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9-22
Electrical Instrumentation
Resistance Meuurmnent
The Pig. 9.17 is the basic circuit of the Kelvin bridge. The resistance Ry represents the resistance of the connecting leads from R3 to R,.. The resistance Rx is the unknown resistance to_ be. measured.
i.....l\� ._____+-lll-----..J
The galvanometer can be connected to either terminal a, b or terminal c. When it is connected to a, the lead �tance Ry gets added to Rx hence the value measured by the bridge, indicates much higher value of R,..
Fig. 9.17 Kelvin bridge
U the galvanometer is connected to terminal c, then R_y gets added to R3• This results in the measurement of Rx much lower than the actual value.
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The point b is in between the points a and c, in such a way that t he ratio of the resistance from c to b and that from a to b is equal to the ratio of R1 and R2•
.•.
asy
... (1)
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Now the bridge balance equation in its standard form is,
R1R3 = R2_R�
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But R3 and Rx now are changed to R3 +. Rab and Rx + Rd> respectively due to lead resistance.
... ...
Now we have,
..
Rcb = RI Rab
R2
Rcb R + 1 :--1+1 Rab R2 Rcb +R ab R1 +R 2 = Rab R2
But
Rcb + Rab = Ry
. .. (3)
net
. .. (4)
... adding 1 to both sides I
.:. (5) ... total lead resistanre
Substituting in (5) we get, R y = R 1 +R 2 ·· Rab R2
... (6)
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9-22
Electrical Instrumentation
Resistance Meuurmnent
The Pig. 9.17 is the basic circuit of the Kelvin bridge. The resistance Ry represents the resistance of the connecting leads from R3 to R,.. The resistance Rx is the unknown resistance to_ be. measured.
i.....l\� ._____+-lll-----..J
The galvanometer can be connected to either terminal a, b or terminal c. When it is connected to a, the lead �tance Ry gets added to Rx hence the value measured by the bridge, indicates much higher value of R,..
Fig. 9.17 Kelvin bridge
U the galvanometer is connected to terminal c, then R_y gets added to R3• This results in the measurement of Rx much lower than the actual value.
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The point b is in between the points a and c, in such a way that t he ratio of the resistance from c to b and that from a to b is equal to the ratio of R1 and R2•
.•.
asy
... (1)
En gi
Now the bridge balance equation in its standard form is,
R1R3 = R2_R�
nee rin g.
... (2)
But R3 and Rx now are changed to R3 +. Rab and Rx + Rd> respectively due to lead resistance.
... ...
Now we have,
..
Rcb = RI Rab
R2
Rcb R + 1 :--1+1 Rab R2 Rcb +R ab R1 +R 2 = Rab R2
But
Rcb + Rab = Ry
. .. (3)
net
. .. (4)
... adding 1 to both sides I
.:. (5) ... total lead resistanre
Substituting in (5) we get, R y = R 1 +R 2 ·· Rab R2
... (6)
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