THE SIMPLE PENDULUM

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WHEATSTONE BRIDGELAB REPORT

PHY 204

OCTOBER 6, 2011Introduction A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. It was invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. The advantage of this device is that it eliminates the internal resistance or current that other measurement devices have, which effect the circuit they are measuring. This is possible because when the two legs of the circuit are balanced there is no current flowing between them, which not only tells you that the circuit is balanced but when the current is zero, there is no effect of the meter on the circuit. When this lab is complete, a student will have a better understanding of circuit testing devices, especially the ohmmeter, their uses, advantages and disadvantages, and specifically how to construct a Wheatstone bridge to make the more accurate resistance measurements. Apparatus

Wheatstone bridge board Resistance Box with adjustable resistance values

2V power supply

Galvanometer

Rheostat

1 meter of NiChrome Wire .010

Meter stick

Micrometer

Digital Multimeter

Single clay resistor in the 5K Ohm range

Procedure Part I. Connect the circuit as shown in Figure 2. Set the resistance box R1 to 7 ohms. Cut 1 meter of wire from the spool and connect one end to the screw in the center of the Bridge board and the other to the alligator clip from the Galvanometer at a distance of 50 Cm from the screw. The rheostat can be used to adjust the sensitivity of the bridge, (but in our case the rheostat was not making a connection anywhere except for the lowest setting position so it could not be properly used.) Take the other end of the galvanometer and connect it near the center of the L1/l2 wire. Observe the needle of the galvanometer as the clip is moved along the L1/L2 wire and find a place where the needle reads zero. This point determines L1 becomes L2. Record the distances of L1 and L2. Repeat these measurements for wire lengths of 60, 70, 80, 90, and 100 Cm.Part II. Take the resistor provided by the TA and read and record the color code. Set the resistance box to a value that is approximately within 20% of the resistor value. Use a DMM set to ohms, measure and record another reading of the resistance value. Clip the resistor in place of the wire in the previous experiment and use the same process as the previous experiment to calculate the resistor value. Record resistor value so you end up using three different measurement methods to find the resistance.Data Book

Experiment I -- Resistance Calculations

Material = 0.0254 (CM) NiChrome

Length of wire (M)R1 value (Ohms)L1 (M)L2 (M)RX (Ohms)

0.4570.580.429.67

0.5570.630.3711.92

0.6570.670.3314.21

0.7570.70.316.33

0.8570.720.2818.00

0.9570.750.2521.00

Experiment I -- Resistivity Calculations

Material = 0.0254 (CM) NiChrome

Slope from Experiment 1 GraphRadius of wire (M)Area (M2 ) Resistivity (Ohm *M)

22.0091.27E-045.067E-081.12E-06

Experiment II Bridge Calculation

Unknown ResistorR1 value (Ohms)L1 (CM)L2 (CM)RX (Ohms)

RX510050.549.55203.03

Experiment II Results

Unknown Resistor

Unknown ResistorBridge Value (Ohms)Color code Value (Ohms)Ohmmeter Value

RX520351005180

Analysis

The idea in this lab is that measuring the resistance in the Wheatstone bridge method give a more accurate reading because the internal resistance of the meters are taken out of the equation. the longer the L1/L2 are the more resolution and less error the setup should have. Since the reading of when the galvanometer shows a balanced circuit is zero, this lowers the complexity of the meter since it can measure zero current relatively accurately. Calculations The calculations is this lab were quite straight forward. Actually I let Excel do all the work. To calculate the resistances of the lengths of nichrome wire, the calculation is simple the ratio of L1 /L2 multiplied by R1To calculate the resistivity we need the slope of our graph, which is just the resistance divided by the length. This is multiplied by the area which of course is pi*R^2

Significant Figures I did not at all feel confident with the equipment used in the lab. I did not have any method of calibrating our results against a positively known result and we did not know the actual error in the resistor decade box or the single clay resistor so I'm concluding an error range of up to 20%Discussion

One point that I felt was significant in this lab is the idea that using some basic equation manipulation combined with some basic hardware, a new device can be made that greatly improves the accuracy of the measuring equipment. This lesson should be remembered and applied to future physics problems or situations.

I suspect that there may be some hidden resistance in the hardware of the bridge equipment. It was very old and to complete the setup, many wire leads had to be connected. If the number of shaky connections could be eliminated, I would expect the accuracy would go up.I would like a resistor of a positively know value to be available. This way a test could be made of the accuracy and boost confidence in the accuracy of the process.Conclusion

In this lab we have successfully used the bridge device to measure resistance. Since we measured a known resistor and had a reading within the tolerance range of the resistor we can conclude that our measurements are at least close to being correct. However, without having any knowledge of the actual value of the resistance of the nichrome wire it would be premature to conclude that out tests are more accurate then the DMM measurementsAnalysis Questions 1. Is there a difference between the resistor color code and the bridge value? Yes. The resistor color code of Green Brown Red Gold indicate a nominal resistance of 5100 ohms with a tolerance of 5% while the bridge measured 5203. The 5% on the tolerance allows a range or 4845 to5355 ohms which could explain the difference. This assumes that our bridge was actually measuring correctly.