Self-inductance of Simple Electrical Circuits in Air
The self-inductance of many types of electrical circuits can be given in closed form. Examples are listed in the table.
Type | Inductance / | Comment |
---|---|---|
Single layer solenoid |
|
: Number of turns r: Radius l: Length w = r/l : Elliptic integrals |
Coaxial cable, high frequency |
a1: Outer radius a: Inner radius l: Length |
|
Circular loop | r: Loop radius a: Wire radius |
|
Rectangle | b, d: Border length d >> a, b >> a a: Wire radius |
|
Pair of parallel wires |
a: Wire radius d: Distance, d ≥ 2a l: Length of pair |
|
Pair of parallel wires, high frequency |
a: Wire radius d: Distance, d ≥ 2a l: Length of pair |
|
Wire parallel to perfectly conducting wall |
a: Wire radius d: Distance, d ≥ a l: Length |
|
Wire parallel to conducting wall, high frequency |
a: Wire radius d: Distance, d ≥ a l: Length |
The symbol μ0 denotes the magnetic constant (4π×10−7 H/m). For high frequencies the electric current flows in the conductor surface (skin effect), and depending on the geometry it sometimes is necessary to distinguish low and high frequency inductances. This is the purpose of the constant Y: Y = 0 when the current is uniformly distributed over the surface of the wire (skin effect), Y = 1/4 when the current is uniformly distributed over the cross section of the wire. In the high frequency case, if conductors approach each other, an additional screening current flows in their surface, and expressions containing Y become invalid.
Read more about this topic: Inductance
Famous quotes containing the words simple, electrical, circuits and/or air:
“A creature not too bright or good
For human natures daily food;
For transient sorrows, simple wiles,
Praise, blame, love, kisses, tears, and smiles.”
—William Wordsworth (17701850)
“Few speeches which have produced an electrical effect on an audience can bear the colourless photography of a printed record.”
—Archibald Philip Primrose, 5th Earl Rosebery (18471929)
“The Buddha, the Godhead, resides quite as comfortably in the circuits of a digital computer or the gears of a cycle transmission as he does at the top of a mountain or in the petals of a flower.”
—Robert M. Pirsig (b. 1928)
“Liberty is the air that we Americans breathe. Our Government is based on the belief that a people can be both strong and free. That civilized men need no restraint but that imposed by themselves against the abuse of freedom.”
—Franklin D. Roosevelt (18821945)