voltage (V)
Rs = internal resistance of power source (Ω)
Rm = internal resistance ammeter (Ω)
R1 = load resistance (Ω)
 If R1 >> Rs and Rm ,
1
RRR
E
I
ms
m
++
=
1R
E
Im =
Rs
E
Rm
R1
Fig. 2-3 Ammeter
circuit
Im

11. Example 2-1
Find the current flowing in the meter in the following circuit
if R1 = 15 kΩ.
Solution :
Since R1 is very much greater
than RS and Rm,
Im = E/R1
= 10/(1.5 x 104
)
= 6.7 x 10 -4
A
= 0.67mA
R1
Rs=9Ω
E=10V
0-1 mA
Rm= 68 Ω
Im

12. Example 2-2
Solution
Since R1 is much greater than Rm, its parallel effect is negligible
mA
V
RR
E
I
ms
m
130
689
10
=
Ω+Ω
=
+
=
Find the current that would flow in the meter in Example 2-1
if it is incorrectly connected in parallel with R1.
The meter current is too high for the full-scale rating (1
mA) and may probably damage the instrument.
Rs=9Ω
E=10
V
R1
0-1 mA
Rm= 68 Ω

13. Effect on Low-resistance Circuit
With same example, what happen if R1 is 150Ω?
Solution :
The approximate current is I = E/R1 = 10/150 = 66.7mA.
Actual current is I = E/(R1+ Rm+ RS) = 10/(150+68+9) = 44.1mA
%2.51%100
1.44
1.447.66
% =
−
= xerror

14. Obtaining Higher Current Scales
 A basic dc meter has a very small and single current scale
due to small wire size (typical range : 0-100 µA, 0-1 mA)
 To measure larger currents, shunt resistor in parallel with
the meter is used as shown in Fig 2-4.
Rm
RS
I Im
IS
Fig 2-4 Extend the range of
moving coil meter

15. Obtaining Higher Current Scales
I = range of ammeter
Im = full scale current of moving coil meter
Is = current flowing in the shunt resistor
RS
Rm
I Im
IS
Vm
Fig 2-5 Ammeter circuit design
Given the full scale
current of the moving coil
meter and the ammeter,
we have to calculate RS.
m
mm
S
m
S
mmm
mS
II
RI
I
V
R
RIV
III
−
==∴
=
−=

16. Example 2-3
A moving coil meter with full scale current of 100 µA and
internal resistance of 500 Ω is used to measure 1mA full scale.
(a) How much current in the meter and RS at full scale flows?
(b) Determine RS.
(a) At full-scale, Im = 100 µA
IS = 1 mA – Im = 0.9 mA
1 mA
RS
0-100 µA
Rm= 500 Ω
Im=100 µA
IS=0.9mA
V
(b) V = ImRm= 0.05 V
RS = V/IS = 0.05/0.0009
= 55.56 Ω
Solution:

17. Example 2-4
A 0-to-50 µA dc meter movement, with a coil resistance Rm
of 1250Ω, is used with a shunt resistor to measure a full-
scale current of 500µA. Sketch the circuit arrangement
and calculate the value of RS.
Solution :

18. R1=11.1
R2=1.01
R3=0.1
1mA
10mA
100mA
0-100uA
R = 100m
I
Ω
Ω
Ω
Ω
Multi-range Ammeter
 In Fig 2-6, the 0-100µA meter
can be used to convert full-
scale readings to 1mA, 10mA
and 100mA by switching to
different shunting resistors.
 The disadvantage of this type
of arrangement is that the shunt
is disconnected during
switching and hence high
current may damage the meter.
 To solve this problem, make-
before-break switch is used.Fig 2-6a

19. Multi-range Ammeter
 Another type of circuit,
universal shunt circuit
shown in Fig 2.6b
resolve the above
problem even ordinary
switch is employed.
 The main point is that
the shunt exist while
switching.
R1=1.11
0-100uA
R = 100m
I
10mA 1 mA
R2=10Ω Ω
Fig 1-6b
Ω

20. Measurement of DC Voltage
Moving coil meter can be used to measure voltage if a
multiplier resistor is connected in series as shown in Fig 2-7.
Fig 2-7 Voltmeter circuit

21. Example 2-5
Calculate the value of the multiplier resistor Rmx required in
Fig. 2-7 for a full-scale voltage E of 10V.
Solution
Ω=
Ω==+
=+
−
kR
k
A
V
R
I
E
RR
mx
mx
fsd
mmx
5.99
100
10
10
500 4

22. Voltmeter Sensitivity & DC Voltmeter Resistance
Voltmeter Sensitivity :

The sensitivity of a voltmeter is specified in terms of ohms
per volt (Ω/V).
 Sensitivity φ = 1/IFS
where IFS is the full-scale current of the moving coil
instrument
Voltmeter Resistance :

The resistance of a dc voltmeter is :
Rm = EFS x φ Ω
where Rm = the resistance of the voltmeter in ohms (Ω)
EFS = the range of the voltmeter in volts (V)
φ = the sensitivity of the meter in ohm per volt (Ω/V)

23. Sensitivity ratings for dc voltmeters :
Full-scale Moving
coil Current
Sensitivity (ψ )
1mA 1 kΩ /V
100μ A 10 kΩ /V
50μ A 20 kΩ /V
20μ A 50 kΩ /V
10μ A 100 kΩ /V

24. Using Voltmeter
Three basic rules :
1. Connect the voltmeter across the load, i.e. in
parallel with the load. (see Fig. 2.8)
2. Select a voltmeter that has a full-scale range that
is greater than the highest potential expected.
3. Make sure that the voltmeter has an input
resistance that is very high (i.e. >100:1)
compared with the circuit resistance.
Fig 2-8
Voltmeter connection

25.  If rule 1 is not obeyed, the voltmeter is connected to a load
in series, this may cause improper operation of the circuit
since the voltmeter resistance is added to the circuit
resistance.
 If rule 3 is not obeyed. Error reading will occur. (See Fig. 2-
9)
Fig 2-9
Loading effect of
voltmeter

26. Ideally, E2 should be
V
Vx
Mk
M
E
RR
R
E
67.6
10
1500
1
21
2
2
=
Ω+Ω
Ω
=
+
=
( )( )
V98.3
V10x
M33.0k500
M33.0
E
RR
R
E
M33.0
M5.0M1
M5.0M1
R
eq1
eq
2
eq
=
+
=
+
=
=
+
=
ΩΩ
Ω
Ω
ΩΩ
ΩΩ
therefore,
Practically, the internal resistance Rm (5V x 100kΩ/V = 0.5MΩ) of
voltmeter is in parallel with R2. Therefore R2 becomes Req.

27. 
 The above example shows the loading of the voltmeter
causes 40% error.
 To reduce the error, digital voltmeter may be employed
since it has larger input resistance (typically 10 MΩ).
%3.40%100
67.6
67.698.3
% −=
−
= xerror

28.  The accuracy of DVM is quite good. It can be described as
, 4 digit or , etc. The half digit refers to
the most significant digit and can be either 0 or 1.
Whereas the other digits can be 0-9.
Alternative Sensing Equipment : Digital Voltmeter
 A digital voltmeter (DVM) uses an analogue-to-digital
converter (ADC) to convert analogue dc voltage to a digital
word.
digit-
2
1
3 digit-
2
1
4
Signal
conditioning
circuit
Analogue to
digital
converter
decoder displayVoltage to
be measured
Fig 2-10 Block diagram of a digital voltmeter

29. Comparison of Analog and Digital Instruments
Feature Digital Meter Analog Meter
Reading error Lower Higher
Accuracy Higher Lower
Resolution Higher Lower
Range
selection
Auto (for some
meters)
Manual
Polarity
selection
Auto (indicates a ‘-’
sign when the
terminal is reversed)
Pointer attempts to
deflect to the left of
zero when the
polarity is reversed
Robustness Not usually damaged
by rough treatment
Can be irreparably
damaged when
dropped

30. Measurement of Resistance
R1 : standard resistance
Rm : meter resistance
Rx : resistance to be measured
Current Im :
mx
b
RRR
E
++
=
1
mI
Fig 2-11a Basic series ohmmeter circuit

31.  If Rx = 0, R1 and Rm are selected so as to give FSD which is
marked as zero ohm (right most).
 When terminal A & B are open-circuited, i.e. Rx is infinity,
the pointer is marked as infinity (left most).
 If Rx with a value between zero & infinity, the pointer
position is on the scale.
 At mid-scale, Rx = R1 + Rm, since Im = IFS/2.
Fig 2-11b Ohmmeter scale

32. Example 2-6
The series ohmmeter in Fig. 2-12 is made up of a 1.5 V
battery, a 100μA meter, and a resistance R1 which makes (R1 +
Rm) = 15 kΩ.
(a) Determine the instrument indication when Rx=0.
(b) Determine how the resistance scale should be marked at
0.5 FSD, 0.25 FSD, and 0.75 FSD.
1.5 V
Ifsd =100μA
Fig 2-12

33. Solution
(a) Im = Eb/(Rx+R1+Rm)
= 1.5/(0+15 kΩ)
= 100 µA (FSD)
(b) At 0.5 FSD : Im = 100 µA/2
= 50 µA
Rx+R1+Rm= Eb/I
Rx = Eb/Im - (R1+Rm)
= 1.5V/50 µA - 15 kΩ
= 15 kΩ
At 0.25 FSD : Im = 100 µA/4
= 25 µA
Rx = 1.5V/25 µA - 15 kΩ
= 45 kΩ

34. At 0.75 FSD : Im = 0.75 x 100 µA
= 75 µA
Rx = 1.5 V/75 µA - 15 kΩ
= 5 kΩ

35. Ohmmeter With Zero Adjust
Figure 2-13

36. Ohmmeter With Zero Adjust
 Since battery in the ohmmeter falls with use, the
instrument scale will be incorrect.
 R1 cannot be used to adjust zero since mid-scale value
will otherwise no longer equal to the resistance as
before.
 Parallel resistor R2 is added for zero control.
 New supply current Ib will be :
the meter voltage is : Vm=Ib(R2//Rm)
the meter current will be :
 Each time ohmmeter is used, terminals A and B are first
short-circuited for FSD. The scale reading then remains
correct.
m21x
b
b
R//RRR
E
I
++
=
m
m2b
m
R
)R//R(I
I =

37. Example 2-7
The ohmmeter circuit in Fig2-13 has Eb = 1.5 V, R1 = 15 kΩ,
Rm=50Ω, and meter FSD=50μA. Determine
(a) the value of R2;
(b) the value of Rx at 0.5 FSD and
(c) the new value of R2 if Eb drops to 1.3 V.

38. Solution
(a) Vm = Im x Rm
= 50μA x 50Ω
= 2.5mV
Ib = (Eb – Vm)/R1
= (1.5 – 0.0025)15000
= 99.83 μA
I2 = Ib - Im
= 99.83 μA - 50μA
= 49.83 μA
R2 = Vm / I2 = 2.5x10-3
/ 49.83x10-6
= 50.17 Ω

39. Solution
(b) At 0.5 FSD, Rx = R1 + (R2 // Rm) = 15000 + (50.17 // 50) =
15.025 k Ω
(c) When Eb drops to 1.3 V
Ib = (Eb – Vm)/R1
= (1.3 – 0.0025)15000
= 86.5 μA
I2 = Ib - Im
= 86.5 μA - 50μA
= 36.5 μA
R2 = Vm / I2 = 2.5x10-3
/ 36.5x10-6
= 68.49 Ω

40. Multi-meter
Fig 2-14
Volt-Ohm-Milliammeter (VOM)

41. Multi-meter
 Multi-meter can measure voltage, current and resistance. The
main selector switch connects the shunt, multiplier, or range
resistors, as required.
 Most instrument include a rectifier to allow reading ac values.
 When using a multimeter, the same rules as in individual
ammeters, voltmeter and ohmmeter should be followed, for
example, connection to circuit in parallel for voltage
measurement.
 It is a good practice to store multimeter in the OFF position. An
analogue passive volt-ohm-milliammeter (VOM) without OFF
position, the switch should be set to the highest DC VOLTS range
position.
 When using a VOM, begin with highest range voltage or current
position, and then work down to readable deflection.
 Neither type of basic dc PMMC meter can correctly indicates the
ac value. However it can be done if a rectifier or integrated
circuit rms-to-dc converter is used.

42.  Digital multi-meter (DMM) uses any of several
technologies : transistor, integrated circuits, or digital
circuitry.
 VOM vs. DMM :
– VOM is better in the presence of strong EM fields.
– DMM may not operate properly in the EM field.
– VOM has low sensitivity, and different input
impedance (internal resistance) in different range.
– DMM has higher input impedance (internal
resistance) (e.g. 10MΩ) for voltage measurement,
and keep constant at various ranges.

43. Wattmeter
Fig 2-15 Electrodynamometer circuit
Electrodynamometer wattmeter is used to measure
power using two sets of coil.
L1, L2 - fixed coils
L3 - moving coil

44. Electrodynamometer
 Unlike PMMC, the electrodynamometer creates magnetic
field from the current flowing in the windings of coils L1
through L3.
 Coils L1 and L2 are stationary, while coil L3 is free to move
and is attached to the meter pointer.
 The magnetic fields of L1 and L2 will reinforce each other
and will interact with the field of L3 to create a rotational
force on coil L3. Hence the pointer deflects an amount that
is proportional to the square of the average current.
 The electrodynamometer used to measure current, the dial
scale is calibrated in terms of rms current.
Electrodynamometer voltmeter can be built from a
multiplier resistor in series with meter movement.

45. Wattmeter
Figure 2-16 Electrodynamometer used as a wattmeter.

46. Electrodynamometer as Wattmeter
 The fixed coils (L1 & L2) are designed to carry a heavy
current and are connected in series with the load as
current-measuring element.
 The moving coil (L3) is wound of a much finer gauge of
wire and is connected across the load and serves as the
voltage-measuring element.
 The deflection of the pointer depends on the
interaction of the magnetic fields produced by
stationary & movable coils. Hence it is proportional to
the product of the V & I and the unit is in Watt.
 Electrodynamometer is suitable for use in d.c. and low
frequency a.c. circuit.

47. F
M
Current (fixed) coils
Voltage (moving)
coil
Deflecting torque
∝ IF IM
∝ IL VL
∝ power
Fig 2-17 Schematic diagram of using wattmeter to measure power

48. Multi-range Wattmeter
Fig 2-18a
 Current ranges (0.5A and
1A) can be changed by
switching two field coils
from series to parallel
connection.
 Voltage ranges (60V, 120V
and 240 V) can be made by
switching different values
of multiplier resistors.

49. Multi-range Wattmeter
Figure 2-18b
The FSD will be the
multiplication of both
current and voltage selection.
Current Voltage FSD
1A 120V 120W
1A 240V 240W

50. Using Wattmeter
 Before connecting a wattmeter into a circuit, check the
mechanical zero of the instrument and adjust it if
necessary.
 While connecting with load, current circuit of the
wattmeter must be connected in series, but voltage
circuit must be in parallel.
 If a multi-range wattmeter is connected into a circuit,
select a voltage range equal or higher than the supply
voltage. Select the highest current, and then switch
down to give the greatest on-scale deflection.
 Electro-dynamic wattmeters are useful for measurement
on supply frequencies up to a max. of 500Hz.

51. Use of Bridge Circuit in typical sensor application
 The operation of many primary sensors depends upon
the variation of the electrical resistance of a
conductor in response to variations in the measured
variable.
 When the variation in resistance is large, the change
can be readily measured directly.
 When the variation in resistance is small, such as
resistance strain gauge and thermo-resistance
temperature sensors, bridge technique is used to give
an accurate measurement.
 The Wheatstone Bridge technique is used in
conjunction with resistive transducers whose
electrical variations are relative small.

52.  There are two ways of using the Wheatstone
Bridge technique:
- in the balanced condition;
- in the unbalanced condition.
The choice of which depends primarily upon the
type of measurement being undertaken.

53. Wheatstone Bridge in balanced condition
R1 , R2 - Precision resistors
R3 - Unknown resistor
R4 - Variable precision
resistor
E
A
B D
C
R1 R2
R4
R3
G
Eo
Fig 2.19
To determine the resistance of R3 , the variable resistor is
adjusted until the zero-center galvanometer G indicates
null.

54.  Initially, the galvanometer should be shunted to protect
it from excessive current level as shown in Fig 2.20.
 As null approaches, the shunting resistance is gradually
increased until G indicates zero with the resistor open-
circuited.
Fig 2.20

55. Balanced condition of Wheatstone bridge
Fig 2.21 shows the voltage
and current throughout the
bridge when it is balanced.
When G indicates zero, IG = 0,
∴ VB = VD
So that V1 = V2 and V3 = V4
∴ I1R1 = I2R2 ………..(2.1)
I1R3 = I2R4 ………..(2.2)
Divide eqt. 2.2 by 2.1, we
have:
4
2
1
3
2
4
1
3
R
R
R
Ror
R
R
R
R
=
=
Fig 2.21

56.  At balance, no current flows through the galvanometer.
The galvanometer appears as an open-circuit and will
not cause loading effect to the circuit
 The accuracy of the measuring result depends on the
accuracy of the precision resistors
 The supply voltage does not affect the balance condition
but the bridge sensitivity

57. Solution:
R3 = R1R4/R2
= Ω=5760
500
)1800)(1600(
Example 2.8
A Wheatstone bridge has the following arm values:
R1 = 1.6 kΩ, R2 = 500 Ω, R3 is unknown, and R4 = 1.8 kΩ.
What value of R3 brings the bridge into the null condition?

58. Example 2.9
A Wheatstone bridge has ratio arms R1 and R2, both of which may
be set to 1 kΩ, 100 Ω or 10 Ω. The variable arm R4 is adjustable
from 1 Ω to 10 kΩ in 1 Ω step. Describe, with the aid of circuit
diagram, how R3 of about 58 Ω may be measured most accurately.
To obtain the most accurate result,
R4 should be as large as possible
while the ratio should be as
small as possible.
4
2
1
3 R
R
R
R =
2
1
R
R
10Ω
E G
1kΩ
R3
≅ 58Ω R4 ≅ 5800Ω
Solution:
Since