Please give step by step when deriving the equation given. Four resistors are used as a Wheastone bridge arrangement. In dynamic deflection operationwith R₁ representing a strain gage and R4 representing a potentiometer, the bridge is firstbalanced by adjusting R4.Vax+R₂When R, R₁ + AR,then ou0+ AVFigure Q1Then obtain the following expression for the ratiosimplifications. (Please show all your workings.)RAVAR,R₁out +R₁ VΔΙVaoutRiAR₁by using Kirchoff's volatge law and someR₁R₂R₂ + R₂VoR₂R₂ + R₂differentialbufferamplifier

The given wheatstone brideg arrangement is shown below,

Answered: Four resistors are used as a Wheastone…

Introductory Circuit Analysis (13th Edition)

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Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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Please give step by step when deriving the equation given.

Four resistors are used as a Wheastone bridge arrangement. In dynamic deflection operation
with R₁ representing a strain gage and R4 representing a potentiometer, the bridge is first
balanced by adjusting R4.
Vax
+
R₂
When R, R₁ + AR,
then ou0+ AV
Figure Q1
Then obtain the following expression for the ratio
simplifications. (Please show all your workings.)
RAV
AR,
R₁
out +
R₁ V
ΔΙ
Va
out
Ri
AR₁
by using Kirchoff's volatge law and some
R₁
R₂
R₂ + R₂
Vo
R₂
R₂ + R₂
differential
buffer
amplifier

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Follow-up Question

how the first line becomes the second line?

From equation A,
AR₁
R₁₁
AR₁
R₁
=
||
R. ( AVan + R)-(1-4V - R2 + R₂)
R3(AV
R₂
R₂
out
out
R₂ Vi
✓in
+ R3
in
R₂ R3
1
ΔV.
R3
out
R₂
Vin
AV out
Vin
out
R₂
(1-AV-243)
+ R3
+1
AV
R₂
R₂ + R3

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Follow-up Question

how R1 become R1+R4?

From equationA,
R₂R₁ = R₂R4 and A R₁ < < (R₁ + R4),
So,
R₂R₁+R₂ AR₁+R₂R₁R₁R3-R₂R₂
(R3+R₂) (R₁ + AR₁+R4)
R3AR₁
in (R3+R₂)(R₁+R4).
V diff=Vi
V
diff=V.
Equation (B).

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Follow-up Question

R4/R1 = R3/R2 for balanced wheatstone bridge,
so why isn't the equation look like (1+ R2/R3 + R3/R2 + R2*R3/R3*R2) for the middle part in the image given

AR₁
R₁
AR₁
R₁
AR₁
R₁
R₂R4 R4
R₂
=
Vouw [(1 + R$ R₁ + R2 + R)]
Vin
=
=
Voule (1+
Nout
V.
Vi
V₁.
R₂
1+2 +
R3
in
2
R₂
+R)².
R3
1+
R₂
R3

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Follow-up Question

why the denominator is equal to 1 and how to know Vout is very small than Vin ?

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