Metallic Conductor

Determination of r for a Metallic Conductor Aim: To determine the resistivity (r) of a given sample of wire Introduction: Physical factors that affect the resistance of a conductor are length, cross sectional area and a constant that depends upon the material called the resistivity. The resistance per unit length is the same all along a uniform wire so if the resistance of different lengths of a wire is found out, the resistivity can be calculated. Resistance of a material, R = Voltage / Current Resistance of a conductor, R = r × Length / Cross sectional area Apparatus: - 12V power supply - Power leads - 6 connecting leads - 2 crocodile clips - given sample of wire (» 5 m) - variable resistor – is used to alter the resistance to change the current and voltage for each length - ammeter – the 5 ampere outlet was used since the current was generally over 1 amperes - voltmeter – the 5 volt outlet was used because voltage was always below 5 volts - meter stick – more appropriate than a 30 cm ruler because the length is changed by 50 cm each time - micrometer – since the wire is very thin an accurate measurement of the diameter can be obtained by using a micrometer with an uncertainty of ± 0.0005mm. Diagram: Method: 1. Set up the apparatus as shown on the diagram. 2. Make sure the voltmeter outlet is at 5 volts and the ammeter outlet is at 1 amp. 3. Measure 50 cm of the wire using the meter stick. 4. Connect this part of the wire to the circuit using the crocodile clips. 5. Make sure the wire is not touching other parts of the wire. 6. Turn the power supply on, record the voltage and current. 7. Using the variable resistor, alter the resistance and take 4 more different readings of voltage and current for this length. 8. Repeat steps 4 to 6 for 5 more times, each time increase the length of wire by 50 cm using the meter stick. 9. Draw a graph of current against voltage for each length and find the resistance of each length by finding out the gradient of the graphs. 10. Measure the diameter of the wire using the micrometer. Take 3 reading at different places on the wire to reduce the uncertainty. 11. Calculate the cross sectional area of the wire, using the formula Area = p ´ radius2 12. Draw a graph of resistance against length. 13. Find the resistivity of the wire by finding the gradient of the graph and multiplying it by the cross sectional area. ( R = r L / A ) Results: Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 0.5 0.70 1.15 0.5 1.30 2.00 0.5 1.90 3.10 0.5 2.45 3.90 0.5 2.90 4.70 Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 1.0 0.55 0.40 1.0 1.05 0.85 1.0 1.60 1.25 1.0 2.50 1.95 1.0 4.05 3.10 Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 1.5 0.80 0.40 1.5 1.50 0.80 1.5 2.45 1.30 1.5 3.80 1.90 1.5 4.50 2.30 Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 2.0 0.90 0.35 2.0 1.30 0.50 2.0 2.20 0.85 2.0 3.40 1.30 2.0 4.30 1.65 Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 2.5 1.20 0.35 2.5 1.40 0.45 2.5 2.35 0.75 2.5 3.35 1.00 2.5 4.70 1.45 Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 3.0 1.00 0.25 3.0 1.70 0.45 3.0 2.80 0.75 3.0 3.80 1.00 3.0 4.90 1.25 Diameter of the wire: 1st reading = 0.709mm ± 0.0005 mm 2nd reading = 0.710mm ± 0.0005 mm 3rd reading = 0.710mm ± 0.0005 mm Analysis & Conclusion: Length (m)± 0.01 Resistance (ohms) 0.5 0.6161 ± 0.00071 1.0 1.306 ± 0.00098 1.5 1.985 ± 0.0025 2.0 2.618 ± 0.00046 2.5 3.263 ± 0.0052 3.0 3.883 ± 0.0049 Average diameter of wire = 0.710mm ± 0.0005 mm = 7.1 ´ 10 –4 m ± 5 ´ 10 –7 m Radius = 3.55 ´ 10 –4 ± 2.5 ´ 10 –7 = 3.55 ´ 10 –4 ± 0.0704 % Area = p ´ radius2 = p ´ (1.26 ´ 10 –7 ± 0.1408 %) = p ´ (1.26 ´ 10 –7 ± 1.77 ´ 10 –10) = 3.96 ´ 10 –7 m2 ± 5.57 ´ 10 –10 m2 Gradient of Resistance against Length graph = 1.307 1.307 = r / Cross sectional area = r / (3.96 ´ 10 –7 ± 5.57 ´ 10 –10 ) r = 5.176 ´ 10 –7 ± 7.28 ´ 10 –10 W m It was concluded from the experiment that the resistivity (r) of the wire is 5.2 ´ 10 –7 ± 7.3 ´ 10 –10 W m. Evaluation: - The actual value for the resistivity is 4.7 ´ 10 –7 W m. The resistivity value from the experiment is 5.2 ´ 10 –7, which is close to this value. - Resistivity is dependant on temperature and the temperatures in which these values were measured are not known. Since the uncertainty of the experimental value is very small, the difference between the values may be due to the temperature difference in which they were found. - Also, the purity of the metal wire is unknown. The metal may not be completely pure; there may be impurities in it and the experimental resistivity value may be different from the actual value because of this. - One of the uncertainties in the experiment was that it was very difficult to measure the length of the wire accurately. The wire was not straight and it was very hard to straighten it since it was very rigid. A new, straight wire should be used in order to avoid this inaccuracy. - The diameter of the wire was also difficult to measure because of the shape of the wire. Since it was twisted, it had dents in some parts and this made the reading inaccurate. This can also be avoided by using a straight wire and taking measurements from different parts of the wire. - In addition, the wire was not connected properly to the circuit since the crocodile clips touched only some parts of the wire. There should be better contacts to the wire; the wire should be surrounded completely. Soldering the contacts to the wire will minimize this uncertainty.