Bab 2

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CHAPTER 2

BASIC METER IN DC MEASUREMENTS

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LECTURE CONTENTS

2.1 Permanent-Magnet Moving-Coil (PMMC) Instrument

2.2 DC Ammeter, Multiple-Range Ammeter

2.3 DC Voltmeter, Multiple-Range Voltmeter

2.4 Calibration of DC Ammeter and DC Voltmeter

2.5 Series and Shunt Ohmmeter 2.6 Megger – Megaohmmeter

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2.1 Permanent-Magnet Moving-Coil (PMMC) Instrument

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Introduction

• The permanent-magnet moving-coil (PMMC) instrument consists of a light weight coil of copper wire suspended in the field of a permanent magnet.

• Current in the wire causes the coil to produce a magnetic field that interacts with the field from the magnet, resulting in partial rotation of the coil.

• A pointer connected to the coil deflects over a calibrated scale, indicating the level of current flowing in the wire.

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Deflection Instrument Fundamentals • A deflection instrument uses a

pointer that moves over a calibrated scale to indicate a measured quantity.

• For this to occur, three forces are operating in the electromechanical mechanism (or movement) inside the instrument: a deflecting force, a controlling force, and a damping force.

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a) The deflecting force in PMMC instrument is provided by a current-carrying coil pivoted in a magnetic field.

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b) The controlling force from the springs balances the deflecting force.

Figure 2.1: The deflecting force in a PMMC instrument is produced by the current ill the moving coil. The controlling force is provided

by spiral springs. The two forces are equal when the pointer is stationary.

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a) Lack of damping causes the pointer to oscillate.

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b) The damping force in a PMMC instrument is provided by eddy currents induced in the aluminium coil former as it moves through the

magnetic field.

Figure 2.2: A deflection instrument requires a damping force to stop the pointer oscillating about the indicated reading. The damping force

is usually produced by eddy currents in a nonmagnetic coil former. These exist only when the coil is in motion.

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PMMC Construction

• Details of the construction of a PMMC instrument or D'Arsonval instrument are illustrated in Figure 2.4.

• The main feature is a permanent magnet with two soft-iron pole shoes.

• A cylindrical soft-iron core is positioned between the shoes so that only very narrow air gaps exist between the core and the faces of the pole shoes.

• The lightweight moving coil is pivoted to move within these narrow air gaps. The air gaps are made as narrow as possible in order to have the strongest possible level of magnetic flux cross ing the gaps.

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Figure 2.4: A typical PMMC instrument is constructed of a horseshoe magnet, soft-iron pole shoe, a soft-iron core and a suspended coil that

moves in the air gap between the core and the pole shoes.

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PMMC Construction cont…• Figure 2.4 also shows one of the two

controlling spiral springs. One end of this spring is fastened to the pivoted coil and the other end is connected to an adjustable zero-position control.

• The current in the coil of a PMMC instrument must flow in one particular direction to cause the pointer to move (positively) from the zero position over the scale.

• When the current is reversed, the interaction of the magnetic flux from the coil with that of the permanent magnet causes the coil to rotate in the opposite direction, and the pointer is deflected to the left of zero (i.e., off-scale).

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PMMC Construction cont…

• The terminals of a PMMC instrument are identified as + and - to indicate the correct polarity for connection, and the instrument is said to be polarized.

• Because it is polarized, the PMMC instrument cannot be used directly to measure alternating current. Without rectifiers, it is purely a DC instrument.

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Torque Equation and Scale

• When a current I flows through a one-turn coil situated in a magnetic field, a force F is exerted on each side of the coil as shown in Figure 2.6(a):

newtons

• where B is the magnetic flux density in tesla, I is the current in amperes and l is the length of the coil in meters.

BIlF

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Torque Equation and Scale cont…• Since the force acts on each side of the coil,

the total force for a coil of N turns is

Newtons (N)

• The force on each side acts at radius r, producing a deflecting torque (TD):

Newton meters (N.m)

N.m

N.m

• where D is the coil diameter, shown in Figure 2.6(b).

BIlNF 2

BIlNDT

rBIlNT

BIlNrT

D

D

D

2

2

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Figure 2.6: The deflecting torque on the coil of a PMMC instrument is directly proportional to the magnetic flux density, the coil dimensions

and the coil current. This gives the instrument a linear scale.

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Torque Equation and Scale cont…

• The controlling torque exerted by the spiral springs is directly proportional to the deformation or "windup" of the springs. Thus, the controlling torque (TC) is proportional to the actual angle of deflection of the pointer:

TC = K

• where K is a constant. For a given deflection, the controlling and deflecting torques are equal:

K = BIlND

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• Since all quantities except and I are constant for any given instrument, the deflection angle is

= CI, ---(2.1) • where C = constant.• Equation 2.1 shows that the pointer

deflection is always proportional to the coil current.

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• Consequently, the scale of the instrument is linear or uniformly divided; that is, if 1 mA produces a 1 cm movement of the pointer from zero, 2 mA produces a 2 cm movement, and so on, shown in Figure 2.6(c).

• As explained before, the PMMC instrument can be used as a DC voltmeter, a DC ammeter and an ohmmeter.

• When connected with rectifiers and transformers, it can also be employed to measure alternating voltage and current.

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Example 2.1

A PMMC instrument with a 100 turns coil has a magnetic flux density in its air gaps of B = 0.2 T. The coil dimensions are D = 1 cm and l = 1.5 cm. Calculate the torque on the coil for a current of I mA.

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Example 2.1 solution

Nm

mA T6

22

103

1011001105.12.0

BIlNDTD

22

2.2 DC Ammeter, Multiple-Range

Ammeter

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Ammeter Circuit

• An ammeter is always connected in series with a circuit in which current is to be measured.

• To avoid affecting the current level in the circuit, the ammeter must have a resistance much lower than the circuit resistance.

• Pointer deflection is directly proportional to the current flowing in the coil.

Rm

Coil resistance, Rm

Shunt resistance, Rs

Meter

Rs

Im

I = Im + IsVm

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Ammeter Circuit cont…

• maximum pointer deflection is produced by a very small current, and the coil is usually wound of thin wire that would be quickly destroyed by large currents.

• For larger currents, the instrument must be modified so that most of the current to be measured is shunted around the coil of the meter. Only a small portion of the current passes through the moving coil. Refer Figure 2.7.

Rm

Coil resistance, Rm


Meter

Rs

Im

I = Im + IsVm

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Rm

Coil resistance, Rm


Meter

Rs

Im

I = Im + IsVm

Figure 2.7: An ammeter circuit with shunt resistance, Rs and coil resistance, Rm.

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Example 2.2

An ammeter (as in Figure 2.7) has a PMMC instrument with a coil resistance of Rm = 99 and FSD current of 0.1 mA. Shunt resistance Rs = 1 . Determine the total current passing through the ammeter at (a) FSD, (b) 0.5 FSD and (c) 0.25 FSD.

Rm

Coil resistance, Rm


Meter

Rs

Im

I = Im + IsVm

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Example 2.2 solution (a) At FSD,

and

(b) At 0.5 FSD,

(c) At 0.25 FSD,

mA mA mA

mA

mV

mV mA

mA mA

5.2025.0475.2

475.21

475.2

475.299025.0

025.01.025.0

ms

s

ms

mmm

m

III

R

VI

RIV

I

mA mA mA

mA

mV

mV mA

mA mA

505.095.4

95.41

95.4

95.49905.0

05.01.05.0

ms

s

ms

mmm

m

III

R

VI

RIV

I

mA mA mA

mA

mV

mV mA

101.09.9,

9.91

9.9

9.9991.0,

ms

s

ms

mss

mmm

IIIcurrenttotal

R

VI

VRI

RIVvoltagemeter

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Ammeter Scale

• The total ammeter current in Example 2.2 is 10 mA when the moving-coil instrument indicates FSD.

• Therefore, the meter scale can be calibrated for FSD to indicate 10 mA. When the pointer indicates 0.5 FSD and 0.25 FSD, the current levels are 5 mA and 2.5 mA, respectively.

• Thus, the ammeter scale may be calibrated to linearly represent all current levels from zero to 10 mA.

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Shunt Resistance

• Refer again to Example 2.2. • If a shunt resistor having a smaller

resistance is used, the shunt current and the total meter current will be larger than the levels calculated.

• In fact, shunt resistance values can be determined to convert a PMMC instrument into an ammeter for measuring virtually any desired level of current.

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Example 2.3

• A PMMC instrument has FSD of 100 A and a coil resistance of 1 k. Calculate the required shunt resistance value to convert the instrument into an ammeter with (a) FSD = 100 mA and (b) FSD = 1 A.

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Example 2.3 solution(a) At FSD = 100 mA,

(b) At FSD = 1 A,

001.19.99

100

9.99100100

1001100

mA

mV

mA A mA

mV kA

s

ms

ms

ms

mmm

I

VR

III

III

RIV

10001.09.999

100

9.9991001

1001100

mA

mV

mA A A

mV kA

s

ms

ms

ms

mmm

I

VR

III

III

RIV

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Multirange Ammeter

• The circuit of a multirange ammeter is shown in Figure 2.8. As illustrated, a rotary switch is employed to select any one of several shunts having different resistance values.

• A make-before-break switch [Figure 2.8] must be used so that the instrument is not left without a shunt in parallel with it even for a brief instant.

• If this occurred, the high resistance of the instrument would affect the current flowing in the circuit.

Rm

Rs1

Rs2

Rs3

Rs4

A

BCD

E

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Multirange Ammeter cont…

• More important, a current large enough to destroy the instrument might flow through its moving coil.

• When switching between shunts, the wide-ended moving contact of the make-before-break switch makes contact with the next terminal before it breaks contact with the previous terminal.

Rm

Rs1

Rs2

Rs3

Rs4

A

BCD

E

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Rm

Rs1

Rs2

Rs3

Rs4

A

BCD

E

Figure 2.8: Multirange Ammeter using switched shunts

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• Figure 2.9 shows another method of protecting the deflection instrument of an ammeter from excessive current flow when switching between shunts.

• Resistors R1, R2, and R3, constitute an Ayrton shunt.

Rm

R1

Im Vs

R2 R3

I Is Is

I

Im

A

B

C

D

+

-

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• In Figure 2.9(a) the switch is at contact B, and the total resistance in parallel with the instrument is R1 + R2 + R3. The meter circuit resistance remains Rm.

• When the switch is at contact C [Figure 2.9(b)], the resistance R3 is in series with the meter, and R1 + R2 is in parallel with Rm + R3.

Rm

R1

Im Vs

R2 R3

I Is Is

I

Im

A

B

C

D

+

-

Rm

R1

Im Vs

R2 R3

I Is Is

I

Im

A

B

C

D

+

-

Im

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• Similarly, with the switch at contact D, R1 is in parallel with Rm + R2 + R3.

• Because the shunts are permanently connected, and the switch makes contact with the shunt junctions, the deflection instrument is never left without a parallel-connected shunt (or shunts).

Rm

R1

Im Vs

R2 R3

I Is Is

I

Im

A

B

C

D

+

-

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Rm

R1

Im Vs

R2 R3

I Is Is

I

Im

A

B

C

D

+

-

Rm

R1

Im Vs

R2 R3

I Is Is

I

Im

A

B

C

D

+

-

Im

(b) (R1 + R2) in parallel with (Rm + R3)

(a) (R1 + R2 + R3) in parallel with Rm

Figure 2.9: An Ayrton shunt used with an ammeter consists of several series-connected resistors all connected in parallel.

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Example 2.4

A PMMC instrument has a three-resistor Ayrton shunt connected across it to make an ammeter as in Figure 2.9. The resistance values are R1 = 0.05 , R2 = 0.45 and R3 = 4.5. The meter has Rm = 1 k and FSD = 50 A. Calculate the three ranges resistor of the ammeter.

Rm

R1

Im Vs

R2 R3

I Is Is

I

Im

A

B

C

D

+

-

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Example 2.4 solutionSwitch at contact B,

Ammeter range 10 mASwitch at contact C,

Ammeter range 100 mASwitch at contact D,

mA mA A

mA mV

mV k A

05.101050

105.445.005.0

50

50150

321

sm

ss

mms

III

RRR

VI

RIV

mA mA A

mA mV

mV k A

05.10010050

10045.005.0

50

505.4150

321

3

sm

ss

mms

III

RRR

VI

RRIV

mA AA

AmV

mV k A

05.1000150

105.0

50

5045.05.4150

321

23

sm

ss

mms

III

RRR

VI

RRRIV

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Ammeter Insertion Effects

• All ammeters contain some internal resistance, which may range from a low value for current meters capable of measuring in the ampere range to an appreciable value of 1k or greater for micrometers.

• Inserting an ammeter in a circuit always increase the resistance of the circuit and reduces the current in the circuit.

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Ammeter Insertion Effects cont…

• The error caused by the meter depends on the relationship between the value of resistance in the original circuit and the value of resistance in the ammeter.

• Inserting an ammeter in a circuit always increase the resistance of the circuit and reduces the current in the circuit.

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Ammeter Insertion Effects cont…• The expected current Ie is the current

without the ammeter connected (Figures 2.9a), while meter current, Im is the current with ammeter in series connected in the circuit (Figures 2.9b) with considering Rm in the ammeter.

• In order to obtain relationship between Ie and Im, the Thevenin theorem can be used for that purpose.

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RA

-

+E

X

Y

Ie

RA

-

+E

X

Y

Im

Figure 2.9a: Expected current value in a series circuit.

Figure 2.9b: Series circuit with ammeter.

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mAm

Ae

RR

EI

R

EI

mA

A

m

e

RR

R

I

I

, without ammeter connected in the circuit

, with ammeter connected in the circuit

, ratio between Ie and Im

Related equation involved for ammeter insertion effects.

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Exercise 2.4a

A current meter that has an internal resistance of 78 is used to measured the current through resistor RC in Figure 2.9c. Determine the percentage of error of the reading due to ammeter insertion.

RA = 1 k

-

+

E = 3 V RB 1 k

RC

1 k

Figure 2.9c: Series-parallel circuit.

Ans: RTH = 1.5 k, Im/Ie = 0.95, eI = 5%

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2.3 DC Voltmeter, Multiple-Range

Voltmeter

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Voltmeter Circuit • The deflection of a PMMC instrument

is proportional to the current flowing through the moving coil.

• The coil current is directly proportional to the voltage across coil.

• Therefore, the scale of the PMMC meter could be calibrated to indicate voltage.

• Without any additional series resistance, the PMMC instrument would only be able to measure very low voltage level.

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Voltmeter Circuit cont…

• The voltmeter range is easily increased by connecting a resistance in series with the instrument.

• Because it increases the range of the voltmeter, the series resistance is termed a multiplier resistance, Rs.

• A multiplier resistance that is nine terms the coil resistance will increase the voltmeter range by a factor of 10.

Rs Rm

V

Coil resistance, Rm

Multiplier resistance, Rs

Meter

Im

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Voltmeter Circuit cont…

Rs Rm

V

Coil resistance, Rm

Multiplier resistance, Rs

Meter

Im

Figure 2.10: A dc voltmeter circuit with multiplier resistance, Rs and coil resistance, Rm.

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Example 2.5

A PMMC instrument with full-scale deflection (FSD) of 100 A and a coil resistance of 1 k is to be converted into a voltmeter. Determine the required multiplier resistance if the voltmeter is to measure 50 V at full scale. Also, calculate the applied voltage when the instrument indicates 0.8, 0.5 and 0.2 of FSD.

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mm

s

mms

msm

RI

VR

I

VRR

RRIV

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Example 2.5 solutionFor V = 50 V FSD,

At 0.8 FSD,

At 0.5 FSD,

At 0.2 FSD,

k k A

A

4991100

50

100

V

R

I

s

m

V

k k A

A A

40

149980

801008.0

msm

m

RRIV

I

V

k k A

A A

25

149950

501005.0

msm

m

RRIV

I

V

k k A

A A

10

149920

201002.0

msm

m

RRIV

I

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Voltmeter Sensitivity • The voltmeter designed in Example 2.5 has

a total resistance of

• Since the instrument measures 50 V at full scale, its resistance per volt is

• This quantity is also termed the sensitivity of the voltmeter.

• The sensitivity of a voltmeter is always specified by the manufactured and it is frequently printed on the scale of the instrument.

k 500msT RRR

Vk V

k

10

50

500

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Voltmeter Sensitivity cont…

• Ideally, a voltmeter should have an extremely high resistance.

• A voltmeter is always connected across or in parallel with the points in a circuit at which the voltage is to be measured.

• If its resistance is too low, it can alter the circuit voltage. This condition is known as voltmeter loading effect.

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Voltmeter Loading Effects

• When the meter is used to measure the voltage across a circuit component, the voltmeter circuit itself is in parallel with the circuit component.

• This condition happen when the parallel combination of two resistors is less than either resistor alone or the resistance seen by the source is less with the voltmeter connected than without.

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Voltmeter loading Effects cont…

• 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 and resulting error and called loading error.

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Example 2.5a

Two different voltmeters are used to measure the voltage across resistor RB in the circuit of Figure 2.10a. The parameters of the meters are as follows.

Meter A: S = 1k/V, Rm = 0.2k, range = 10V.

Meter B: S = 20k/V, Rm = 1.5k, range = 10V.

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Example 2.5a

RB = 5 k

RA = 25 k

-

+

E = 30 V

Figure 2.10a: Circuit for showing voltmeter loading effect.

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Example 2.5a solution

The voltage across RB without either meter connected is found using the voltage divider equation.

Vkk

kV 5

525

530

BA

BR RR

REV

B

Starting with meter A, the total resistance it presents to the circuit is

kVk

10101

VRangeSR

AT

The parallel combination of RB and meter A is

k

kk

kk33.3

105

1051

A

A

TB

TBe RR

RRR

a)

b)

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

Vkk

kV 53.3

2533.3

33.330

1

1

Ae

eR RR

REV

B

The total resistance that meter B presents to the circuit is

kVk

2001020

VRangeSR

BT

The parallel combination of RB and meter B is

k

kk

kk88.4

2005

20052

B

B

TB

TBe RR

RRR

c)

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

Vkk

kV 9.4

2588.4

88.430

2

2

Ae

eR RR

REV

B

%2%1005

9.45

%4.29%1005

53.35

V

VVerror BVoltmeter

V

VVerror AVoltmeter

d)

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Exercise 2.5aFind the voltage reading across RB and the percentage of error of each reading obtained with a voltmeter on (refer Figure 2.10b),

a) Its 3 V range.

b) Its 10 V range.

c) Its 30 V range.

RB = 4 k

RA = 36 k

-

+

E = 30 V

Figure 2.10b

Ans: Req1 = 3.75 k, VRB = 2.8 V, eL = 6.66%

Ans: Req2 = 3.92 k, VRB = 2.95 V, eL = 1.66%

Ans: Req2 = 3.97 k, VRB = 2.98 V, eL = 0.66%

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Multirange Voltmeter

• A multirange voltmeter consists of a deflection instrument, several multiplier resistors and a rotary switch.

• Two possible circuits are illustrated in Figure 2.11, they are multirange voltmeter using switched multiplier resistors and multirange voltmeter using series-connected multiplier resistors.

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V

Rm

Meter resistance

Multiplier resistors

Meter

Im

R1

R2

R3(a) Multirange voltmeter using switched multiplier resistors

V

Rm

Meter resistance

Multiplier resistorsMeter

Im

R1 R2 R3

(b) Multirange voltmeter using series-connected multiplier resistors

Figure 2.11: A multirange voltmeter consists of a PMMC instrument, several multiplier resistors and a switch for range selection.

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Multirange Voltmeter cont…• In Figure 2.11(a) only one of the three-

multiplier resistors connected in series with the meter at any time. The range of this voltmeter is

• In Figure 2.11(b) the multiplier resistors are connected in series and each junction is connected to the one of the switch terminals. The range of this voltmeter can also be calculated from the equation,

RRIV mm where R can be R1, R2 or R3.

RRIV mm where R can be R1, R1 + R2 or R1 + R2 + R3.

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Example 2.6

A PMMC instrument with FSD = 50 A and Rm = 1700 is to be employed as a voltmeter with ranges of 10 V, 50 V and 100 V. Calculate the required values of multiplier resistors, Rs, for the circuits of Figures 2.11(a) and 2.11(b).

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Example 2.6 solution Circuit as in Figure 2.11(a),

M A

V

k A

V

k A

V

9983.1170050

100

3.998170050

50

3.198170050

10

3

2

1

1

R

R

RI

VR

I

VRR

mm

mm

V

Rm

Meter resistance

Multiplier resistors

Meter

Im

R1

R2

R3

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Example 2.6 solution Circuit as in Figure 2.11(b),

M k k A

V

k k A

V

k A

V

117003.19880050

100

80017003.19850

50

3.198170050

10

123

3

3321

12

2

221

1

1

mm

mm

mm

mm

mm

mm

RRRI

VR

I

VRRRR

RRI

VR

I

VRRR

RI

VR

I

VRR

V

Rm

Meter resistance

Multiplier resistorsMeter

Im

R1 R2 R3

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2.4 Calibration of DC Ammeter and DC

Voltmeter

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Calibration of DC Ammeter and DC Voltmeter

• Calibration means to compare a given instrument against a standard instrument to determine its accuracy.

• A dc voltmeter may be calibrated by comparing it with one of the standards or with a potentiometer (standard instrument).

• The circuit shown in Figure 2.12 may be used to calibrate a dc voltmeter, the test voltmeter reading, V, is compared to the voltage reading obtained with the standard instrument, M.

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Calibration of DC Ammeter and DC Voltmeter cont…

MV RRegulated DC voltage

source

Voltmeter under test

Standard instrument

Figure 2.12: Calibration circuit for a dc voltmeter

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• A dc ammeter is usually calibrated by using a standard resistor R, and either a standard voltmeter or a potentiometer M.

• The circuit shown in Figure 2.13 may be used to calibrate an ammeter.

• The test ammeter reading, A, is compared to the calculated Ohm's law current from the voltage reading obtained across the known standard resistor using the standard voltmeter M.

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A

MRRegulated DC voltage

sourceAmmeter under test

Standard instrument

Figure 2.13: Calibration circuit for a dc ammeter

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• The ohmmeter circuit designed around the d'Arsonval meter movement is usually considered to be an instrument of moderate accuracy.

• The accuracy of the instrument may be checked by measuring different values of standard resistance and noting the reading obtained.

• However, when precise resistance measurements are required, a comparison-type resistance measurement using a bridge is preferable.

76

2.5 Series and Shunt Ohmmeter

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Series Ohmmeter - Basic Circuit

• An ohmmeter (ohm-meter) is normally part of a volt-ohm-milliammeter (VOM), or multifunction meter or Multimeter.

• Ohmmeters do not usually exist as individual instruments.

• The simplest ohmmeter circuit consists of a voltage source connected in series with a pair of terminals, a standard resistance, and a low-current PMMC instrument.

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• Such a circuit is shown in Figure 2.14(a). The resistance to be measured (Rx) is connected across terminals A and B.

• The meter current indicated by the instrument in Figure 2.14(a) is (battery voltage)/(total series resistance):

mx

bm RRR

EI

1

---Eqn 2.4

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• When the external resistance is zero (i.e., terminals A and B short-circuited), Equation 2.4 becomes

m

bm RR

EI

1

---Eqn 2.5

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RSTD

Rm

-

+

RX

Eb

A B

Im

Resistance to be measured

Standard resistance

Baterry

Figure 2.14: (a) Basic series ohmmeter circuit

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• If R1(RSTD) and Rm are selected (or if R1 is adjusted) to give FSD, only when A and B are short-circuited, FSD is marked as zero ohms. Thus, for Rx = 0, the pointer indicates 0 , shown Figure 2.14(b).

• When terminals A and B are open-circuited, the effective value of resistance Rx is infinity.

• No meter current flows and the pointer indicates zero current. This point (zero current) is marked as infinity () on the resistance scale, shown in Figure 2.14(b).

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0 1 FSD (A)

0.250.5

0.75

largemedium

small

0 (

Figure 2.14: (b) Ohmmeter scale

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• If a resistance Rx with a value between zero and infinity is connected across terminals A and B, the meter current is greater than zero but less than FSD.

• The pointer position on the scale now depends on the relationship between Rx and R1 + Rm.

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Example 2.7

The series ohmmeter in Figure 2.14(a) is made up of a 1.5 V battery, a 100 A meter and a resistance R1 which makes (R1 + Rm) = 15 k. Determine:

(a) the instrument indication when Rx = 0.

(b) how the resistance scale should be

marked at 0.5 FSD, 0.25 FSD, and 0.75

FSD.

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Example 2.7 solution(a) At Full scale, equation 2.4

(b) At 0.5 FSD

From equation 2.4

At 0.25 FSD

At 0.75 FSD

(FSD) A k

V 100150

5.1

1

mx

bm RRR

EI

k k A

V

A A

451525

5.1

2510025.0

1

mm

bx

m

RRI

ER

I

k k A

V

A A

51575

5.1

7510075.0

1

mm

bx

m

RRI

ER

I

k k A

V

A A

151550

5.1

501005.0

1

mm

bx

m

RRI

ER

I

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Therefore, the scale of ohmmeter shown as follows,

0 100 A

2550

75

45 k15 k

5 k

0

Kuiz 3: give a model of potential difference in analogy term.

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Series Ohmmeter - Ohmmeter with Zero Adjust • The simple ohmmeter described before

will operate satisfactorily as long as the battery voltage remains exactly at 1.5 V.

• When the battery voltage falls (and the output voltage of all batteries fall with use), the instrument scale is no longer correct.

• Even if R1 were adjusted to give FSD when terminals A and B are short-circuited, the scale would still be in error because now midscale would represent a resistance equal to the new value of R1 + Rm.

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• Falling battery voltage can be taken care of by an adjustable resistor connected in parallel with the meter (R2 in Figure 2.15).

• In Figure 2.15 the battery current Ib splits up into meter current Im and resistor current I2.

• With terminals A and B short-circuited, R2 is adjusted to give FSD on the meter. At this time the total circuit resistance is R1 + (R2//Rm).

Series Ohmmeter - Ohmmeter with Zero Adjust

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R1

Rm

-

+

RX

Eb

A B

Im

VmR2Zero

Control

Ib

I2

Figure 2.15: An adjustable resistor (R2) connected in parallel with the meter provides an ohmmeter zero control.


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• Since R1 is always very much large than R2//Rm, the total circuit resistance can be assumed to equal R1.

• When a resistance Rx equal to R1, Rx is connected across terminals A and B, the circuit resistance is doubled and the circuit current is halved.

• This causes both I2 and Im to be reduced to half of their previous levels (i.e., when A and B were short-circuited).

• Thus, the middle scale of measured resistance is again equal to the ohmmeter internal resistance R1.


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The equation for the battery current in Figure 2.15 is


--- (2.6)

If R2//Rm << R1,

1RR

EI

x

bb --- (2.7)

Also the meter voltage is

mbm RRIV //2

Which gives meter current as

m

mbm R

RRII

//2

--- (2.8)

--- (2.9)

21 // RRRR

EI

mx

bb

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• Each time the ohmmeter is used, terminals A and B are first short-circuited and R2 is adjusted for zero-ohm indication on the scale (i.e., for FSD).

• If this procedure is followed, then even when the battery voltage falls below its initial level, the scale remains correct.


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Example 2.8

The ohmmeter circuit in Figure 2.15 has Eb = 1.5 V, R1 = 15 k, Rm = 50 , R2 = 50 and FSD = 50 A. Determine the ohmmeter scale reading at 0.5 FSD and determine the new resistance value that R2 must be adjusted to when Eb falls to 1.3 V. Also recalculate the value of Rx at 0.5 FSD when Eb = 1.3 V.

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Example 2.8 solution At 0.5 FSD with Eb = 1.5 V,

k k k k

k A

V

A A A

A

mV

mV A

15153030

3050

5.1

502525

2550

25.1

25.15025

1

1

2

22

RRx

I

ERRx

III

R

VI

RIV

b

b

mb

m

mmm

R1

Rm

-

+

RX

Eb

A B

Im

VmR2Zero

Control

Ib

I2

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With Rx = 0 and Eb = 1.3 V,

A

mV

mV A

A A A

A k

V

18.6867.36

5.2

5.25050

67.365067.86

67.86150

3.1

1

22

2

I

VR

RIV

IIIRRx

EbI

m

mmm

STDmb

b

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At 0.5 FSD with Eb = 1.3 V,

k k k k

k A

V

A A A

A

mV

mV A

15153030

3033.43

3.1

33.432533.18

33.1818.68

25.1

25.15025

1

1

2

22

RRx

I

ERRx

III

R

VI

RIV

b

b

mb

m

mmm

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Shunt Ohmmeter • The series ohmmeter circuit could be

converted to a multirange ohmmeter by employing several values of standard resistors (R1 in Figure 2.15) and a rotary switch.

• The major inconvenience of such a circuits the fact that a large adjustment of the zero control (R2 in Figure 2.15) would have to be made every time the resistance range is changed.

• In the shunt ohmmeter circuit, this adjustment is not necessary; once zeroed, the instrument can be switched between ranges with only minor zero adjustments.

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The Operation of Shunt Ohmmeter

• Figure 2.16 shows the circuit of a typical multirange shunt ohmmeter.

• The deflection meter used gives FSD when passing 37.5 A, and its resistance (Rm) is 3.82 k.

• The zero control is a 5 k variable resistance, which is set to 2.875 k when the battery voltages are at the normal levels.

• Two batteries are included in the circuit; a 1.5 V battery used on all ranges except the R x 10 k range, and a 15 V battery solely for use on the R x 10 k range.

• Rx is the resistance to be measured and is connected at the terminals of the circuit.

• The terminals are identified as + and – because the ohmmeter circuit is part of an instrument that also functions as an ammeter and as a voltmeter.

• It is important to note that the negative terminal of each battery is connected to the + terminal of the multifunction instrument.

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The Operation of Shunt Ohmmeter

• The range switch in Figure 2.16 has a movable contact that may be step-rotated clockwise or counterclockwise.

• The battery terminals on the rotary switch are seen to be longer than any other terminals, so that they make contact with the largest part of the movable contact, while the other (short) terminals reach only to the tab of the moving contact.

• In the position shown, the R x 1 k terminal is connected (via the movable contact) to the + terminal of the 1.5 V battery.

• If the movable contact is step-rotated clockwise, it will connect the 1.5 V battery in turn to R x 100, R x 10, and R x 1 terminals.

• When rotated one step counterclockwise from the position shown, the movable contact is disconnected from the 1.5 V battery, and makes contact between the R x 10 k terminal and the + terminal of the 15 V battery.

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Rm

9 k 900 10

+

-

90

14 140 1470 20 k236 k

Rx

+

-

+ -

R x 10 k

R x 1 k

R x 100

R x 10

R x 1

15 V 1.5 V

3.82 k

5 k

37.5 A

2.875 k

Zero control

Range switch

Figure 2.16: Multirange ohmmeter

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Rx

2.875 k14 1.5 V

10

37.5 A

Ib

9.99 k

Im

3.82 k

Figure 2.17: Equivalent circuit of the multirange shunt ohmmeter on the range R x 1 (refer Figure 2.16)

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2.6 Megger – Megaohmmeter

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Megger (Megaohmmeter) • When very high resistances are to

be measured the current produced with batteries are too small to be measured; it is therefore necessary to use much higher voltages.

• Another reason for the use of higher potential is to test of insulation breakdowns.

• This high potential is placed between the conductor and the outside surface of the insulation.

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Megger (Megaohmmeter)

The megger is a portable instrument consisting of two primary elements:

1)A hand-driven dc generator G that is supplies the necessary high voltage for making the test or measurement.

2)The instrument portion, which indicates the value of the resistance being measured.

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The Operation of Megger

• Coils a and b are mounted on the movable member with a fixed angular relationship to each other and are free to move as a unit in the magnetic field.

• Coil a tends to move the pointer clockwise, and coil b tends to move the pointer counterclockwise.

• Coil a is connected in series with R3 and Rx. • The combination of R3 and Rx and coil a form a

direct series path between the + and - brushes of the dc generator.

• Coil b is connected in series with R2, and these, again, are both connected across the generator.

• There is no restraining springs on the indicating portion of the megger.

• Therefore, when the generator is not being operated, the pointer floats freely and may come to rest at any position on the scale.

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The Operation of Megger• If the test leads are open-circuited, no current flows in

coil a. However, current flows in coil b and deflects the pointer to infinite resistance, which indicates a resistance too large to measure.

• When resistance Rx is connected between the test probes, current flows through coil a also, tending to move the pointer clockwise.

• At the same time, coil b still tends to move the pointer counterclockwise.

• Therefore, the moving element composed of both coils and the pointer comes to rest at a position at which the two forces are exactly balanced.

• This position depends on the value of the external resistance being measured, which controls the relative magnitude of the current in coil a.

• Because changes in voltage affect both coils a and b in the same proportion, the position of the moving system is independent of voltage.

• If the test leads are shorted, the pointer rests at zero because the current in coil a is relatively large.

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The Operation of Megger• To avoid excessive test voltage, most meggers are

equipped with friction clutches, so that if the generator is cranked faster than its rated speed, the clutch slips and the generator speed and output are not permitted to exceed their rated values.

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Figure 2.18: Circuit diagram of Megger (Megaohmmeter)

Bab 2

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