INTRODUCTION
Theory
Electrical resistance is one of the most important properties of materials. It is defined mathematically as the ratio of voltage to the current passing through a conductor. In physical sense, it is opposition a material offers to the current flowing through it. This opposition to the passage of electricity is a result of collisions between charge carriers and other sub atomic particles. The collisions reduce the drift speed of electrons that carry charges. Materials that offer greatest opposition to current flow are called insulators while those that allow current to flow through them with minimal hindrance are called insulators.
The resistance of a material reduces with its increase in its cross sectional area. On the other hand, it increases with increase in the length of the material (Meier 9). The longer the wire the greater the number of collision between charges carriers and atoms of the conductor. Consequently, the resistance increases. Conversely, the wider the cross sectional area of the wire the higher the number of charges that can flow through it. Hence, the resistance reduces. The other factor that affects the resistance of a material is the materials itself. Each material has its own ability to resist charges from passing through it. This property is called resistivity. Copper for instance has a lower resistivity than glass.
Resistance of a conductor can be measured directly or indirectly. A digital multimeter can be used to measure the resistance of any material. The process involves connecting the ends of the material (resistor) to the two jacks found in the meter. The other indirect method is by getting the corresponding voltage and current passing through the material and then applying Ohm’s law to find the resistance. The direct method was used in the experiment.
The purpose of the experiment was to measure the resistances of a set of resistors and compare the experimental values with nominal and calculated values. Resistors manufactures often provide the values of resistances of the resistors they distribute in the market. These values are commonly coded using Institute of Electrical and Electronic Engineers color codes. The nominal values of the resistances given by the manufacturers are not expected to differ significantly from experimental values. They are expected at least to remain within the tolerance levels. This experiment was interested in finding out whether large differences exist between the nominal and measured values of resistances.
HYPOTHESIS:
It was hypothesized that the percentage errors would be within the tolerance level. The differences would be higher in series and parallel resistors because of propagated errors.
MATERIALS:
- Digital Multimeter
- Six 110 ohm, 220 ohm, 420 ohm 670 ohm, 840 ohm and 1000ohm resistors
- Probes
PROCEDURE:
The multimeter was switched on and the meter function switch set to Ohms. Two probes were inserted into two ports labeled COM and V (Ω).The two probes were touched together and the meter indicated o zero resistance. The resistance of each resistor was measure by connecting it between the probes and observing the reading on the meter. The readings were recorded.
DATA
The Table 1: Nominal and Measured Resistance Values of the Resistors
RESULTS:
Percentage Errors Calculations
Percentage errors were computed by dividing the difference between nominal values and measured values by nominal values and multiplying the result by 100.
Percentage Error=Nominal Value-Measured ValueNominal ValueX 100%
Resistor #1: 100 Ω
Percentage Error=110-106.7110X100%
3.30%
Resistor #2: 200 Ω
Percentage Error=200-192.5200X100%
3.75%
Resistor #3: 420 Ω
Percentage Error=420-406.4420X100%
3.24%
Resistor #4: 670 Ω
Percentage Error=670-645.90670X100%
3.60%
Resistor #5 840 Ω
Percentage Error=840-817.3840X100%
2.70%
Resistor #6 1000 Ω
Percentage Error=1000-966.21000X100%
3.38%
Parallel Resistors Connection Calculations
The effective resistance of resistors connected in parallel is given by the sum of reciprocal of individual resistances. For series connection, effective resistance is calculated by adding individual resistances
First Connection
1RE=1R1+1R4+1R6
1RE=1110+1670+11000
1RE=8,537737,000
86.3Ω
Percentage Error
% Error= Calculated Value-Measured ValueMeasured Value
86.3-76.186.3
11.8%
Second Connection
1RE=1R2+1R3+1R5
1RE=1200+1420+1840
1RE=3350
116.7Ω
Percentage Error
% Error= Calculated Value-Measured ValueMeasured Value
116.7-105.9116.7
9.3%
Series resistors Connection Calculations
First Connection
RE=R1+R4+R6
110+670+1000
1,780Ω
Percentage Error
% Error= Calculated Value-Measured ValueMeasured Value
1,780-1,619.71,780
9.0%
Second Connection
RE=R2+R3+R5
200+420+840
1,460
1,780Ω
Percentage Error
% Error= Calculated Value-Measured ValueMeasured Value
1,460-1,310.81,460
10.2%
DISCUSSION
The percentage differences between the nominal and measured values of the resistance were below the tolerance level of 5%. Consequently, the hypothesis that the error shall remain within the limits of tolerance level was upheld. The highest difference was 3.75%. These figures indicate that the multimeter had acceptable degree of accuracy. The fact that there was small variation between the percentage errors indicates that these errors were systematic. Perhaps, the instrument was not very sensitive.
The percentage errors of the values of resistors connected in series and parallel were approximately three times the average error in individual cases. The highest percentage error in connected resistors was 10.2%. This was expected because the calculations of effective resistance involved addition and division that propagated the errors. To this end, the second hypothesis that the percentage errors in combined resistance would be higher than individual resistance was upheld.
The accuracy of the experimental process can be improved by using very sensitive meters. In addition, the results should be confirmed independently by indirect methods that involve measurements of current and voltages.
CONCLUSION:
The small percentage errors are an indication that the experiment was successful. The objective of the experiment was achieved because the resistances of the resistors were measured. The results were compared with calculated and nominal values as required.
Work Cited
Meier, Alexandra . Electric Power Systems: A Conceptual Introduction. Hoboken, N.J: IEEE Press, 2006. Print.
