│ Topic 2 │

Voltage, current, resistance and

power measurements

EE2201 Measurements

& Instrumentation

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

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.

Construction of PMMC instrument

Fig. 2-1

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.

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)

Fig. 2-2a

Fig. 2-2b

At equilibrium,

Deflecting = Controlling, torque, Td torque, Tc

Since Td I and

Tc

I

i.e. current proportional to angle of deflection, the meter has a linear scale

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)

Ammeter Circuit

The current flowing in the meter is :

where Im= meter current (A)E = source voltage (V)Rs = internal resistance of power source ()Rm = internal resistance ammeter ()R1 = load resistance ()

If R1 >> Rs and Rm ,

1RRRE

Ims

m

1R

EIm

Rs

E

Rm

R1

Fig. 2-3 Ammeter circuit

Im

Example 2-1

Find the current flowing in the meter in the following circuit if R1 = 15 k.

Solution :

Since R1 is very much greaterthan RS and Rm, Im = E/R1

= 10/(1.5 x 104) = 6.7 x 10 -4A = 0.67mA

R1Rs=9

E=10V

0-1 mARm= 68

Im

Example 2-2

Solution

Since R1 is much greater than Rm, its parallel effect is negligible

mA

VRR

EI

msm

130689

10

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=9

E=10V

R10-1 mA

Rm= 68

Effect on Low-resistance Circuit

With same example, what happen if R1 is 150?

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%1001.44

1.447.66%

xerror

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 A, 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

Obtaining Higher Current Scales

I = range of ammeterIm = full scale current of moving coil meterIs = 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

mS

mmm

mS

II

RI

I

VR

RIV

III

Example 2-3A moving coil meter with full scale current of 100 A and internal resistance of 500 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 A

IS = 1 mA – Im = 0.9 mA

1 mA

RS

0-100 ARm= 500

Im=100 A

IS=0.9mA

V

(b) V = ImRm= 0.05 V

RS = V/IS = 0.05/0.0009

= 55.56

Solution:

Example 2-4

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

Solution :

R1=11.1

R2=1.01

R3=0.1

1mA10mA

100mA

0-100uAR = 100m

I

Multi-range Ammeter

In Fig 2-6, the 0-100A 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

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

0-100uAR = 100m

I

10mA 1 mA

R2=10

Fig 1-6b

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

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

kR

kA

VR

IE

RR

mx

mx

fsd

mmx

5.99

10010

10500 4

Voltmeter Sensitivity & DC Voltmeter Resistance

Voltmeter Sensitivity :

The sensitivity of a voltmeter is specified in terms of ohms per volt (/V).

Sensitivity = 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

where Rm = the resistance of the voltmeter in ohms () EFS = the range of the voltmeter in volts (V) = the sensitivity of the meter in ohm per volt (/V)

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

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

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

Ideally, E2 should be

V

VxMk

M

ERR

RE

67.6

101500

121

22

V98.3

V10xM33.0k500

M33.0

ERR

RE

M33.0M5.0M1

M5.0M1R

eq1

eq2

eq

therefore,

Practically, the internal resistance Rm (5V x 100k/V = 0.5M) of voltmeter is in parallel with R2. Therefore R2 becomes Req.

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 M).

%3.40%10067.6

67.698.3%

xerror

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-21

3 digit-21

4

Signal conditioning circuit

Analogue to digital converter

decoder displayVoltage tobe measured

Fig 2-10 Block diagram of a digital voltmeter

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

Measurement of Resistance

R1 : standard resistanceRm : meter resistanceRx : resistance to be measured

Current Im :

mx

b

RRR

E

1mI

Fig 2-11a Basic series ohmmeter circuit

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

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

Solution

(a) Im = Eb/(Rx+R1+Rm) = 1.5/(0+15 kΩ) = 100 A (FSD)

(b) At 0.5 FSD : Im = 100 A/2 = 50 A Rx+R1+Rm= Eb/I Rx = Eb/Im - (R1+Rm) = 1.5V/50 A - 15 kΩ = 15 kΩ

At 0.25 FSD : Im = 100 A/4 = 25 A Rx = 1.5V/25 A - 15 kΩ = 45 kΩ

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

Ohmmeter With Zero Adjust

Figure 2-13

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

bb R//RRR

EI

m

m2bm R

)R//R(II

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.

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

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

Multi-meter

Fig 2-14

Volt-Ohm-Milliammeter (VOM)

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.

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. 10M) for voltage measurement, and keep constant at various ranges.

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

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.

Wattmeter

Figure 2-16 Electrodynamometer used as a wattmeter.

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.

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

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.

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

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.

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.

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.

Wheatstone Bridge in balanced condition

R1 , R2 - Precision resistors

R3 - Unknown resistor

R4 - Variable precision resistor

E

A

B D

C

R1 R2

R4R3

G

Eo

Fig 2.19

To determine the resistance of R3 , the variable resistor is adjusted until the zero-center galvanometer G indicates null.

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

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:

42

13

2

4

1

3

RRR

Ror

RR

RR

Fig 2.21

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

Solution:

R3 = R1R4/R2

= 5760500

)1800)(1600(

Example 2.8

A Wheatstone bridge has the following arm values: R1 = 1.6 k, R2 = 500 , R3 is unknown, and R4 = 1.8 k.

What value of R3 brings the bridge into the null condition?

Example 2.9

A Wheatstone bridge has ratio arms R1 and R2, both of which may be set to 1 k, 100 or 10 . The variable arm R4 is adjustable from 1 to 10 k in 1 step. Describe, with the aid of circuit diagram, how R3 of about 58 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.

42

13 R

R

RR

2

1

R

R

10

E G

1k

R3

58 R4 5800

Solution:

Since