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Whetastone bridge is an electrical bridge circuit used to measure the resistance.
Typology: Study notes
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It may be shown by experiment that the electrical resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. The resistivity ρ is then defined by the equation
R = ρL/A
The Wheatstone Bridge is an instrument designed for measuring an unknown resistance by comparing it with a known, or standard, resistor.
In the schematic diagram in section IV, R 1 is an unknown resistor whose value is to be determined. Three known resistors are required, as well as a galvanometer and a cell (battery). In use, the bridge is "balanced" by adjusting one or more of the known resistors until there is no current through the galvanometer. When this is done, R 1 may be calculated from the three known resistors by an equation derived below.
Although four separate resistors may be used, there are simpler forms of the bridge.
In the box form of bridge, used in Experiment 9, R 2 consists of a 4-dial resistance box with one dial for each of thousands, hundreds, tens and units of ohms. R 3 and R 4 are combined into the multiplier dial.
In the slide wire form of bridge, used in this experiment, R 2 is a plug resistance box. R 3 and R 4 together make up a one-meter length of uniform wire. Point D is a sliding contact on the wire. S 1 is a switch whose purpose is to avoid running the cell down when the bridge is not being used. S 2 , R 5 , and G together make up the "three-button galvanometer". Pushing different buttons S 2 varies the sensitivity of the galvanometer by selecting different values of R 5.
When the current through the galvanometer has been reduced to zero by moving the sliding contact point D, then points B and D must be at the same potential. Also, since no current is going through the galvanometer, the current through R 1 must be the same as the current in through R 2 ; it is labeled I 1. For the same reason, the current through R 3 must be the same as the current through R 4 ; it is labeled I 2.
The fact that VAB = VAD means that I 1 R 1 = I 2 R 3. The fact that VBC = VDC means that I 1 R 2 = I 2 R 4. Dividing these two equations, we obtain R 1 /R 2 = R 3 /R 4.
Since R 3 and R 4 are two parts of the same continuous piece of wire, they have the same resistivities and cross-sectional areas. It follows that the ratio of their resistances is the same as the ratio of their lengths, R 3 /R 4 = L 3 /L 4.
As a result, R 1 /R 2 = L 3 /L 4 or R 1 = R 2 L 3 /L 4.
The main advantage of the slide wire form of Wheatstone Bridge is that it requires only one standard resistor, R 2. In addition, its open design allows the student to see exactly how it works. The box form of bridge, on the other hand, is more accurate and quite portable.