The Wheatstone Bridge

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description

Combining the above gives the Wheatstone Bridge (WB) equation:. The Wheatstone Bridge. Using Kirchhoff’s Voltage Law:. red loop: E i = I 1 R 1 + I 2 R 2. green loop: E i = I 3 R 3 + I 4 R 4. blue loop: E o = I 4 R 4 - I 2 R 2. gold loop: E o = -I 3 R 3 + I 1 R 1. - PowerPoint PPT Presentation

Transcript of The Wheatstone Bridge

Page 1: The Wheatstone Bridge
Page 2: The Wheatstone Bridge

The Wheatstone Bridge

Figure 4.10

Using Kirchhoff’s Voltage Law:

red loop: Ei = I1R1 + I2R2

green loop: Ei = I3R3 + I4R4

blue loop: Eo = I4R4 - I2R2

gold loop: Eo = -I3R3 + I1R1

Using Kirchhoff’s Current Law:

Combining the above gives the Wheatstone Bridge (WB) equation:

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3

21

1

RR

R

RR

REE io

I1 = I2 (at top node) I3 = I4 (at bottom node).

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• What is the Wheatstonebridge equation if anotherresistor, Rx, is added in parallel with R1 ?

Rx

• 1/Rnew = 1/Rx+1/R1

• To solve, simply substitute

Rnew = R1Rx / (R1+Rx)

into the original WB equation for R1.

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• One advantage of using two resistors in parallel in one leg of the WB is that the added resistor can be located remotely from the actual WB, such as in a flow.Here, that resistor can serve as a sensor.

Rx

FLOW

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1

RR

R

RR

R

• When Eo = 0, the WB is said to be ‘balanced’ →

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1

RR

R

RR

REE io

4321 // RRRR →

• When the WB is balanced and 3 of the 4 resistances are known, the 4th (unknown) resistance can be foundusing the balanced WB equation. The is called the null method.

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RR

R

RRR

RREE io )(

)(

• Now consider the case when all 4 resistors are thesame initially and, then, one resistance, say R1, is changedby an amount R. This is called the deflection method.

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RR

R

RR

REE io

RR

RREi /24

/

• Often, R is associated with a change in a physical variable.

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In-Class Example

Figure 4.18

RTD: RTD = 0.0005 / ºC; R = 25 at 20.0 ºCWheatstone Bridge: R2 = R3 = R4 = 25 Ei =5 VAmplifier: Gain = GMultimeter: 0 V to 10 V range (DC)Experimental Operating Range: 20 ºC to 80 ºC

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In-Class Example

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Cantilever Beam with Four Strain Gages

• When F is applied as shown (downward), R1 and R4 increase by R (due to elongation), and R2 and R3 decrease by R (due to compression). Here, R is

directly proportional to the strains.

Figure 4.11

• From solid mechanics, for a cantilever beam, both the elongational strain, L, and the compressive strain, C, are directly proportional to the applied force, F.

Figure 6.2

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The Cantilever Beam with Four Gages

• The WB equation

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1

RR

R

RR

REE io

)()(

)(

)()( RRRR

RR

RRRR

RREE io

• This instrumented cantilever beam system is the basis for many force measurement systems (like force balances and load cells.

• Because R ~ (L or C) and (L or C) ~ F, Eo = constant x F

becomes

which reduces to Eo = Ei (R/R).