What is an Electric Coil?

An electric coil (also known as an electromagnetic coil) is a fundamental electrical component consisting of conductive wire wrapped around a core. The core can be ferromagnetic (like iron or steel) to amplify the magnetic field, or it can be air/non-magnetic for specific applications.

How it Works: When electric current flows through the wire, it generates a magnetic field around the coil. This interaction allows coils to perform three main functions:

1. Inductance: Resisting changes in current flow.
2. Electromagnetism: Creating a magnetic force to move objects (e.g., in motors or solenoids).
3. Induction: Transferring energy between circuits (e.g., in transformers).

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Types of Electrical Coils

Coils are categorized based on their core material, winding shape, and function. Below are the most common types used in electronics and engineering.

1. Structural & Core Variations

• Bobbin Wound Coils: The wire is wound onto a plastic "bobbin" or spool. This is common for relays and sensors where the coil needs a rigid structure.
• Toroidal Coils: Wire is wound around a donut-shaped (ring) core. This shape confines the magnetic field within the core, preventing leakage and interference with nearby components.
• Air Core / Self-Supported Coils: Used when a magnetic core is undesirable (e.g., high-frequency radio circuits) or space is limited. The wire is stiff enough to hold its own shape.

2. Functional Variations

• Choke Coils: Designed specifically to block (choke) high-frequency Alternating Current (AC) while letting Direct Current (DC) pass through.
• Solenoid Coils: These convert electrical energy into linear motion. When energized, the magnetic field pulls a metal plunger inside the coil.
• Tesla Coils: A resonant transformer circuit used to produce high-voltage, low-current, high-frequency alternating-current electricity.
• Transformer Coils: Used in pairs (primary and secondary) to step voltage up or down via electromagnetic induction.

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Coil Formulas & Calculations

To design a coil, you must calculate physical properties like wire length, resistance, and the number of turns.

Key Variables:

• $N$: Number of turns
• $d$: Wire Diameter
• $D_{bobbin}$: Diameter of the Bobbin (Inner Diameter)
• $L_{bobbin}$: Length of the Bobbin
• $D_{coil}$: Outer Diameter of the finished coil

Common Formulas

1. Cross-Sectional Area of Wire ($A$) $A = \pi \times r^2$ (Where $r$ is the radius of the wire)

2. Radius of Middle of Coil ($r_{mid}$) Used to calculate the average length of one turn. $r_{mid} = \frac{(N \times d) + D_{bobbin}}{2}$

3. Total Wire Length ($L_{total}$) $L_{total} = 2 \times \pi \times r_{mid} \times N$

4. Electrical Power ($P$) $P = V \times I$ (Where $V$ is Voltage and $I$ is Current)

5. Ohm's Law (Voltage & Resistance) $V = R \times I$

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How to Calculate Coil Properties

1. Calculating Number of Turns

The number of turns ($N$) is critical for determining the strength of the magnetic field.

• By Dimensions: If you know the bobbin length ($L_{bobbin}$) and wire diameter ($d$), the turns per layer is roughly $L_{bobbin} / d$. Multiply this by the number of layers.
• By Voltage (Transformers): The formula is derived from the core's magnetic flux: $Turns \ Per \ Volt = \frac{1}{4.44 \times F \times M \times A_{core}}$ (Where $F$ = Frequency, $M$ = Magnetic Flux, $A_{core}$ = Core Area).

2. Calculating Inductance

Inductance ($L$) measures the coil's ability to store energy. For a simple air-core coil, the approximation is: $L (\mu H) = \frac{d^2 \times N^2}{18d + 40l}$ (Where $d$ is coil diameter in inches and $l$ is coil length in inches).

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AWG Wire Gauge Chart

Use this chart to determine the resistance and diameter of copper wire for your coil. Thicker wire (lower AWG) handles more current but takes up more space.

AWG	Diameter (mm)	Resistance ($\Omega$/m)	AWG	Diameter (mm)	Resistance ($\Omega$/m)
4/0	11.7	0.000161	22	0.644	0.0530
3/0	10.4	0.000203	23	0.573	0.0668
2/0	9.26	0.000256	24	0.511	0.0842
1/0	8.25	0.000323	25	0.455	0.106
1	7.35	0.000407	26	0.405	0.134
2	6.54	0.000513	27	0.361	0.169
3	5.83	0.000647	28	0.321	0.213
4	5.19	0.000815	29	0.286	0.268
5	4.62	0.00103	30	0.255	0.339
6	4.11	0.00130	31	0.227	0.427
7	3.66	0.00163	32	0.202	0.538
8	3.26	0.00206	33	0.180	0.679
9	2.91	0.00260	34	0.160	0.856
10	2.59	0.00328	35	0.143	1.08
11	2.30	0.00413	36	0.127	1.36
12	2.05	0.00521	37	0.113	1.72
13	1.83	0.00657	38	0.101	2.16
14	1.63	0.00829	39	0.0897	2.73
15	1.45	0.0104	40	0.0799	3.44
16	1.29	0.0132	41	0.0711	4.34
17	1.15	0.0166	42	0.0633	5.47
18	1.02	0.0210	43	0.0564	6.90
19	0.912	0.0264	44	0.0502	8.70
20	0.812	0.0333	45	0.0447	10.98
21	0.723	0.0420