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