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. Va R₂ R₁ Vo differential buffer

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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
Transcribed Image Text: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 Questions
Read through expert solutions to related follow-up questions below.
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
Transcribed Image Text: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
Solution
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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).
Transcribed Image Text: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).
Solution
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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
Transcribed Image Text: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
Solution
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Follow-up Question

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

Solution
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