Understanding Coil Inductance
Inductance is a property of an electrical conductor by which a change in current through it induces an electromotive force in both the conductor itself and in any nearby conductors. Coil inductance is particularly important in the design of transformers, inductors, and other electromagnetic devices.
Formula:
The formula used in this calculator is an approximation for air-core coils:
\(L = \frac{r^2 \cdot N^2}{9r + 10l}\)
Where:
- \(L\) = Inductance in µH (microhenries)
- \(r\) = Radius of the coil in cm
- \(N\) = Number of turns
- \(l\) = Length of the coil in cm
Example 1:
Given:
- Diameter: 5 cm (radius = 2.5 cm)
- Length: 10 cm
- Number of turns: 100
Calculation:
\(L = \frac{2.5^2 \cdot 100^2}{9 \cdot 2.5 + 10 \cdot 10} = \frac{62500}{122.5} \approx 510.2 \, \mu H\)
Example 2:
Given:
- Diameter: 10 mm (radius = 5 mm = 0.5 cm)
- Length: 5 cm
- Number of turns: 50
Calculation:
\(L = \frac{0.5^2 \cdot 50^2}{9 \cdot 0.5 + 10 \cdot 5} = \frac{625}{50.5} \approx 12.38 \, \mu H\)
Unit Conversion: \(12.38 \, \mu H = 0.01238 \, mH\)
Example 3:
Given:
- Diameter: 20 cm (radius = 10 cm)
- Length: 15 cm
- Number of turns: 200
Calculation:
\(L = \frac{10^2 \cdot 200^2}{9 \cdot 10 + 10 \cdot 15} = \frac{400000}{240} \approx 1666.67 \, \mu H\)
Unit Conversion: \(1666.67 \, \mu H = 1.66667 \, mH = 0.00166667 \, H\)
Factors Affecting Coil Inductance:
- Number of turns: More turns increase inductance.
- Coil diameter: Larger diameter generally increases inductance.
- Coil length: Longer coils typically decrease inductance.
- Core material: Air core (as assumed in this calculator) vs. ferromagnetic cores.
Applications:
- RF circuits and antennas
- Power supplies and voltage regulators
- Filters in audio equipment
- Sensors and measuring instruments
