The Wheat Stone Bridge Lab Report

Wheatstone Bridge Name: Emily A. Gatlin Partner: Whitney Heaston Date Performed: February 4th, 2009 Date: February 11th, 2009 T.A. John Caruth

PURPOS E In many common electronic devices, a device called a Wheatstone bridge establishes a reference voltage or maintains a constant electric potential ratio within linear operational amplifier circuits. This experiment teaches the how to use a potentiometer in order to understand the basic This lab shows the basic concept of how a Wheatstone bridge operates to allow the calculation of an unknown resistance using a standard resistance with the relationships between the resistance of a specified material, its resistivity, the length involved and the cross-sectional area. Lastly, this experiment requires the calculation of several conductors’ resistivities.

INTRODUC TION The Wheatstone bridge gives a precise method to measure resistance against a known standard. Within a Wheatstone bridge, a comparative device measures two additional relative resistances from two separate resistors. The relative resistance equals the lengths of a divided wire wound in a coil of ten-turns within a potentiometer, a device allowing the manipulation of this resistance ration. Thus, the Wheatstone bridge utilizes repetitive comparisons of potentials to find the equipotential settings. Within this experiment, a voltmeter is used as the null detector and is placed as shown in the diagram. From the diagram, the Wheatstone bridge achieves balance when point B is at the same potential as point C—where no current flows from B  through the voltmeter.

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Emily A. Gatlin

Wheatstone Bridge

Rx A

I

Rs

C V

I2 R1

February 11, 2009

I2

B

D

R2

I1

I1

I

Power Supply + ― Therefore:

Divide these equations together to get: The Wheatstone bridge uses the potentiometer whose sliding contact manipulates the resistance to be proportional to the length of the wire where this sliding contact is located. The bridge is balanced by manipulating this contact until no potential difference is detected. At the balance point (B), the divisions of the wire lengths,

and

exist in proportional quantities to the

resistance. and

where

and since length is proportional to the

number of turns, the length ratio equals the ration to turns.

Clearly, the Wheatstone bridge uses the standard and the relative lengths/turns of a divided uniform wire to compute the unknown resistance. Page 2

Emily A. Gatlin

Wheatstone Bridge

February 11, 2009

It follows that the since the uniform conducting material directly correlates to the length of the material, but is inversely proportional to the cross-sectional area, the constant of proportionality or resistivity for a certain temperature varies across materials. However, if a conductor shaped in a long cylindrical fashion (wire), then resistance is:

Therefore, this constant allows the calculation of the resistance. PROCEDURE The apparatus for the Wheatstone bridge is a ten-turn potentiometer, a voltmeter, a standard decade resistance box, set of resistance spools of wire, a power supply, a momentary contact switch, and a set of connecting wires. After the apparatus is assembled correctly, using the concept that at equal resistance, the potential is zero at the null point of the Wheatstone bridge. After we found the null point, the ratios from the length along with the known resistivities provide the necessary data to calculate the various resistors’ resistances.

DATA

Coil No.

n1

10.00-n1

1 2 3 4 5

3.92 5.31 5.04 5.90 5.07

6.08 4.69 4.96 4.10 4.93

Data Table I Rs 1.00E+00 2.00E+00 1.00E+00 3.00E+00 9.00E+00

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Rx 6.45E-01 2.26E+00 1.02E+00 4.32E+00 9.26E+00

Emily A. Gatlin

Wheatstone Bridge

February 11, 2009

Coil No.

Resistivity

Length

Data Table II Cross-Sectional Area

Resistance

1 2 3 4 5

ρ (10-8 Ω∙m) 1.70E-08 1.70E-08 1.70E-08 1.70E-08 3.20E-08

L (m) 10.00 10.00 20.00 20.00 10.00

A (10-8 m2) 3.22E-07 8.04E-08 3.22E-07 8.04E-08 3.22E-07

R (Ω) 5.28E-01 2.11E+00 1.06E+00 4.23E+00 9.95E-01

RESULTS Coil No.

Measured Resistance

Calculated Resistance

Percent Difference

1 2 3 4 5

R (Ω) 6.45E-01 2.26E+00 1.02E+00 4.32E+00 9.26E+00

R (Ω) 5.28E-01 2.11E+00 1.06E+00 4.23E+00 9.95E+00

% -22.11% -7.32% 4.14% -2.06% 6.98%

The resistance of the wire appears to be proportional to the length of the wire and inversely proportional to the radius of the wire. The data consists of a slight error, but this could be from the use of a voltmeter as the determinate of the null point versus a galvanometer. Additionally, there is always the possibility for human error and mechanical error in the apparatus. However, the data appears to be consistent with the equation,

CONCLUSION This lab effectively showed how the Wheatstone bridge provides a mechanism to calculate an unknown resistance using the known relationships given through the resistivity correlation to length. It demonstrated how to set-up a Wheatstone bridge and how to manipulate a Wheatstone bridge in a laboratory setting. In addition, the lab provided a demonstration of the aforementioned linear relationships. Although significant error existed in this lab, the results still reflect the relationships governing the Wheatstone bridge sufficiently for understanding in an experimental contextual environment.

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