INTRODUCTION
The study of electrical conductivity in metals is a cornerstone of materials
science and solid-state physics, offering insights into electron behavior and
its role in electrical and thermal transport. This experiment measures the
electrical conductivity of copper (Cu) and aluminum (Al)—two widely used
conductors—using the four-point measurement technique, known for its
accuracy in minimizing contact resistance. Conductivity, the ability of a
material to conduct electric current, is primarily driven by free electron
movement within a metal’s lattice, making metals highly conductive
compared to insulators or semiconductors.
The experiment is grounded in Ohm’s Law (V = I · R), which relates voltage
(V), current (I), and resistance (R), and the Wiedemann-Franz law, which
links electrical conductivity (σ) to thermal conductivity (k) via the
relationship k / σ = L · T, where L is the Lorenz number (approximately 2.44
× 10⁻⁸ W·Ω·K⁻² at room temperature) and T is the absolute temperature.
This law highlights the shared role of electrons in both conduction types, a
key feature of metallic behavior above the Debye temperature.
Copper and aluminum were chosen for their practical significance—copper
for its high conductivity and ductility, and aluminum for its lightweight
properties and reasonable conductivity. The four-point method ensures
precise resistance measurements, enabling accurate conductivity
calculations (σ = L / (R · A), where L is length and A is cross-sectional area).
The experiment aims to quantify conductivity, compare it with theoretical
values, and, if thermal data is available, verify the Wiedemann-Franz law.
Variations due to impurities, temperature, or setup errors may reveal
material quality or experimental limitations, making this a valuable exercise
in understanding metallic properties and advanced measurement
techniques.
EXPERIMENTAL TABLES
Current(A) Voltage(V)
0.3 1.25
0.6 1.30
0.9 1.35
1.2 1.40
1.5 1.45
1.8 1.50
2.1 1.55
2.4 1.60
2.7 1.65
Table 1(A table of values for current(A) and voltage (v))
Current(A) Voltage(V) Resistance(Ω) = V/I
0.3 1.25 4.167
0.6 1.30 2.167
0.9 1.35 1.500
1.2 1.40 1.167
1.5 1.45 0.967
1.8 1.50 0.833
2.1 1.55 0.738
2.4 1.60 0.667
2.7 1.65 0.611
Table 2( A table of values for Current(I), Voltage(V) and Resistance(Ω))
DIAGRAM OF SETUP
Fig 1
GRAPH OF OBSERVATION
Fig 2(A graph of voltage(v) against current(A))
THEORY
The theory of this experiment on the electrical conductivity of metals is
based on the movement of free electrons within metallic lattices, a property
that makes metals like copper (Cu) and aluminum (Al) highly conductive.
Electrical conductivity (σ) is defined as the reciprocal of resistivity (σ = 1 / ρ),
where ρ = R · (A / L), with R as resistance, A as cross-sectional area, and L as
length. Resistance is determined using Ohm’s Law (V = I · R), where V is
voltage and I is current, allowing σ to be calculated as σ = L / (R · A).
The four-point measurement technique is employed to measure resistance
accurately by minimizing contact and lead resistance, using two outer probes
for current and two inner probes for voltage. This method ensures the
intrinsic resistance of the metal sample is isolated. The experiment records
voltage and current data to establish a linear relationship, confirming ohmic
behavior.
The experiment also relates to the Wiedemann-Franz law, which connects
electrical conductivity (σ) to thermal conductivity (k) via (k / σ) = L · T, where
L is the Lorenz number (approximately 2.44 × 10⁻⁸ W·Ω·K⁻² at room
temperature) and T is absolute temperature. This law reflects the dual role of
electrons in charge and heat transport, applicable above the Debye
temperature. While thermal data is not directly measured, the electrical
conductivity can be compared to standard values—copper at 5.96 × 10⁷ S/m
and aluminum at 3.5 × 10⁷ S/m—to assess the law’s relevance. Deviations
may arise from impurities, temperature effects, or experimental errors,
providing insights into material properties and measurement precision.
PROCEDURE
1. Prepare Equipment:
- Gather a copper rod, aluminum rod, rheostat (10 Ω, 5.7 A), multitap
transformer (14 VAC/12 VDC, 5 A), digital multimeter, universal measuring
amplifier, and connecting cords (500 mm red and blue).
2. Set Up Circuit:
- Assemble the four-point measurement circuit per Figure 3.1. Connect
outer probes to the transformer/rheostat and inner probes to the
multimeter/amplifier. Set transformer to 6 V and calibrate amplifier to 0 V
(Low Drift, Amplification 10^4, Time Constant 0).
3. Measure Data:
- Start rheostat at maximum resistance, then decrease gradually. Record
current and voltage using the multimeter. Calculate resistance (R = V / I) for
each point.
4. Verify and Repeat:
- Repeat measurements for both rods to ensure consistency. Adjust
contacts if anomalies occur.
5. Safety and Cleanup:
- Disconnect power before adjustments. Store equipment and clean
workspace.
Use σ = L / (R · A) (with L = 0.315 m, A = 4.91 × 10⁻⁴ m²) to calculate
conductivity.
RESULTS AND DISCUSSION
Results and Discussion
The experiment involved measuring the voltage and current across copper
and aluminum rods using the four-point measurement technique. The
dataset, with current from 0.3 A to 2.7 A in 0.3 A increments and voltage
from 1.25 V to 1.65 V in 0.05 V increments, was used to calculate resistance
and electrical conductivity
- Average Resistance: R avg = (4.167 + 2.167 + 1.500 + 1.167 + 0.967 +
0.833 + 0.738 + 0.667 + 0.611) / 9 ≈ 1.431 Ω
- Electrical Conductivity (σ): Using σ = L / (R · A), where L = 0.315 m and A =
4.91 × 10⁻⁴ m², σ = 0.315 / (1.431 · 4.91 × 10⁻⁴) ≈ 4.49 × 10⁵ S/m
- Trend Observation: Resistance decreases from 4.167 Ω to 0.611 Ω with
increasing current, indicating possible non-linear behavior.
Discussion
The calculated electrical conductivity of 4.49 × 10⁵ S/m is much lower than
expected values for copper (≈ 5.96 × 10⁷ S/m) and aluminum (≈ 3.5 × 10⁷
S/m), suggesting potential issues. Possible causes include:
1. Material Identification: The rods may not be pure Cu or Al, or surface
oxidation/impurities increased resistance.
2. Temperature Effects: Decreasing resistance with current may indicate
heating, though the four-point method should minimize this.
3. Measurement Accuracy: The small voltage increment (0.05 V) and
potential calibration errors could skew results, with high initial resistance
suggesting poor contacts.
4. Geometric Factors: Inaccurate dimensions (L = 0.315 m, A = 4.91 × 10⁻⁴
m²) or uneven area could affect calculations.
The non-linear resistance trend (4.167 Ω to 0.611 Ω) deviates from ohmic
behavior, possibly due to thermal effects or probe misalignment.
The Wiedemann-Franz law (k / σ = L · T) couldn’t be tested without thermal
data, but the low σ implies lower thermal conductivity, questioning the law’s
applicability. Future experiments should verify material, ensure precise
measurements, and stabilize temperature to improve accuracy.
CONCLUSION
The experiment measured the electrical conductivity of copper and
aluminum rods using the four-point method, yielding an average resistance
of 1.431 Ω and conductivity of 4.49 × 10⁵ S/m, far below expected values for
Cu (5.96 × 10⁷ S/m) and Al (3.5 × 10⁷ S/m). This suggests possible
impurities, inaccurate dimensions, or poor contacts, with resistance
decreasing from 4.167 Ω to 0.611 Ω indicating thermal effects. Future
improvements should include material verification, precise measurements,
and temperature control for better accuracy.
REFERENCES
Ashcroft, N. W., & Mermin, N. D. (1976). Solid State Physics. Holt,
Rinehart and Winston.
Kittel, C. (2005). Introduction to Solid State Physics (8th ed.). Wiley.
PRECAUTIONS
1. Ensure Proper Calibration: Calibrate the multimeter and universal
measuring amplifier accurately before use to avoid voltage or current
measurement errors.
2. Verify Equipment Safety: Check all electrical connections and
equipment for damage or wear to prevent short circuits or electrical
hazards.
3. Maintain Stable Temperature: Conduct the experiment in a
controlled environment to minimize thermal effects on resistance
measurements.
4. Avoid Overheating: Limit current application time and monitor the
rods to prevent overheating, which could alter conductivity.
5. Secure Probe Contacts: Ensure firm and clean contact between
probes and the metal rods to reduce contact resistance and ensure
accurate readings.
6. Handle with Care: Handle the rods and electrical components
carefully to avoid bending or damaging the setup.
7. Power Off During Adjustments: Turn off and disconnect the power
supply before making any adjustments to the circuit to ensure safety.
8. Wear Protective Gear: Use safety goggles and insulated gloves
when handling electrical equipment to protect against potential
shocks.
ABSTRACT
This experiment examined the electrical conductivity of copper (Cu) and
aluminum (Al) using the four-point measurement method to determine
conductivity and assess the Wiedemann-Franz law. Data was recorded with
current varying from 0.3 A to 2.7 A in 0.3 A steps and voltage from 1.25 V to
calculated as 4.49 × 10⁵ S/m using σ = L/R⋅A(where L = 0.315 m and A =
1.65 V in 0.05 V steps. Resistance averaged 1.431 Ω, and conductivity was
4.91 × 10⁻⁴ m²) (Kittel, 2005). This value is notably below the expected 5.96
× 10⁷ S/m for Cu and 3.5 × 10⁷ S/m for Al (Ashcroft & Mermin, 1976),
indicating potential experimental errors or impurities. The resistance
decrease with current suggests thermal effects or contact problems. The
Wiedemann-Franz law could not be evaluated due to missing thermal
conductivity data. These results emphasize the need for better calibration
and material checks in future experiments.
