Bridge Methods

8/9/2019 Bridge Methods

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Bridge methods

ABE425 Engineering Measurement Systems


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Measurement pro!edure using "al#anometer and

de!ade resistor bo$

32

2 1 3

32

2 1 3

d i i

x

d i

x

RRV V V

R R R R

RRV V

R R R R

= + +

= + +

Decade Box

Galvanometer

Unknown resistor

Known, constant

At balance:2

1

30d x

R

V R R R= =


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"al#anometers are %E&' SENS()(%E instruments to

dete!t zero current

D'Arsonval galvanometer


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)hompson mirror type gal#anometer *+,,./ Note the

0antenna1 to !ompensate or ele!tri!magneti! ields


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Null-type AC Wheatstone bridge or impedan!e

measurement

'he bridge is balanced $hen the oltage Vdis adusted

to ero by tuning

12

3

x

ZZ Z

Z

=

1 2 3, orZ Z Z

1 3 2x = +

3 1 2x

Z Z Z Z=


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Null-type 3arallel-&esistan!e-Capa!itan!e bridge or

!apa!itan!e and dissipation a!tor measurement

3 1 2xZ Z Z Z=

2 1

3 1 11 1

x

x x

R R R

j R C R j R C = + +

21

3

31

2

Re :

nde!endent o"

m:

x

x

RR R

R

RC C

R

= =

}

}

3 3

1

1 11

1 11

1

2 2

1

1 1

Known, "ixed

1

1 1

Known, "ixed

x

x xx

x xx

x

R

j C RZj R C

Rj C

Z R

R

j C RZj R C

Rj C

Z R

= = ++

=

= =++

=

( ) ( )3 1 1 1 21 1x x xR R j R C R R j R C + = +


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Ma$ell bridge to measure indu!tan!e resistan!e

and 6uality a!tor o lo 6uality !oils *78+.

1 3 2uZ Z Z Z=

( ) 1 2 31 11

u u

RR j L R R

j R C

+ = +

2 3

1

2 3 1

Re :nde!endent o"

m:

u

u

R RR

R

L R R C

= =

1 1u

u

LQ R CR

=

1

1 11

1 11

1

2 2

3 3

1

1 1

Known, "ixed

u u uZ R j L

Rj C R

Zj R C

Rj C

Z R

Z R

= +

= =++

= =

( ) ( )1 2 3 1 11u uR R j L R R j R C + = +


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)he !oil !hara!teristi!s indu!tan!e and series resistan!e !an be

measured by e6uali;ing the #oltage a!ross a #ariable resistor

and the !oil itsel

L L

R

Z R j L

Z R

= +=

( )LV i R j L iR= + =

( )22

LV i R L iR = + =

( )22 2

LR L R+ =

2 21

LL R R

=

Series resistance of the

coil RLmeasured with a DVM


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Dele!tion type DC Wheatstone bridge

32

2 1 3

32

2 1 3

d i i

x

d i

x

RR

V V VR R R R

RRV V

R R R R

= + +

= + +


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+


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?in@s

,chneider N+ 1234+ 5lectrical instruments and testing+

,ponand Chamberlain Ne$ 6or*+
http://books.google.com/books?id=ZZ83AAAAMAAJ&pg=PA13&sig=v31U_QMaInWIfs6Q2g7aSCtkHrQhttp://books.google.com/books?id=ZZ83AAAAMAAJ&pg=PA13&sig=v31U_QMaInWIfs6Q2g7aSCtkHrQhttp://books.google.com/books?id=ZZ83AAAAMAAJ&pg=PA13&sig=v31U_QMaInWIfs6Q2g7aSCtkHrQhttp://books.google.com/books?id=ZZ83AAAAMAAJ&pg=PA13&sig=v31U_QMaInWIfs6Q2g7aSCtkHrQhttp://books.google.com/books?id=ZZ83AAAAMAAJ&pg=PA13&sig=v31U_QMaInWIfs6Q2g7aSCtkHrQhttp://books.google.com/books?id=ZZ83AAAAMAAJ&pg=PA13&sig=v31U_QMaInWIfs6Q2g7aSCtkHrQ


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)he End

Bridge Methods

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