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MEASUREMENT OF RESISTANCE

by WHEATSTONE'S BRIDGE

There are several methods of determining resistance. One of the more common techniques is to use the Wheatstone Bridge. The "bridge" consists of a network of four resistors, three of which are known and the fourth determined. Your text describes it well. The values of the known resistances can be adjusted until the current through the galvonometer is zero. In that condition, the bridge is balanced. Since A and B are at the same potential we can say that:

VAC = VBC

(1)

and

VAD = VBD

(2)

or

I1R1 = I3R3

(3)

and

I2R2 = I4R4

(4)

Since the current in the galvonometer is zero,

I1 = I2

(5)

and

I3 = I4

(6)

thus

R2 / R1 = R4 / R3

(7)

Figure 1: Schematic Representation of the Wheatstone Bridge.

In the laboratory your set-up will include a slide-wire resistance apparatus as follows:

Figure 2: Slide-wire Wheatstone Bridge Apparatus.

A resistance box will be used for R₁ and the unknown resistor is R₂. Since the wire from C to D is uniform and

R = L/A

(8)

i.e., resistance is proportional to the length of the wire. Thus the ratio of R₄ to R₃ is simply the ratio of the two lengths b to a. Then R₂ can be found:

R2 = R1 R4 / R3 = R1 b / a

(9)

OBJECTIVES:

• To study the design and use of the Wheatstone Bridge.
• To measure resistances of several conductors.

APPARATUS:

• 1 Power Supply
• 1 Slide-Wire Resistance Apparatus
• 2 Switch Devices
• 1 Resistance Box
• X Known Resistances

PROCEDURE:

1. Arrange the apparatus as shown in Figures 1 and 2.
   
   
2. Have your instructor check the apparatus.
   
   
3. Calculate the values of several unknown resistances.
   
   
4. Compare these values with known values according to color charts.
   
   
5. In your write-up include:
   1. List and explain any limitations
   2. Record your data in a table similar to the one below:

      R	b(R4)	Q(R3)	R2(Unknown)	R2(Actual)	% Error
      10	10±.02	5±.02	20±.12	21	5

   3. Show all calculations of unknown resistances and errors.
   4. Summarize.
   5. Conclusions and Recommendations.
   
   
6. Answer the following questions:
   1. When the Wheatstone Bridge is balanced is there any current in the resistor being measured?
   2. What are some possible errors in using a Wheatstone Bridge?
   3. If your uncertainty is ± .02 cm in determining the length of the wires, what % uncertainty is expected in the result?
   
   
7. Most problems with this lab occur with loose wires at the terminals.

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