Ch-4 Meter and Bridges1

8/8/2019 Ch-4 Meter and Bridges1

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Chapter 4

Meters and bridges

4.1 PMMC Meters

PMMC Permanent Magnet moving coil

Analog meters indicate the quantity to be measured

by a pointer and scale that is interoperated by the

user.

The D'Arsonval ammeter uses a simple

electromechanical movement to indicate the

current.


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Current in the coil induced a magnetic field which

interacts with permanent magnet. The interaction

produces a force proportional to the enfettered

current, so the pointer rotates.

The sensitivity of PMMC meter is measured by the

full-scale deflection current (IfS).

Laboratory meter can be made highly sensitive, but

not are generally portable.

They usually used a mirrored scale (mirror under

the pointer) to avoid parallax


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Taut-band meter

is a version of the D'Arsonval meter (no need to

pivots, bearing and spiral spring), so it is cheap,but have less accuracy (2A)

Ideal for applications with measurements

under 100ADC

Withstands non-operating shock - good for

portable equipment

Can be viscous damped for vibration


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Electrodynamometer

One of the oldest meter still used until now is the

Electrodynamometer, invented in 1842

Used to measure

DC, AC current

Modified to serve as wattmeter

Modified to serve as power factormeter

Its operation like D'Arsonval meter

Use two coils instead of permanent magnet to establish

the magnetic field.


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For measurement of current, all 3 coils are

connected in series, so the pointer deflected

whatever the polarity

It is not sensitive like D'Arsonval meter, but can

measure larger current.

Electrodynamometer Advantages

1-Since both of the fixed and moving coils are in

series, the magnetic flux produced is proportional

to current and pointer movement is proportional

to I2.

2-The meter's inertia tends to dampen the effect ofac variations, so it can be calibrated to measure

the RMS value of ac current


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ANALOG AMMETERS

The D'Arsonval meter is sensitive for

small current (50A-1mA)

To measure larger current added shunt

resistance Rsh.

The meter has an internal resistance Rm

and a meter current Im

The total measured current is split intofraction that goes through Rsh and Rm

IT = Ish + Ifs

Ish = IT -Ifs (1)

Where

IT total current entering ammeter, A

Ifs Full-scale meter current, A (Max. value of Im)

Ish shunt current, A


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Ish*Rsh= Ifs*Rm (2)

Substitute by Ish from Eq.(2) into Eq. (1)

fsT

mfssh

IIRIR

=(3)

Methods to measure Rm

Meter calibrator

Which is an instrument connected to ammeter, so

when the current is full scale deflection, the voltage

is measured, then the resistance can be calculated.

Full scale deflection method

which can be done as follows:

(a)Added larger resistance RA as shown to

minimize the current in meter resistance


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(b)Change the value of Vs to have full scale

deflection and record VSFD

(c)Added resistance RB shunt with the internal

meter resistance

(d)Adjust RB until the read less than half full-

scale deflection

(e)Double the value of VSFD recorded in step (b),

so the pointer move to nearly full-scale

deflection

(f) Adjust RB to read exactly full-scale deflection,

at this point Rm = RB.

(g)Switch off the supply and measure RB, so the

internal resistance of ammeter is known.


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Example-1

Assume a PMMC meter has full-scale deflection

current of 100A and the internal resistance is

200.

a-What is the shunt resistance to make meter read

1.0 mA at full-scale

b-What is the shunt resistance to make meter read

100 mA at full-scale

a- =

=

=

=

2.2210*)1001000(

200*10*100

1001

200).100(6

6

AmA

A

II

RIR

fsT

mfs

sh

b- =

=

=

=

2.010*)100100000(

200*10*100

100100

200).100(6

6

AmA

A

II

RIR

fsT

mfssh

To measure larger current, need small resistanceand vice versa.


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Multiple Range ammeters

1- Switching arrangement

disadvantages

When the switch is not perfect and be in-between

two position, all the input current will pass through

the ammeter, which can damage itsresiatnce and

sensitivity

2-Ayrton Shunt arrangement

when the switch inbetween two position, not all

the urrent pass through the ammter


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Example-2

For the circuit shown below, calculate the values of

Ayrton resistances Ra, RB, RC

For the 3 v- range

3= Ifs*Rt = 50*10-3 (Ra+Rm)

3= 50*10-3

(Ra+1K)

Ra =59 K

For the 10 v- range

10= Ifs*Rt = 50*10-3

(Ra+ Rb +Rm)

10= 50*10-3

(59 K +Rb+1K)

Rb =140 K

For the 30 v- range

30= Ifs*Rt = 50*10-3(Ra+ Rb + Rc +Rm)

30= 50*10-3

(59 K +140+Rc+1K)

Rc =400 K

Rc

RaRb

Ifs A

RmA


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Restriction for using the Ammeter

The ammeter is connected in series with

circuit under test (CUT), so the circuit pathmust be broken to connect the ammeter

Polarity must take into consideration to avoid

reverse pointer deflection

Use highest voltage range when measure

unknown current, then choose the suitable

range

The internal resistance of the ammeter must be

very small when compared with the circuit

under test(CUT), so very small voltage drop

happened which not change the measured

current

For ideal ammeter we consider Rm=0

If the meter resistance is 1% of the CUT

resistance, then 1% reduction in current will

occur

CUTCUTCUTCUTCUTm R

V

R

V

RR

V

RR

VI 99.001.101.0

==+

=+

=

Such error is called Loading Error


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ANALOG VOLTMETER

PMMC meter can be converted to

Voltmeter by addition of seriesresistance Rs

VFs = IFs ( Rm + RS )

m

fs

Fss R

I

VR =

VFs voltage reading at full scale deflection

Rs Series resistance used to convert PMMC to voltmeter

Ammeter is connected in series with the

circuit, so PMMC needs parallel resistance

Voltmeter is connected in parallel with the

circuit, so PMMC needs series resistance

Example-3

Compute the series resistance required to convert

an ammeter with full-scale current of 250A and an

internal resistance of 250 into a voltmeter that

reads 10V full scale

=== KA

VR

I

VR m

fs

Fss 75.39250

250

10


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Multiple range voltmeters Types

1-Conventional arrangement

Disadvantge

If the switch is between

two resistance, the meter

will measure nothing

Only one resisatance will

be in series with Rm

2-Modified arrangement

Resistor RD is always in the circuit

RD must be selected for the practical meterresistance, Where RD is the replacement of RS

all other resistor can be standards resistor

m

fs

FsD R

I

VR =


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Restriction of Using the Voltmeter

Voltmeter connected with CUT in parrallel

connection

Polarity must be take into consideration

Use large scale at first, and then choose the

suitable scale

The greatest accuracy occur when the meter is

reading near close to full-scale deflection.

Voltmeter should have much greater resistance

than resistance of CUT, Otherwise loading

effect happenend

There are other errors such as calibration or

reading error.

Ideal voltmeter must have internal

resistance equal to


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Voltmeter Sensitivity

The voltmeter sensitivity is measured by/V

FS

m

FS V

R

IS ==

1

S sensitivity, /V

IFs full-scale meter current, A

Calculation of the loading error is done by using

Thevining resistance

Requivalent = RTh +Rm

RTh

VTh


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Example-4

(a) Compute the sensitivity of the meter,

when it have 250A full-sacle

defelection and the interenal meter

resistance is 40K. while the full-

scale deflection is 10V.

(b) Compute the loading effect when the

meter is used to measure VAB

(a) S= (1/IFs) = (1/250A) = 4K/v

Or S=Rm/VFs = 40 K /10V = 4K/v

(b) RTH = 10K //10K = 5K

VTH = 20*10/(10+10) = 10V

Vmeas (A-B) = 10*40/(40+5) = 8.89V

Loading Error = [(10-8.89)/10]*100=11.1%


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Example-5

For the figure shown

calculatethe loading effect for

the following cases:

(a) Meter with S=1K/v,internal resistance 0.2 K

(b) Meter with S=20K /v, internal resistance1.5 K and the VFS=10V

(a) VTh= 30*5/(5+25)=5V

RT=S*Vfs= 1K/V*10V=10K

RTH =25K //5K = 4.1666 K

Vmeas (A-B)= 5*10/(10+4.1666) = 3.53V

Loead error =[(5-3.53)/5]*100 =29.4%

(b) VTh= 30*5/(5+25)=5V

RTH =25K //5K = 4.1666 K

RT =S*Vfs = 20K /V*10V = 200K


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When V=10V

Vth= 10*4/(36+4) =1V

Rth = 36//4 =3.6 KRT=S*V = 20 KV *1V = 20K

Vab=(1*20/(3.6+20) =0.8467 V

% of Error =[(1-0.8467)/1]*100 =15.33%

When V=30V

Vth= 30*4/(36+4) =3V

Rth = 36//4 =3.6 K

RT=S*V = 20 KV *3V = 60K

Vab=(3*60/(3.6+60) =2.83 V

% of Error =[(3-2.83)/3]*100 =5.66 %

As voltage scale or the meter

internal resitance increase as the

loading error decreases

As the sensitivity increases as theloading error decreases


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AC voltemeter

For AC, the average value will be zero, so

the signal must full-wave rectifierd , so atthis point an average value will be present

Although the meters respond to the

average value it can be calibrated to read

rms value.

Crest factor = (peak value/rms value)

Die- Electrode -- Diode


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For type-1 (left) color band

R = AB*10multiplier

R=R+T*R

For other (middle and right) color band

R = ABC*10multiplier

R=R+T*R

Temperature Coeff. PPM/Co

Tolerance %

1 2 0.5 0.25 0.1 0.05 5 10

multiplier

1 10 10

10

10

10 10

10

10

10

10-

10-

Significant Figures

Date post:	10-Apr-2018
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