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
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
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ffb5940-8759-4322-8c6c-95ef762da973%2Fc0d1267d-86a0-42e5-ac97-eb76ba473f05%2Fyq9uqyi_processed.jpeg&w=3840&q=75)
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
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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](https://content.bartleby.com/qna-images/question/58dd768f-8c36-4170-80fa-1dffd6b7b187/90e2f7ea-626f-4f50-969c-1dabb2d1a74e/rd3dndr_thumbnail.png)
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
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).](https://content.bartleby.com/qna-images/question/9ffb5940-8759-4322-8c6c-95ef762da973/e7bc97ef-9911-400b-a0ca-2461072ff205/n9560ha_thumbnail.png)
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
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](https://content.bartleby.com/qna-images/question/9ffb5940-8759-4322-8c6c-95ef762da973/f408458f-4819-409d-9665-89cd7b331651/e8n8ndf_thumbnail.png)
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
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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