Experiment: Measurement of DC Resistance of Inductor Coils
Learning Outcomes
- Understand the concept of DC resistance in wire-wound inductors.
- Learn to calculate theoretical resistance from wire length, diameter, and material resistivity.
- Use a multimeter to measure actual inductor resistance.
- Compare theoretical and experimental values and calculate percentage difference.
Theory
The DC resistance of a wire-wound inductor is calculated using:
\[
R = \rho \frac{L}{A}
\]
Where:
- \(R\) = resistance in ohms (Ω)
- \(\rho\) = resistivity of the material (Ω·m) [Copper: \(1.68 \times 10^{-8}\), Ni-Ag: \(2.28 \times 10^{-7}\)]
- \(L\) = length of the wire in meters (m)
- \(A = \pi r^2\) = cross-sectional area of the wire (m²), with \(r = \frac{\text{diameter}}{2}\))
Percentage difference between theoretical and measured resistance is calculated as:
\[
\% \text{Difference} = \frac{|R_\text{theoretical} - R_\text{measured}|}{R_\text{theoretical}} \times 100
\]
Materials
- Inductors (5 spools with the following specifications):
- Inductor 1: Copper, L = 10 m, Diameter = 0.0644 cm
- Inductor 2: Copper, L = 20 m, Diameter = 0.0644 cm
- Inductor 3: Copper, L = 20 m, Diameter = 0.0321 cm
- Inductor 4: Copper, L = 10 m, Diameter = 0.0321 cm
- Inductor 5: Ni-Ag, L = 10 m, Diameter = 0.0644 cm
- Digital multimeter (for measuring resistance)
- Connecting wires (optional)
Procedure
- Inspect each inductor to ensure wire ends are clean and free of insulation.
- Set the multimeter to resistance (Ω) mode.
- Short the multimeter probes together and record the reading as Probe Resistance (\(R_\text{probe}\)).
- Measure the raw resistance of each inductor by connecting the probes firmly to the two terminals, obtaining \(R_\text{measured, raw}\).
- Calculate the actual inductor resistance by subtracting the probe resistance:
\[
R_\text{measured} = R_\text{measured, raw} - R_\text{probe}
\]
- Calculate the theoretical resistance using:
\[
R_\text{theoretical} = \rho \frac{L}{A}, \quad A = \pi r^2, \quad r = \frac{\text{diameter}}{2}
\]
- Calculate the percentage difference between theoretical and measured values:
\[
\% \text{Difference} = \frac{|R_\text{theoretical} - R_\text{measured}|}{R_\text{theoretical}} \times 100
\]
- Record all values, including probe resistance, in the observation table.
Observation Table
Submit your observation table based on the measured and theoretical resistance values. Show sample calculations (theoretical resistance, probe correction, and percentage difference) for each spool.
| Inductor |
Material |
Length (m) |
Diameter (cm) |
Theoretical Resistance (Ω) |
Probe Resistance (Ω) |
Measured Resistance (Ω) |
% Difference |
| 1 |
Copper |
10 |
0.0644 |
|
|
|
|
| 2 |
Copper |
20 |
0.0644 |
|
|
|
|
| 3 |
Copper |
20 |
0.0321 |
|
|
|
|
| 4 |
Copper |
10 |
0.0321 |
|
|
|
|
| 5 |
Ni-Ag |
10 |
0.0644 |
|
|
|
|
Conclusion
Submit your conclusion based on the measured and theoretical resistance values.