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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 $hen the oltage Vdis adusted
to ero by tuning
12
3
x
ZZ Z
Z
=
1 2 3, orZ Z Z
1 3 2x = +
3 1 2x
Z Z Z Z=
8/9/2019 Bridge Methods
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8/9/2019 Bridge Methods
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Null-type 3arallel-&esistan!e-Capa!itan!e bridge or
!apa!itan!e and dissipation a!tor measurement
3 1 2xZ Z Z Z=
2 1
3 1 11 1
x
x x
R R R
j R C R j R C = + +
21
3
31
2
Re :
nde!endent o"
m:
x
x
RR R
R
RC C
R
= =
}
}
3 3
1
1 11
1 11
1
2 2
1
1 1
Known, "ixed
1
1 1
Known, "ixed
x
x xx
x xx
x
R
j C RZj R C
Rj C
Z R
R
j C RZj R C
Rj C
Z R
= = ++
=
= =++
=
( ) ( )3 1 1 1 21 1x x xR R j R C R R j R C + = +
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Ma$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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8/9/2019 Bridge Methods
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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_QMaInWIfs6Q2g7aSCtkHrQ8/9/2019 Bridge Methods
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)he End