Inductance Calculation
CHAPTER 55.3 Definition and Calculation of Inductance
Let us assume that a structure carries a current I. This current generates the magnetic field around it. The inductance is defined as the magnetic flux generated per unit of current flowing into it.
This equation can be used to calculate the inductance of some regular isolated structures. Following are the steps used in calculation of the inductance of regular structure.
1. Find the magnetic field generated by the current carrying structure at point some distance away from the structures using Biot Savart law (not mentioned here, Ampere’s circuital law can also be used).
2. Find the infinitesimal magnetic flux in an infinitesimal area due to the magnetic field.
3. Integrate the infinitesimal magnetic flux to find the total flux.
4. Inductance is the magnetic flux per unit of current.
5.4 Magnetic Field Line Loops
Calculating the magnetic flux using the surface integral of the magnetic filed requires knowledge of vector calculus and vector integral. It does have value in deriving the formula for inductance of common structures. However, it does not appeal to our intuition. An easier equivalent and intuitive way to express inductance is in terms of magnetic field line loops.
A current carrying wire can be assumed to be encircled by magnetic field line loops. These magnetic field line loops are spaced closer when we are close to the wire. The magnetic field line loops start to spread out as we go farther and farther away from the wire.
The number of magnetic field line loops will depend upon the current flowing in the wire. If we double the current in the wire, the number of magnetic field line loops will double. The magnetic field line loops will depend upon the length of the wire. If we increase the length of the wire there will be an increase in the number of magnetic field line loops. The number of magnetic line loops will also weakly depend upon the thickness of the material of the wire. A wire with larger diameter will produce slightly smaller number of magnetic field line loops.
Inductance is then defined as the number of the magnetic field line loops per unit of current flowing in the wire. Unit of the magnetic field line loops is Webers. The unit of Inductance, it therefore, Webers/Ampere. Henry is another name for the unit of inductance.
L = N/I [5 4]
where,
L = Inductance in Henry or Weber/Ampere
N = Number of Magnetic field line loops in Webers,
I = Current through the conductor.
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