To measure voltage (ac,dc), current (ac, dc) and resistance, two types of instruments, analog and digital meters, are utilized. The measurements of these fundamental electrical quantities are based on either one of the following: i) Current sensing. The instruments are mostly of the electromagnetic meter movement type, such as an analog multimeter. ii) Voltage sensing. The instruments are mostly electronic in nature, using amplifiers and semiconductor devices, such as a digital multimeter.
1) ANALOG MULTIMETER
The main part of an analog multimeter is the D’Arsonval meter movement also known as the permanent-magnet moving-coil (PMMC) movement. This common type of movement is used for dc measurements. The basic construction of a such meter movement is shown in
Figure 1.
Figure 1.
When the meter current I m
flows in the wire coil in the direction indicated in Figure 1, a magnetic field is produced in the coil. This electrically induced magnetic field interacts with the magnetic field of the horseshoe-type permanent magnet. The result of such an interaction is a force causing a mechanical torque to be exerted on the coil. Since the coil is wound and permanently fixed on a rotating cylindrical drum as shown, the torque produced will cause the rotation of the drum around its pivoted shaft.

When the drum rotates, two restraining springs, one mounted in the front onto the shaft and the other mounted onto the back part of the shaft, will exhibit a countertorque opposing the rotation and restraining the motion of the drum. This spring-produced countertorque depends on the angle of deflection of the drum,
θ, or the pointer. At a certain position (or deflection angle), the two torques are in equilibrium.
Each meter movement is characterized by two electrical quantites:
1.
R m
: the meter resistance which is due to the wire used to construct the coil.
2.
I
FS
: the meter current which causes the pointer to deflect all the way up to the full-scale position on the fixed scale (this is marked FS in Figure 1). This value of the meter current is always referred to as the fullscale current of the meter movement.
Figure 2 indicates the electrical circuit symbol of the meter movement that will be used.
I m
R m
Figure 2.
The meter sensitivity S, also referred as the ohm/volt rating of the meter movement, is the reverse of the full-scale current.
S
=
1
I
FS
Ω
V (1)
I
FS
or S (fixed value) is defined for a given meter movement and is usually noted on its casing or in the manufacturer's data sheets. The meter becomes more sensitive as its full-scale current decreases. Typically the minimum value of I
FS
is 50
µ
A and hence the maximum value of S is 20 K
Ω
/V.
The PMMC movement cannot be used directly for ac measurements since the inertia of
PMMC acts as an averager. Because ac current has zero average value and it produces a torque that has also zero average value, the pointer just vibrates around zero on the scale. In order to make ac measurements, a bridge rectifier circuit is combined with PMMC as shown in Figure 3. i

I i(t) i
1
(t) i (t)
Bridge rectifier
I i
1
(t)
-I
T/2
0
T
Figure 3.
T/2 T
In Figure 3 the bridge rectifier rectifies the ac current i and produces the current i
1
=|i| which has a mean value (average or dc value). i
1 , mean
=
1
T / 2
T /
0
∫
2 i
1
( t ) dt
=
1
T / 2
T /
∫
0
2
I sin(
ω t ) dt
=
2
π
I
(2)
The rms (root-mean-square) value of a periodic waveform i(t) of period T is defined as i rms
=
1
T
T
∫
0 i 2 ( t ) dt (3)
The form factor of the same waveform is the rms value divided by the mean value of the full-wave rectified waveform or equivalently
Form Factor ( FF )
= i rms i
1 , mean
(4)
On the ac scale, an analog multimeter is calibrated to read the rms value of a sine wave.
Since the rms value and the form factor of a sine wave of peak value I are I / 2 and 1.11, respectively, the meter indication corresponds to the value 1 .
11
× i
1 , mean
(
=
I / 2 ) .

When measuring the rms values of other waveforms, the analog multimeter measures the mean value of the rectified signal and multiplies with 1.11 as if it is a sine wave. Thus, the analog multimeter gives wrong results for rms values of other waveforms. In order to calculate true rms values of other waveforms, their form factors should be taken into account, e.g., the factor of a triangular wave is 1.155 and the form factor of a square wave is 1.0. Then for a triangular wave the analog multimeter indication corresponds to 1.11/1.155 times the true rms value and it corresponds to 1.11/1.0 times the true rms value for a square wave.
A) AMMETER
As pointed out above, the deflection of the pointer in the D’Arsonval meter movement is proportional to the meter current I. Therefore, this instrument can be used to measure current.
However, the meter movement by itself is of limited use and capability, since its full-scale current value I
FS
is practically too small (at most in the order of milliamperes). If the current allowed to flow in the movement, I m
, exceeds I
FS
, permanent damage can result, in particular to the restraining springs.
To be able to measure currents higher in value than I
FS
of a given meter movement, the division principle is applied. Figure 4 shows the construction of an ammeter.
I
A
Symbol
I
Ammeter
Actual circuit
I sh
I m
R m
R sh
Figure 4.
Here I m
=
I
R m
R sh
+
R sh
(5) where I m
is the movement current, I the circuit current being measured, R m
the resistance of the movement, and R sh
the "shunt" resistance connected in parallel with the movement to provide a path for the portian of the circuit's current not allowed to flow though the meter movement.

A given meter movement can be used to build a multirange ammeter. Each range requires a different value of the shunt resistance. A three-range ammeter, requiring three different shunt resistors, is shown in Figure 5.
R m
R sh1
Multi-position switch
R sh2
R sh3
Figure 5.
The resistance of the ammeter R
A
is thus
R
A
=
R
R m m
+
R sh
R sh
(6)
Because usually R sh
<< R m
then R
A
≈
R sh that is the equivalent resistance, R
A
is approximately equal to the smaller of the two parallel connected resistors, R sh
.
It is indicated that as the range of a multirange ammeter is changed, R sh
will be different and the ammeter's resistance, R
A
, will be different for the different ranges.
The ammeter must be connected in series with a terminal pair through whieh the current is to be measured. For example, to measure the current I flowing through terminals A and B in
Figure 6(a), the ammeter is conneeted as shown in Figure 6(b).
A A
I
A
E E
B
(b)
B
(a)
Figure 6.
In order for this measurement process not to disturb the value of the current being measured, the resistance of the ammeter (which is series connected) should ideally be zero so that the circuit remains unchanged. However, a practical ammeter has a finite but small

resistance, R
A
, which could disturb the circuit conditions and change the current distribution in the circuit. This is what is called the meter's loading effect.
B) VOLTMETER
The meter movement is modelled as a resistance of value R m
, as shown in Figure 7.
Therefore, Ohm's law applied to this movement provides (8)
V m
=
R m
I m
(7) where V m
is the voltage across the meter movement when the current flowing in it is I m
.
When the current in the movement is I
FS
,
V
FS
=
R m
I
FS
(8)
To increase the full-scale voltage range of the movement when functioning as a voltmeter, the meter movement current I m has to be lowered. This can easily be achieved by inserting a large resistance, called the multiplier resistance, R mult
, in series with the meter movement, as shown in Figure 7.
Voltmeter
Actual circuit
I m
V
V
Symbol
R mult R m
V
Figure 7.
The resistance of the voltmeter, R v
, is the series combination of R m
and R mult
as can be seen from Figure 7.
R v
=
R mult
+
R m
=
V max
I
FS
=
V max
×
1
I
FS
= range of voltmeter
×
S (9)
Eq. (9) is quite important. It indicates that the higher the range of the voltmeter, the larger would be internal resistance of the voltmeter, R v
. This is a clear since a higher voltage range requires a larger multiplier resistance. Also, Eq. (9) indicates that a more sensitive meter movement (higher S or lower I
FS
) also results using a larger voltmeter resistance.

Using the same meter movement, a multirange voltmeter can be designed. A three-range voltmeter is shown schematically in Figure 8.
Multi-position switch R mult1
R mult2
R mult3
R m
Figure 8.
The voltmeter must be connected in parallel with a terminal pair across which the potential difference is to be measured. For example, to measure the voltage V’ across the terminals A and B in Figure 9(a) the voltmeter is connected as shown in Figure 9(b).
A
A
V’
E E
V
B
(b)
B
(a)
Figure 9.
In order for this measurement process not to disturb the value of the potential difference being measured, the resistance of the voltmeter (which is parallel connected) should ideally be infinity so that the circuit remains unchanged. However, a practical voltmeter has a finite but large resistance, R v
, which could disturb the circuit conditions and result in reading errors called loading effect errors. To reduce the loading effect, I m
must be very small or R v
must be made as large as possible. Examining Eq. (10) reveals that R v
is increased by using a higher sensitivity meter movement or 'by using a higher range to read the voltage which may not always be acceptable because of the reading errors near the lower end of the scale.
C) OHMMETER
If the meter movement current I m
is somehow made to be proportional to the value of an unknown resistance to be measured, the meter's scale can be calibrated to read resistance directly. Here, however, a voltage source (e.g., a battery) must be added to the meter’s circuit to drive the current necessary for the deflection of the pointer. A typical ohmmeter circuit is

shown in Figure 10.
Zero-adjust resistor
I
E
R
2
I m
R
1
R m
Black
I
R x
Resistance being measured
Ohmmeter’s circuit
Figure 10.
The total resistance seen by the voltage source E is
Red
R
T
=
R x
+
R
2
+
R
R
1
1
+
R m
R m
=
R x
+
R
MS
(10) where the quantity R
2
+
R
R
1
R
1
+ m
R m
is denoted by R
MS
. The current I flowing in the source and
I
=
E
R
T
=
R x
+
E
R
MS
(11)
The meter movement current I m
can be determined using the current-division principle,
I m
=
I
R
1
R
1
+
R m
=
R x
+
E
R
MS
×
R
1
R
1
+
R m
(12)
When R x
=
∞
(i.e., an open circuit), I m
= 0 but when R x
= 0 (i.e., a short circuit), I m should be at its maximum value, as the total resistance of the circuit is at its minimum value
[see Eqs. (11) and (12)]. Therefore, R x
= 0
Ω
should correspond to I m
becoming I
FS
, the full-scale current of the meter movement. Thus from Eq. (12),
I
FS
=
E
R
MS
×
R
1
R
1
+
R m
(13)
Hence, the ohmmeter (resistance) scale is inverted with respect to the current and voltage scales (Figure 11). Eq. (12) indicates that the resistance scale is nonlinear; it is sparse near the R x
= 0 position and crowded near the R x
=
∞
position. When R x
= R
MS
is substituted in
Eq. (12), then

I m
=
E
2 R
MS
×
R
1
R
1
+
R m
=
I
FS
(14)
2
This indicates that the meter movement current will be half its full-scale value when the value of the unknown resistance is R
MS
.
Figure 11.
Referring to Figure 10, one should note that
1. The battery is connected so that it drives the meter movement current I m into the positive (red) terminal of the movement, in order to cause an upscale deflection of the pointer.
Therefore, the current in the external resistance flows from the negative (black) terminal toward the positive (red) terminal, as shown, due to the battery polarity connections.
2. R
2
is a series connection of two resistors: one of them fixed and the other one (about
20% of Rı) variable. The variable resistor is called the "zero-adjust resistor". When R is zero
(i.e., a short circuit is connected across the ohmmeter terminals), the pointer should deflect all the way up to the full-scale position [see Eq. (13)]. Because the battery voltage E does decay
(change) with time, readjustment of the value of R
2
, through the zero-adjust resistor, is necessary to compensate for this battery voltage change. This is usually an initial checking procedure to ensure that the ohmmeter would function properly; otherwise, the source should be replaced by a new battery.

Figure 12. The analog multimeter used in the laboratory.
D) CURRENT MEASUREMENT
To measure current, the instrument should be set to a A.C. or D.C. range (lower-left part in Figure 12), and the range should be set from lower-right part. Red values and black values, which are maximum values to be measured, are for AC current and DC current measurements, respectively. Then multimeter should be connected in series apparatus to be tested. The currents are measured from the middle-upper part of the multimeter that again red and black scales are for AC and DC current measurements, respectively. To give an example, if it is set to DC and 5 mA scales, then the current should be measured from 0-50 scale on the highest scale which 50 corresponds to 5 mA. Then if the drum is steady at 10, the current measured is 1 mA.
Generally speaking, the power absorbed in the instrument is negligible, but in cases of low voltage heavy current networks, theinclusion of a meter may reduce the current appreciably below the value which would otherwise prevail. The potential drop at full scale deflection across the meter terminals is in the order of 500 mV on all D.C. ranges, except the
50
µ
A range which has a drop of 125 mV. In the case of A.C., it is less than 250 mV on all ranges.
The care should be taken to ensure that the circuit is "dead" before breaking into it to make current measurements.

E) VOLTAGE MEASUREMENT
To measure voltage, the instrument should be set to a suitable A.C. or D.C. range, and then connected parallel across the source of voltage to be measured. The range should be set from upper-right part. If the expected magnitude of the voltage is within the range of the meter, but its actual value is unknown, the instrument should be set to its highest range, connected up and if below 1000 V the appropriate selector knob should be rotated decreasing the ranges step by step, until the most suitable range has been selected.
On D.C. ranges, the meter consumes only 50
µ
A at full scale deflection, this sensitivity corresponding to 20,000 ohms/volt. In the case of A.C. ranges from 10 V upwards, full-scale deflection is obtained with a consumption of 1 mA (1000 ohms/volt). The 2.5 V A.C. range consumes 10 mA at full scale deflection.
F) RESISTANCE MEASUREMENT
On resistance ranges, the meter must not merely start from its instrument zero, but must have, in addition a resistance zero corresponding to the full scale deflection of the meter.
Before carrying out tests for resistance a check and, if necessary, adjustment should be carried out to ensure that when the leads are joined, together the meter actually indicates zero ohms, irrespective of the condition of the battery (within the limits of adjustment). The method of adjustment is given below.
1. Set left-hand knob at “
Ω
-OHMS”.
2. Join probes together.
3. Set right-hand knob to “x 1 k
Ω
” or “x 100
Ω
” from the middle-right part (green part).
4. The drum should be steady at zero on the green scale. If it is not, arrange knob on the upper-left part until the drum is steady at zero.
If it is not possible to obtain zero ohms setting, or furthermore the pointer position does not remain constant, falls steadily, the internal battery (or batteries) should replaced. To test a resistance, the right-hand knob should be at the range required, the leads being connected across unknown component. However, the value, where the drum is steady, should be multiplied by the selected ohm range. For example, if “x 1 k
Ω
” is selected and the drum is on
10 on the green scale, the value of the resistance is 10 k
Ω
.
It should be noted that a positive potential appears at the negative terminal of the

instrument when set for resistance tests. A resistance of component should be measured when it is not connected to any circuit that resistance test should never be carried out on components which are already carrying current on or when it is connected to a circuit.
2) DIGITAL MULTIMETER
While most analog meters require no power supply, give a better visual indication of trends and changes, suffer less from electric noise and isolation problems, and, are simple and inexpensive, digital meters offer higher accuracy and input impedance, unambiguous readings at greater viewing distances, smaller size, and a digital electrical output (for interfacing with external equipment) in addition to visual readout.
The main part of most of the digital multimeter (DMMs) is the analog to digital converter (A/D) which converts an analog input signal to a digital output. While specifications may vary, virtually such multimeters are developed around the same block diagram of Figure 13.
Figure 13.
Since the DMM is a voltage sensing meter; current is converted to volts by passing it through a precision low resistance shunt while ac is converted to dc at the AC converter by employing rectifiers and filters. Most of the AC converters detect the peak value of the signal and are calibrated to give the rms value of a sine wave. However, some measures the mean of the rectified signal such as the digital multimeter Agilent 34401A. Finally, this dc level is applied to the A/D converter to obtain the digital information.

For resistance measurement, the meter includes a precision low current source that is applied across the unknown resistor. Then the dc voltage drop across the resistor, which is proportional to the value of the unknown resistor, is measured.
For AC measurements, the digital multimeter is a true rms instrument that it measures true rms value of any periodic signal.
Figure 14. The digital multimeter used in this laboratory.
A) VOLTAGE MEASUREMENT
To measure voltage, the instrument should be set to a A.C. or D.C. range (the buttons of
“DC V” and “AC V”). The red probe should be connected to upper-right socket and black one to middle-right socket as indicated in Figure 14. The digital multimeter is an auto-range device that it is not needed to arrange the range of voltage.
B) CURRENT MEASUREMENT
To measure current, the instrument should be set to a suitable A.C. or D.C. range. For this purpose, firstly, blue “Shift” button is depressed then “DC V” or “AC V” button is depressed. The red probe should be connected to lower-right socket and black one to middle-right socket.
C) RESISTANCE MEASUREMENT
To measure resistance, the “
Ω
2W” button should be depressed without selecting blue
“Shift” button. The red probe should be connected to upper-right socket and black one to middle-right socket as in voltage measurement.