EKT112PRINCIPLES OF MEASUREMENT

AND INSTRUMENTATIONWEEK 4

CURRENT, VOLTAGE & RESISTANCE

MEASUREMENT

Topics Outline1.0 Device for Current Measurement

1.1 Analog ammeter1.2 Galvanometer

2.0 Device for Voltage Measurement2.1 Analog voltmeter2.2 Oscilloscope2.3 Potentiometer

3.0 Device for Resistance Measurement3.1 Ohmmeter3.2 Megger

4.0 Multimeter

2.0 VOLTAGE MEASUREMENT

2.1 Voltmeter

A voltmeter is an instrument used for measuring the potential difference between two points in an electric circuit.

A voltmeter is placed in parallel with a circuit element to measure the voltage drop across it and must be designed to draw very little current from the circuit so that it does not appreciably change the circuit it is measuring.

To accomplish this, a large resistor is placed in series with the galvanometer.

Its value is chosen so that the design voltage placed across the meter will cause the meter to deflect to its full-scale reading.

A galvanometer full-scale current is very small: on the order of milliamperes.

Voltmeter – Principle of Operation

The moving coil galvanometer is one example of this type of voltmeter. It employs a small coil of fine wire suspended in a strong magnetic field.

When an electrical current is applied, the galvanometer's indicator rotates and compresses a small spring.

The angular rotation is proportional to the current that is flowing through the coil.

For use as a voltmeter, a series resistance is added so that the angular rotation becomes proportional to the applied voltage.

8

D’Ársonval Meter Movement Used In A DC Voltmeter

The basic d’Ársonval meter movement can be converted to a dc voltmeter by connecting a multiplier Rs in series with the meter movement

The purpose of the multiplier: is to extend the voltage range

of the meter to limit current through the

d’Arsonval meter movement to a maximum full-scale deflection current.

Fig 2-1 The basic d’Arsonval meter Movement Used In A DC Voltmeter

9

Cont.

To find the value of the multiplier resistor, first determine the sensitivity, S, of the meter movement.

/V)( 1

ySensitivit fsI

Resistance InternalRange SRs

10

Example 1-4

Calculate the value of the multiplier resistance on the 50V range of a dc voltmeter that used a 500A meter movement with an internal resistance of 1k.

11

Solution:

Sensitivity, VkI

Sfs

2500

11

Multiplier, Rs = S X Range – internal Resistance

= (2k X 50) – 1k = 99k

Multirange volmeter : Example 1

A D’Arsonval movement with a full scale deflection of 50µA and having an internal resistance of 500 Ω is to be converted into a multirange voltmeter. Determine the value of multiplier required for 0-20 V, 0 – 50 V and

0-100V using individual multipliers for each range. Calculate the values of the individual resistor.

Multirange voltmeter: Example 2

Convert a basic D’Arsonval movement with a full scale deflection of 10mA and having an internal resistance of 100 Ω into a multirange voltmeter with ranges from 0-5 V, 0 – 50 V and 0-100V .

14

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 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.

15

Example 1-5Two different voltmeters are used to

measure the voltage across resistor RB in the circuit of Figure 2-2. The meters are as follows.

Meter A : S = 1k/V, Rm = 0.2k, range = 10VMeter B : S = 20k/V, Rm = 1.5k, range=10V

Calculate:(a) Voltage across RB without any

meter connected across it.(b) Voltage across RB when meter A is

used.(c) Voltage across RB when meter B is

used(d) Error in voltmeter readings.

Fig. 2.2

16

Solution:

(a) The voltage across resistor RB without either meter connected is found Using the voltage divider equation:

V5

5k25k

kΩ5V30

BA

BRB RR

REV

17

Cont.(b) starting with meter A, the total resistance it presents to the circuit is

The parallel combination of RB and meter A is

Therefore, the voltage reading obtained with meter A, determined by the voltage divider equation, is V

RR

REV

Ae

eRB

53.3kΩ25kΩ33.3

kΩ33.3V30

1

1

kΩ33.310kΩ5kΩ

10kΩ5kΩ

1

TAB

TABe RR

RRR

kΩ10V10k/V1Range SRTA

18

Cont.

(c) The total resistance that meter B presents to the circuit is

RTB = S x Range = 20k/V x 10 V = 200 k

The parallel combination of RB and meter B is

Re2 = (RB x RTB)/(RB + RTB) = (5kx200k)/(5k+200k) = 4.88 k

Therefore, the voltage reading obtained with meter B, determined by use of the voltage divider equation, is

VRB = E(Re2)/(Re2+RA) = 30 V x (4.88k)/(4.88k+25k) = 4.9 V

19

Cont.(d)

Voltmeter A error = (5 V – 3.53 V)/5 V x (100%

= 29.4%Voltmeter B error = (5 V – 4.9 V)/5 V x

(100%) = 2 %

%100 valueExpected

value)Measured- value(ExpectederrorA Voltmeter

20

Five principal meter movements used in ac instrument

1. Electrodynamometer2. Iron Vane3. Electrostatic4. Thermocouple5. D’Arsonval with rectifier

21

Application of meter movements:

Meter Movement

DC Use AC Use Applications

Electrodynamometer YES YES Standards meter, wattmeter, frequency meter“Indicator” applications such as in automobiles

Iron Vane YES YES “Indicator” applications such as in automobiles

Electrostatic YES YES Measurement of high voltage when very little current can be supplied by the circuit being measured

Thermocouple YES YES Measurement of radio frequency ac signal

D’Arsonval YES YES with rectifier

Most widely used meter movement for measuring direct current or voltage and resistance

22

The PMMC instrument is polarized (terminals +ve & -ve) - it must be connected correctly for positive (on scale) deflection to occur.

When an AC with a very low frequency is passed through a PMMC, the pointer tends to follow the instantaneous level of the AC

As the current grows positively, the pointer deflection increases to a maximum at the peak of the AC

As the instantaneous current level falls, the pointer deflection decreases toward zero. When the AC goes negative, the pointer deflected (off scale) to the left of zero

This kind of pointer movement can occur only with AC having a frequency of perhaps 0.1Hz or lower

PMMC Instrument on AC

23

PMMC Instrument on AC

• At 50Hz or higher supply frequencies - the damping mechanism of the instrument and the inertia of the meter movement prevent the pointer from following the changing instantaneous levels.

• The average value of purely sinusoidal AC is zero.

• Therefore, a PMMC instrument connected directly to measure 50Hz AC indicates zero average value.

• It is important to note that although a PMMC instrument connected to an ac supply may indicating zero, there can actually be very large rms current flowing in its coils

24

1. Half wave rectification2. Full wave rectification

Two types of PMMC meter used in AC measurement :

25

D’Arsonval meter movement used with half wave rectification

To convert alternating current (AC) to unidirectional current flow, which produces positive deflection when passed through a PMMC, the diode rectifier is used. Several types of rectifiers are selected such as a copper oxide rectifier, a vacuum diode, or semiconductor or “crystal diode”.

pVV

V Prms 5.0

2

rmsrmsp

ave VVV

V 45.02

pdcave V318.0VV

26

• For example, if the output voltage from a half wave rectifier is 10Vrms so the dc voltmeter will provide an indication of approximately 4.5V dc Therefore, the pointer deflected full scale when 10V dc signal is applied.

• When we apply a 10Vrms sinusoidal AC waveform, the pointer will deflect to 4.5V This means that the AC voltmeter is not as sensitive as DC voltmeter.

• In fact, an AC voltmeter using half wave rectification is only approximately 45% as sensitive as a dc voltmeter.

Cont…

27

• Actually, the circuit would probably be designed for full-scale deflection with a 10V rms AC applied, which means the multiplier resistor would be only 45% of the value of the multiplier resistor for 10V dc voltmeter. Since we have seen that the equivalent dc voltage is equal to 45% of the rms value of the ac voltage.

Cont…

mdc

rmsm

dc

dcs R

I

E45.0R

I

ER

Sac = 0.45Sdc

28

Commercially produced ac voltmeters that use half wave rectification also has an additional diode and a shunt as shown in Figure below:

Cont..

29

• The additional diode D2 is reverse biased on the positive half cycle and has virtually no effect on the behavior of the circuit.

• In the negative half cycle, D2 is forward biased and provides an alternate path for reverse biased leakage current that would normally through the meter movement and diode D1.

• The purpose of the shunt resistor Rsh is to increase the current flow through D1 during positive half cycle so that the diode is operating in a more linear portion of its characteristic curve.

• Although this shunt resistor improves the linearity of the meter on its low voltage ac ranges, it also further reduces the AC sensitivity.

Cont…

30

Example 1-6

Compute the value of the multiplier resistorfor a 15Vrms ac range on the voltmetershown in Fig. 1.

Fig. 1: AC voltmeter using half wave rectification

RS

Ein = 15Vrms

Ifs = 1mA

Rm = 300Ω

31

Solution:

Method 1The sensitivity of the meter movement,

V/k1m1

1

I

1S

fsdc

Rs = Sdc × Rangedc – Rm

= 1k × 1

E45.0 rms - Rm

= 1k × 0.45(10) – 300

= 4.2k

32

Cont.

Method 2The AC sensitivity for half wave rectifier,

Sac = 0.45Sdc = 0.45(1k) = 450/V

Rs = Sac × Rangeac – Rm

= 450 × 10 –300

= 4.2k

33

Cont.

Rs = mfs

rms RI

E45.0

300m1

1045.0

= 4.2k

=

Method 3

34

Example 1-7

Calculate the ac and dc sensitivity and the value of the multiplier resistor required to limit the full scale deflection current in the circuit shown in Fig above.

35

D’Arsonval meter movement used with full wave

rectification

Fig. 2: Full bridge rectifier used in an ac voltmeter circuit

During the positive half cycle, currents flows through diode D2, through the meter movement from positive to negative, and through diode D3. The polarities in circles on the transformer secondary are for the positive half cycle. Since current flows through the meter movement on both half cycles, we can expect the deflection of the pointer to be greater than with the half wave cycle, which allows current to flow only on every other half cycle; if the deflection remains the same, the instrument using full wave rectification will have a greater sensitivity.

36

Consider the circuit shown in Fig. 1-2

Fig. 1-2: AC voltmeter using full wave rectification

37

Cont.

When the 10Vrms of AC signal is applied to the circuit

above, where the peak value of the AC input signal is V14.14)10(x414.1xE2E rmsp

And the average full wave output signal is

V914.14x636.0xE636.0EE pdcave

Therefore, we can see that a 10Vrms voltage is equivalent to 9Vdc for full-scale deflection.

38

Cont.

Sac = 0.9 Sdc

rmsrmspavg E9.0)xE2(636.0E636.0E

Or

This means an ac voltmeter using full wave rectification has a sensitivity equal to 90% of the dc sensitivity

39

Example 1-8Compute the value of the multiplier resistor for a 10Vrms ac range on the voltmeter in Figure 1-2.

Fig. 1-2: AC voltmeter circuit using full wave rectification

40

Solution 1-8

The dc sensitivity is

V/k1mA1

1

I

1S

fsdc

The ac sensitivity is

Sac = 0.9Sdc = 0.9 (1k) = 900 /V

41

Cont.

Therefore the multiplier resistor is

Rs = Sac x Range – Rm

= 900 x 10Vrms – 500

= 8.5k

42

Cont.

Note: Voltmeters using half wave and full

wave rectification are suitable for measuring only sinusoidal ac voltages.

2.2 Oscilloscope An oscilloscope is a piece of

electronic test equipment that allows signal voltages to be viewed, usually as a two-dimensional graph of one or more electrical potential differences (vertical axis) plotted as a function of time or of some other voltage (horizontal axis

Perform some computations using data taken from the voltage waveform that is displayed such as: * Rms value* Average Amplitude* Peak-to-peak Amplitude* Frequency

Oscilloscope

An oscilloscope is easily the most useful instrument available for testing circuits because it allows you to see the signals at different points in the circuit.

Using for signal/wave display – Winamp Music Player, Electrocardiogram,

2.3 Potentiometer

A potentiometer is a variable resistor that functions as a voltage divider

It is a simple electro-mechanical transducer

It converts rotary or linear motion from the operator into a change of resistance, and this change is (or can be) used to control any volume.

Potentiometer

Schematic symbol for a potentiometer. The arrow represents the moving terminal, called the wiper.

Usually, this is a three-terminal resistor with a sliding contact in the center (the wiper) - user-adjustable resistance

If all three terminals are used, it can act as a variable voltage divider

If only two terminals are used (one side and the wiper), it acts as a variable resistor

Potentiometer Circuit

Any current flow through the Galvanometer, G, wpuld be a result of an imbalance in the measured voltage, Vm and the voltage imposed across points A to B, VAB.

If Vm is not equal to VAB, a current will flow through the galvanometer, G.

Galvanometer detects current flow due to imbalance in voltage Vm and VAB. When Vm = VAB, there is a balance and no current, means no displacement in Galvanometer.

Potentiometer – Application In modern usage, a potentiometer is a

potential divider, a three terminal resistor where the position of the sliding connection is user adjustable via a knob or slider. For instance, when attached to a volume control, the knob can also function as an on/off switch at the lowest volume

Potentiometers are frequently used to adjust the level of analog signals (e.g. volume controls on audio equipment) and as control inputs for electronic circuits (e.g. a typical domestic light dimmer).

3.0 RESISTANCE MEASUREMENT

Resistance Measurement

The resistances are classified as follow: 1. Low Resistance : All resistances of the order of 1 ohm and

below. example: Machine armature, series field

winding shunt etc. 2. Medium Resistance : All resistances of the order of 1 ohm to

100,000 ohms. example: Winding resistance, multiplier

resistance.

Cont…

3. High Resistance : All resistances of the order of 100,000

ohm and above. example: Insulation resistance of

machines, cables, porcelain insulator etc.

3.1 Ohmmeter

The purpose of an ohmmeter, is to measure the resistance placed between its leads.

This resistance reading is indicated through a mechanical meter movement which operates on electric current. The ohmmeter must then have an internal source of voltage to create the necessary current to operate the movement, and also have appropriate ranging resistors to allow just the right amount of current through the movement at any given resistance.

Ohmmeter

The original design of an ohmmeter provided a small battery to apply a voltage to a resistance. It used a galvanometer to measure the electric current through the resistance.

The scale of the galvanometer was marked in ohms, because the fixed voltage from the battery assured that as resistance decreased, the current through the meter would increase.

A more accurate type of ohmmeter has an electronic circuit that passes a constant current I through the resistance, and another circuit that measures the voltage V across the resistance.

Ohmmeter

The standard way to measure resistance in ohms is to supply a constant voltage to the resistance and measure the current through it.

That current is of course inversely proportional to the resistance according to Ohm's law, so that you have a non-linear scale.

The current registered by the current sensing element is proportional to 1/R, so that a large current implies a small resistance.

The Ohmmeter (Series type ohmmeter)

Cont…

Cont…

The Ohmmeter (Shunt type ohmmeter)

Megger

The megger is an instrument used for the measurement high resistance and insulation resistance. The constructional details are shown in fig.2.15

Multimeter

Multimeter is basically a PMMC meter.

Consists of an ammeter, voltmeter and ohmmeter combined, with a function switch.

DC voltmeter section. The meter movement

has a resistance of 2000 ohms.

Suitable resistor are added as multiplier to get voltage range from 2.5V to 250V.

DC currrents are measured making use a suitably designed shunt resistors.

Multirange ohm-meter is built with the meter movement, battery cells,shunt and series resitors

To measure AC voltage the output voltage is rectified before the current passes through the meter using half wave rectifier.

Merits and demerits of multimeter.

Merits(i) It is single meter

that performs several measuring functions.

(ii) It has a small size and portable.

(iii) It can made measurements with reasonable accuracy

Demerits(i) It cannot make

precise and accurate measurements due to the loading effect.

(ii) Technical skill is required to handle it

4.0 Digital Multimeter

A multimeter or a multitester is an electronic measuring instrument that combines several functions in one unit.

The most basic instruments include an ammeter, voltmeter, and ohmmeter

4.1Digital Multimeter – Capabilities

DC Voltage Measurements AC Voltage RMS Measurements DC and AC Current Measurements Resistance Measurements Capacitance/Inductance Measurements Frequency/Period Measurements Diode Measurements

THANK YOU